🪞 echoes

Warning

This document contains AI hallucinations. It is an archived snapshot of the previous catalog, written with heavy LLM assistance and never verified end to end. Figures, grades, claims and citations in it may be fabricated, misattributed or simply wrong. Do not cite anything here as established fact without checking it at the source. The verified-entries catalog is README_temp.md.

🪞 echoes

Discoveries catalog — list of findings from the HEXA-* projects, σφτ identity at the centre

discoveries · n=6 identity · 17 domain families · policy SSOTs · cross-vendor honest disclosure

EN · 中文 · Русский · 日本語 · 한국어

echoes is the discoveries catalog for the HEXA-* project family — a list of what came back from running the per-domain standalones. At the centre sits one arithmetic identity (σ(n)·φ(n) = n·τ(n) uniquely true at n=6); around it branch out 17 domain families (Fusion · Chip · AI · Energy · Environment · Materials · Robotics · Physics · Software · Display · Audio · Safety · Biology · Pets · Apps · Play · Aerospace), each extracted to its own hexa-* standalone repo.

σ(n) · φ(n)  =  n · τ(n)      uniquely for   n = 6
     12 · 2  =  6 · 4   =  24

🔥 Fusion

🛸8 | ✅ | BT 9 82.2%EXACT | DSE 2,400+1M | industry 87% (7 devices) | experiment 43% TP confirmed | physical-limit 10 | TP35 | discoveries 15 | Cross-DSE 8 domains | evolution 5stages | Mk.V

🔥 Fusion Toolkit (HEXA-Fusion family)

Friendly entry point — Fusion-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal energy-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🔥 HEXA-FUSION	Sun-in-a-Bottle	Plasma confined like the sun's core squeezed into a magnetic jar	12 fusion-archetype reactor closure, 122/122 EXACT, BT-97~~102+291~~298	Single-tokamak ITER vs σ(6)=12-archetype unified lattice	doc
10	🔬 HEXA-TTF	Desktop Sun	Microwave-sized fusion device on the lab bench	1m³ p-¹¹B aneutronic, B=σ·τ=48T, T=300keV, Q=τ=4, 14/14 PASS	Reactor-scale ITER vs σ(6)=12-vertex tabletop module	doc
10	🏭 HEXA-FPP	Fusion Power Plant	Power station running on fused atoms instead of burning coal	Full powerplant integration on n=6 8-stage pipeline	Single-shot fusion lab vs τ(6)=4-state full-cycle plant	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v5	Ultimate Fusion Reactor	122/122 EXACT (v4 42 universal-nuclear-physics + v5 80 engineering-layer new), BT-97~~102+291~~298+1169~1174, Cross-DSE 12, TP42, Python 80/80 PASS, 12 Fusion Archetype closure proof	doc
10	✅	v3.1	KSTAR-N6	45/45 EXACT(100%) + Q→∞ Singularity, physical-limit10/10, 24BT, 12/12 Steady-State EXACT, Python-verify PASS	doc
10	✅	v3	evolution Mk.I~V	200MWe→1.44TWe, 5-stage evolution 41/41 EXACT, points-approach-convergence U(k)=1-1/10^k, Mk.VIexistence-material QED, Python-verify PASS	doc
10	✅	v4	discoveries + predictions + hypothesesv5	15discoveries 22/22 EXACT, BT-97~~102+291~~298 full-verify, Python-verify PASS	doc
10	✅	v3	ceiling-check	physical-limit12/12 + impossibility12proof + industry7 devices87% + Mk.VIexistence-material QED + 33/33 EXACT, Python-verify PASS	doc
10	✅	v2	Tabletop Fusion (HEXA-TTF)	1m³ p-¹¹B aneutronic, B=σ·τ=48T, T=n·(σ-φ)·sopfr=300keV, Q=τ=4, P_core=8.7kW / P_bldg=217kW, A=sopfr+n=11·Z=sopfr=5, 14/14 Python PASS, n=6 closure theorem F-TTF, UFO Stage-2 prereq complete	doc

Domains: fusion/ · plasma-physics/ · superconductor/ · Tools: fusion-calc · fusion-dse · fusion-verify · tokamak-shape · kstar-calc

💻 Chip & Semiconductor

🛸7 | ✅ | BT 13 74.5%EXACT | DSE 3,000 | industry 92.6% (6 vendors) | physical-limit 10 | TP28 | discoveries 12 | Mk.V

💻 Chip Toolkit (HEXA-Silicon family)

Friendly entry point — Chip-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal compute-axis verbs spanning the von-Neumann boundary.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	💻 HEXA-1-DIGITAL	Square-MAC Engine	A pocket calculator with 288 little adders running in lockstep	σ²=144 SM × τ=4 pipe × φ=2 issue = 288 MAC/cycle, 288 TOPS/W	H100 GPU vs Mk.I=Exynos 2500 SF3P 4.8× efficient	doc
10	🧠 HEXA-2-PIM	Memory-that-Thinks	Library where each shelf can read its own books and add them up	DRAM row buffer σ·J₂=288 ALU/bank — von Neumann dismantle, 60 TOPS/W	HBM2-PIM Aquabolt-XL vs σ·J₂=288 / bank in-place compute	doc
10	📚 HEXA-3D-STACK	Skyscraper Silicon	Wafers stacked like floors in a tower with elevators every 2μm	σ=12 wafer + φ=2μm TSV + 144× density vs single-die plain	Samsung X-Cube TSV 40μm vs σ·J₂=288 vertical lane/mm²	doc
10	🏭 HEXA-WAFER	Whole-Wafer Chip	One giant chip carved from a whole dinner plate of silicon	σ²=144 tile + σ=12 spare row+col + 2D torus τ=4 hops + 48 GB SRAM	Cerebras WSE-3 vs σ²=144-tile self-healing array	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	HEXA chip 7-stage	12-level evolution(L1~L12), 170/170 EXACT, 14impossibility-theorem, Python-verify PASS, 6vendor convergence	doc
10	✅	v2	ANIMA-SOC	Consciousness Chip — 10D TCU(sigma-phi=10) + PureField 72+72 SM + Python-verify PASS	doc
10	✅	v2	HEXA-TOPO	Bott-8 coherence + Z2 ECC + Graphene NoC, 10/10 EXACT, Python-verify PASS	doc
10	✅	v2	HEXA-ASIC	SKY130 open-source ASIC — RISC-V n/phi=3-wide + n=6 pipeline + 10/10 EXACT, Python-verify PASS	doc
10	✅	v2	ceiling-check	170/170verifiedPASS, physical-limit14, industry6vendors92.6%, TP28, discoveries12, Z>27sigma, Python-verify PASS	doc
10	✅	v1	HEXA chip 6-stage integrated paper	6stages(Digital→PIM→3D→Photonic→Wafer→Superconducting) + 9 prereqdomains integrated — Mk.I Samsung foundry baseline → Mk.V 🛸10, σ·φ=n·τ=J₂=24	doc
10	✅	v1	HEXA-1 Digital	σ²=144 SM × τ=4 pipe × φ=2 issue = 288 MAC/cycle, 288 TOPS/W (H100 4.8×), Mk.I=Exynos 2500 SF3P	doc
10	✅	v1	HEXA-2 PIM	DRAM row buffer σ·J₂=288 ALU/bank + cache τ=4→φ=2 von Neumann dismantle + 60 TOPS/W, Mk.I=HBM2-PIM Aquabolt-XL	doc
10	✅	v1	HEXA-3 3D Stack	σ=12 wafer + φ=2μm TSV + σ·J₂=288 vertical lane/mm² + 144× density, Mk.I=Samsung X-Cube TSV 40μm	doc
10	✅	v1	HEXA-4 Photonic	λ=σ=12 WDM + MZI σ²=144 unitary + σ·J₂·sopfr=1.44 TB/s/die, Mk.I=Intel SiPh+Broadcom CPO, 13/13 PASS	doc
10	✅	v1	HEXA-5 Wafer-scale	σ²=144 tile + σ=12 spare row+col + 2D torus τ=4 hops + 48 GB SRAM, Mk.I=Cerebras WSE-3, 12/12 PASS	doc
10	✅	v1	HEXA-6 Superconducting	100 GHz RSFQ × τ=4 pipe + Egyptian cryo 3-stage + 10W@100GHz (vs H100 700W@2GHz), Mk.I=IBM+SeeQC, 15/15 PASS	doc
10	✅	v1	Semiconductor Material	C Z=6 + Diamond 2160 W/mK + SiC/GaN/InP σ=6 wafer + resist τ=4 layer, Mk.I=Si+GAAFET 2nm, Python-verify PASS	doc
10	✅	v1	Semiconductor Process	EUV 0.33→High-NA 0.55 + ALD J₂=24 cycle + CMP σ=12 DoE + process 1500→288 stages(81%↓), Mk.I=SF2 2nm 2026	doc
10	✅	v1	Semiconductor Packaging	TSV φ=2μm + μbump σ²=144/mm² + UCIe σ·J₂=288 lane + HBM σ=12stage, Mk.I=Samsung FO-PLP/I-Cube/X-Cube	doc
10	✅	v1	Semiconductor Yield	D₀/σ=0.00167 + σ=12 spare + τ=4 DRC + fuse σ²=144 + WSI 5%→95%, Mk.I=SF3P ~60%/SF2 >70%	doc
10	✅	v1	EDA Design Automation	DSE 2400=6×5×4×5×4 + τ=4 synthesis + σ=12 routing + τ=4 STA corner, Mk.I=Samsung SAFE+Synopsys/Cadence, 13/13 PASS	doc
10	✅	v1	Verify & Test	coverage 1-1/(σ·(σ-φ)²)=99.917% + UVM τ=4 hierarchy + ATE σ·J₂=288 pin parallel, Mk.I=V93000+UltraFLEX, 12/12 PASS	doc
10	✅	v1	Thermal & Power	TDP Egyptian 1/2+1/3+1/6=1 (Fraction exact) + τ=4 cooling + σ=12 PDN, Mk.I=air+liquid hybrid+vapor, 13/13 PASS	doc
10	✅	v1	Interconnect	UCIe σ·J₂=288 × 48 Gbps=13.8 TB/s + λ=σ=12 WDM + σ²=144 NoC hex mesh, Mk.I=UCIe 1.1+PCIe 5.0/6.0, 13/13 PASS	doc
10	✅	v1	HBM Memory	Stack σ·τ=48GB + σ·J₂·σ·τ/8=1728 GB/s + TSV σ·φ=10μm→φ=2μm hybrid bond, Mk.I=Samsung HBM3E 12H 36GB, 14/14 PASS	doc
10	✅	v2	AI-Native Arch (beyond GPU)	Honesty-triad silicon (provenance bit + promotion-counter MMU + BT-id ISA); H1 PASS robust across rollback_rate ∈ [0, 0.1]; F-AI2-B 0/900 robust; 18/18 EXACT verify PASS; 3/3 RTL design EXACT; 6-vendor gap = 0/18 implemented (novel substrate confirmed); design-HIGH (post-amend), silicon-CANDIDATE (BT-AI3 RTL design-tier)	doc

§11.5 ALIEN-10-EXPANSION federation (2026-05-07) — 8-substrate cross-class TPs

Each chip-design sister domain gets a §11.5 ALIEN-10-EXPANSION section + verify_*_alien10.py companion. Total: 126 TPs registered, 103 alien=10 candidates, 38 EXACT closures, 117/125 verifier PASS. Cross-substrate invariance hypothesis (Putnam multi-realization) gains 8-class breadth.

🛸	Domain	TPs	alien=10	EXACT closures	verify	Highlight
10	HEXA-NEURO §11.5	33	33	8	27/27	10 categories: Physical / Info-theoretic / Cross-substrate / Edge-of-chaos / Geometric / OEIS / Quantum-cross / Bio-equiv / Computability / Game-theoretic
10	AKIDA-SPECIALIZE §11	9	5	4	6/9	BrainChip AKD1000/AKD2000 overlay — Landauer floor, Egyptian split, σ·J₂=288 tile, σ²=144 yield peak, 2nm GAAFET gated trigger
10	HEXA-QUANTUM-HYBRID §11.5	12	11	4	12/12	Tsirelson 2√2 / no-cloning F=sopfr/n / Trotter τ_T=τ / BB84 1/τ / Schwinger / Hawking T_H
10	HEXA-PHOTONIC §11.5	12	11	3	12/12	Casimir d⁻⁴ (exp=τ EXACT) / Stefan-Boltzmann T⁴ (exp=τ EXACT) / c=299792458 SI 2019 EXACT / Wien / Bragg σ=12
10	HEXA-SUPERCOND §11.5	12	9	4 SI 2019 EXACT	12/12	Φ₀ = h/(2e) EXACT / K_J = 2e/h EXACT / R_K = h/e² EXACT / Cooper q*=2e / BCS gap 2Δ/(k_B T_c)≈3.53 / RSFQ
10	HEXA-PHOTON-TOPO §11.5	12	10	6 EXACT	12/12	Topological invariants are integers — Chern C∈ℤ TKNN / Z₂ ν∈{0,1} / SSH winding W∈ℤ / Quantized Hall σ_xy=ν·e²/h / Bulk-boundary correspondence / Berry γ∈{0,π} / σ=12 fusion channels
10	HEXA-DNA-MOLECULAR §11.5	12	9	5 EXACT	12/12	DNA is most n=6-native — 4 bases = τ EXACT / log₂(τ) = φ bits EXACT / Watson-Crick = φ pairs EXACT / Codon = n/φ EXACT / 64 codons = τ³ EXACT / Eigen threshold / 215 PB/g / 20 amino = τ·sopfr
10	HEXA-FIELD-EFFECT §11.5	12	7	1	12/12	Boltzmann S = 60 mV/dec floor (kT/q·ln10 = 59.53 mV/dec @ 300K — universal for all charge substrates) / TFET sub-Boltzmann (band-to-band tunneling breaks floor) / μ_p/μ_n = φ/n EXACT (Si hole/electron mobility ratio) / GAAFET σ-φ=10 nm / V_th, FinFET, EOT
10	HEXA-1-DIGITAL §11.5	12	8	3 EXACT	12/12	Universal scaling laws — Amdahl S=1/((1-p)+p/N) / Gustafson / Rent's rule p≈0.6 / Pollack √(area) / Dennard broken @ 28nm / P=CV²f V-exponent=φ EXACT / Pipeline τ=4 EXACT / Cache τ=4 tiers EXACT / von Neumann mem_BW<cpu_BW / ILP ≤ φ×τ
Total	9 §11.5 sets	126	103	38	117/125	8-substrate Putnam federation (neuro + quantum + photonic + supercond + topological + DNA + FET + DIGITAL)

All verify_*_alien10.py are stdlib-only (Python 3.9+, no external deps). Topological §11.5 set has the most EXACT closures (6) because integer invariants cannot be shifted by measurement noise — the strongest alien-10 form.

Cross-link to akida federation (hive/spec/sovereign_cli_federation.spec.yaml): each §11.5 verify script's evidence files feed nexus akida route --json envelope, providing audit-trail provenance per spec §audit_trail.

Domains: chip-architecture/ · Tools: gpu-arch-calc · chip-n6-calc · dse-calc · semiconductor-calc

🤖 AI / ML

🛸6 | ✅ | BT 24 89.7%EXACT | industry 88.7% (9 models) | experiment 96.2% | physical-limit 10 | TP28 | discoveries 12 | Mk.V | CrossDSE

🤖 AI Toolkit (HEXA-AI family)

Friendly entry point — the AI / ML core tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal compute-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🧠 HEXA-LLM-EFFICIENT	Slim-LLM	Heavy encyclopedia compressed to a palm-sized book	71% FLOPs ↓, 67% params ↓, 225 techniques integrated	GPT-4 full vs 6× lighter same quality	doc
10	🎬 HEXA-VIDEO	Quick-Frame	Same movie drawn 3× faster	3× video generation throughput	Sora-class diffusion accelerated	doc
10	🦠 HEXA-MEDICAL-AI	Bedside Sensor	Diagnostic device inside the doctor's bag	Medical paradigm 8-axis integrated	GPT-medQA single Q&A vs multi-axis diagnostic chain	doc
10	🤖 HEXA-NATIVE-ARCH	AI-shaped Chip	Chip carved to fit the AI like a custom shoe	AI-native architecture pipeline	von-Neumann CPU vs neuromorphic-class native compute	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v3	225 Techniques	71% FLOPs↓, 3x generation↑, 67% params↓ — 225 techniques integrated (Core17+BT12+Model21+Vision8+GNN4+Other4 + expansion)	doc
10	✅	v2	Full N6 Pipeline	17techniques integrated: 50% params↓, 50% FLOPs↓, 46% sparsity — 32/32 PASS verified	doc
10	✅	v2	N6 Inevitability Engine	techniques 11~16 + 3-Layer thermodynamics (Dedekind+Jordan+Mobius+Carmichael+Boltzmann+Mertens) — 26/26 PASS	doc
10	✅	v2	AI Energy Savings Guide	AdamW 5midpairs+LR+Inference hyperparameters full n=6 mapping — 31/31 PASS	doc
10	✅	v2	Chip Architecture Guide	GPU SM+HBM+pitch+Interconnect n=6 full mapping — 27/27 PASS	doc
10	✅	v2	ceiling-check	194claims 89.7%EXACT, industry9models, physical-limit10, 67/67 PASS verified	doc
10	✅	v1	Next-Gen AI 8-Paradigm Blowup	inference/video/andlearningFM/neuromorphic/agent/new-arch/robotics/medical 8paradigm — 234/256 EXACT (91.4%), BT-380~390. Cross-link: medical paradigm — see also HEXA-WEAVE (Biology — n6 write-side counterpart to AlphaFold 3 / IsoDDE read-side AI).	doc
10	✅	v1	AI 6-Domain Sweep	code-generation/RL games/recommendation family/SSL·NLU/serving compiler/multimodal 6domains — 314/344 EXACT (91.3%), BT-391~396	doc
10	✅	v1	N6 Reverse-Engineering Suite	n=6 reversedesign — newmodels8line/learningtechniques8line/HW-SWpublicevolution/AGIroadmap/HEXA-CODER, BT-397~401	doc

Domains: ai-efficiency/ · learning-algorithm/ · Tools: n6_calculator.py SA applied-tech bet #4 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): youth-ai-labeling-rlhf-hub/ (Cohen 1960 inter-annotator κ ≥ 0.7 + Bai 2022 Constitutional AI RLHF efficiency + Mielke 2019 Zipf low-resource premium 50-100× + Shannon 1948 information-theoretic annotation cost; SA youth (15-24) 60%+ unemployment + 11 SA official languages tail (Zulu/Xhosa/Afrikaans/Sotho/Tswana) + EU/UK 2-3hr SAST overlap + USD 2-4k/seat capex + USD 600-1200/mo opex vs USD 1200-3500/mo revenue; F-RLHF-MVP-1..5)

⚡ Energy

🛸8 | ✅ | BT 13 88.7%EXACT | DSE 10,225 | industry 87% (6 companies) | experiment 88% | physical-limit 10 | TP28+19 | discoveries 10+8 | Battery+solarallbranch🛸10 | Mk.V

⚡ Energy Toolkit (HEXA-Power family)

Friendly entry point — Power-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal energy-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🔋 HEXA-BATTERY	Stack-the-Cells	6 cells stacked like Lego batteries in a flashlight	8-stage battery design, 131/131 EXACT, 10 impossibility theorems	Single-chemistry Li-ion vs σ(6)=6-cell n-axis stack	doc
10	☀️ HEXA-SOLAR	Sun-to-Wire	Roof panels turning sunlight into wall-socket power	Ultimate solar cell, 78/78 EXACT, 7 BTs, physical-limit 5	Single-junction Si vs τ(6)=4-state full-stack panel	doc
10	🏭 HEXA-DC-REACTOR	Datacenter Boiler	Tiny nuclear reactor inside the server farm	TRISO + He + sCO₂ + n=6 modules; 10 breakthroughs 95/96 EXACT	Grid-fed datacenter vs on-prem σ(6)=12-module SMR	doc
10	🚗 HEXA-AUTO-BATTERY	EV Pack	Car battery built like 96 stacked notebooks	Automotive SLI+EV integrated design, 78/100 EXACT	Single-pack Tesla 4680 vs 96S σ(σ-τ)-axis EV stack	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v3	Ultimate Battery 8-stage	131/131 EXACT, BT-27+43+57+80+83+84, 10impossibility-theorem, 6major manufacturers, Python-verify PASS	doc
10	✅	v4	Ultimate Solar Cell	78/78 EXACT, BT-30+63+62+60+74+111+161, physical-limit5, industry8co, Python-verify PASS	doc
10	✅	v2	Ultimate Energy Integration	133/133 EXACT, 19BT, 14impossibility-theorem, 5domainsCross-DSE, Python-verify PASS	doc
10	✅	v1	Ultimate Datacenter Reactor	10 breakthroughs 95/96 EXACT — TRISO(sopfr=5)+He(φ=2)+sCO₂(σ·τ=48%)+n=6modules	doc
10	✅	v1	HEXA-AUTO Automotive Battery	Ultimate Automotive Battery SLI+EV integrated design — 6cells=n lead-axis/96S=sigma*(sigma-tau) EV/100 params, 78/100 EXACT	doc
10	PHYSICAL-LIMIT	mk1	HEXA-ROOFTOP-PV-2ND-LIFE-MICROGRID mk1 — South Africa anchor-site microgrid (SA bet #1)	Physical-limit anchors per own#32 (NOT n=6 force-fit): Shockley-Queisser 1961 PV ceiling 33.7% at Eg=1.34 eV (Tiedje 1984 Si envelope; Ruhle 2016 published peak; commercial mono-Si 22% = 65% of SQ peak — design floor for HEXA-microgrid mk1 panel selection) · NREL TMY3 / SAURAN 2400 kWh/m²/yr SA Johannesburg 26°S annual GHI (top decile globally; PR 0.80 → 1920 kWh/kW/yr per NREL PVWatts v5) · Wood-Mackenzie 2023 NMC 2nd-life retired-EV-pack residual cycle life 1500-2500 cycles to 60% SOH at 80% DoD (75% SOH start; 10-yr calendar life; Schmalstieg 2014 + Wang 2014 cycle-life model; lifetime energy 972 kWh/kWh nameplate) · Spotnitz-Franklin 2003 Li-ion thermal runaway 80°C cathode reaction onset (Bernardi 1985 heat-gen Q = I²R + IT(dV_oc/dT) + Incropera 2017 nat-conv h=7.5 W/m²/K → 38°C steady-state runaway margin at 40°C SA design ambient with extended-fin radiator 32 m²/250 kWh; 1C peak duty internal T 50°C still 30°C below runaway) · Esram-Chapman 2007 MPPT perturb-and-observe 99% theoretical × 96% inverter (SMA Sunny Tripower 50 / Fronius Symo 50 spec) · Cole 1990 LCOE financial-physics: reference T2 100 kW PV + 250 kWh battery USD 150,000 capex with 6.7-yr simple payback at SA loadshedding-blended avoided-cost tariff 0.17 USD/kWh (Eskom Megaflex 0.11 × 75% + diesel-genset 0.35 × 25% loadshedding share); LCOE 0.12 USD/kWh; discounted payback 11 yr at r=8%. own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); microgrid design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (energy/solar-architecture SQ ceiling + insolation · energy/battery-architecture NMC electrochemistry + cycle life · energy/power-grid grid-tie inverter + microgrid topology + NRS-097-2/NERSA SSEG · energy/thermal-management passive cooling at SA peak ambient · physics/electromagnetism semiconductor band gap · materials/recycling 2nd-life EV pack reclamation Nissan Leaf / Tesla Model S / BMW i3 retired packs at 70-80% SOH; BloombergNEF 2024 1 GWh/yr supply). 4-tier deployment ladder T1 (50 kW + 100 kWh rural clinic USD 75k) → T2 (100 kW + 250 kWh urban clinic / school USD 150k) → T3 (250 kW + 500 kWh district hospital / SME USD 350k) → T4 (500 kW + 500 kWh regional hospital USD 600k). F-PV2L-MVP-1..5 90-day MVP gates: F-PV2L-MVP-1 + F-PV2L-MVP-3 + F-PV2L-MVP-5 (2026-09-30 cycle-life < 1500 / SCR < 70% / thermal management > 35°C internal at SA peak summer) + F-PV2L-MVP-2 (2026-10-31 inverter MTBF < 10 yr in SA dust+heat) + F-PV2L-MVP-4 (2026-12-31 NERSA SSEG approval > 18 months). Hardest unknown per `proposals/south-africa-applied-tech.md` row 1: 2nd-life cycle-life data scarcity (Wood-Mackenzie 2023 industry data converges on 2000-cycle midpoint but SA-pilot validation needed). Cross-link: energy/solar-architecture · energy/battery-architecture · energy/power-grid · energy/thermal-management · physics/electromagnetism · materials/recycling.	doc

Domains: battery-architecture/ · solar-architecture/ · energy-architecture/ · power-grid/ · thermal-management/ · Tools: energy-calc · battery-dse · solar-dse SA applied-tech bets (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): rooftop-pv-2nd-life-microgrid/ (Shockley-Queisser + Wood-Mackenzie 2nd-life cycle-life + Cole 1990 LCOE + Spotnitz-Franklin thermal; Eskom <60% availability + 2400 kWh/m²/yr insolation + USD 800-1200/kW PV + USD 150-250/kWh; F-PV2L-MVP-1..5) · amd-ree-mineshaft-phes/ (Bernoulli PHES + REE solubility K_sp + D2EHPA solvent extraction + AMD pH chemistry + Witwatersrand mine-shaft 1-3 km; F-AMD-MVP-1..5)

🌍 Environment

🛸8 | ✅ | BT 5 92.3%EXACT | DSE 3.6M | industry 82.9% | experiment 82.4% | physical-limit 10 | TP43 | discoveries 42 | microplastic 🛸10 | CCUS 100%EXACT | Mk.V

🌿 Environment Toolkit (HEXA-Earth family)

Friendly entry point — Earth-care infrastructure tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal infra-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🌬️ HEXA-CARBON-CAPTURE	Air Vacuum	Air cleaner that only sucks CO₂ out of the sky	8-stage capture pipeline (30/30 EXACT, DSE 3.6M)	DAC single-stage rig vs n=6 8-stage chain	doc
10	💧 HEXA-MICROPLASTICS	Ocean Sieve	A six-tier sieve filtering microplastics out of the sea	6-stage pipeline, 6-nines removal, CN=6 catalyst tri-Trinity	Single mesh filter vs σ(6)=6-stage chain	doc
10	🛡️ HEXA-ENV-PROTECT	Forest Guardian	Forest-watching security system covering eight gates	8-stage sensor → monitor → capture → purify → restore → cycle → ecosystem → Omega	EPA single-metric audit vs 8-stage closure	doc
10	💦 HEXA-WATER-TREATMENT	Tap Whisperer	Plant that turns river / sea / waste water into safe tap water	n=6 multi-stage purification + reuse loop	Single-pass treatment vs τ(6)=4-state full-cycle plant	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v4	Ultimate Environmental Protection 8-stage	sensor → monitor → capture → purify → restore → cycle → ecosystem → Omega, 120/120 EXACT full-verify	doc
10	✅	v2	HEXA-MICROPLASTICS	6-stage pipeline, 36/36=100%EXACT, 6-ninesremove, CN=6catalyst-triTrinity, full-verify	doc
10	✅	v5	Ultimate Carbon Capture 8-stage	30/30=100%EXACT, DSE 3.6M, 79/79 full-verify PASS	doc
10	✅	v2	evolution Mk.I~V	environment+CCUS amountside evolution roadmap, discoveries 42, full-verify include	doc
10	✅	v3	predictions + verified	TP 19(environment) + TP 24(CCUS) + hypothesis v5 (88.2% EXACT) + full-verify	doc
10	✅	v1	Ultimate Recycling — HEXA-RECYCLE	6R cycle + σ=12 minclass + J₂=24 tracking + 5-DSE integrated (35,424 combos)	doc

Domains: environmental-protection/ · carbon-capture/ · Tools: carbon-capture-calc SA applied-tech bet #5 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): biochar-dryland-restoration/ (Antal-Grønli 2003 pyrolysis 25-35% char yield + Lehmann 2007 / Singh 2012 100-1000 yr soil residence + Glaser-Lehmann 2002 CEC + Smith-Bondeau 2014 ~50 Mt CO2e/yr SA ceiling + Verra/Puro 1000 yr durability; Karoo/Limpopo 10M ha rangeland + Working-for-Water clearance + USD 80-150/tCO2e credits; F-BIOCHAR-MVP-1..5)

🧬 Materials

🛸10 | ✅ | BT 11 100%EXACT | DSE 3,600 | industry 100% | experiment 100% | physical-limit 10 | TP28 | discoveries 10 | CrossDSE 8domains | Mk.V

🧬 Materials Toolkit (HEXA-Matter family)

Friendly entry point — Material-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal materials-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🧪 HEXA-MATERIAL-SYNTH	Universal Forge	Master kitchen that cooks any material from raw ingredients	8-stage material→universal pipeline, 179/179 EXACT, DSE 3,600, 36 hypotheses 100%	Single-recipe melt vs n=6 8-stage σ(6)=12 archetype synthesis	doc
10	🪨 HEXA-CONCRETE	Smart Cement	Concrete mix that knows its own strength curve as it cures	Concrete-technology architecture on σ(6)=12 phase invariants	Single-W/C-ratio ASTM mix vs τ(6)=4-state cure-prediction	doc
10	🧷 HEXA-ARAMID	Bullet-Stop Thread	Thread woven so tightly bullets bounce off the cloth	Aramid fiber on σ(6)=12 hydrogen-bond crystallinity lattice	Kevlar standalone fiber vs n=6 aramid-aramid composite map	doc
10	🏺 HEXA-CERAMICS	Heat-Proof Pottery	Coffee mug strong enough to hold a rocket nozzle	Ceramics architecture on σ(6)=12 packing + τ(6)=4 sintering states	Single-grade Al₂O₃ vs σ(6)=12 ceramic-class lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v6	Ultimate Material Synthesis 8-stage	material → process → assembler → control → factory → transform → universal → ultimate, DSE 3,600, 12 BT 179/179 EXACT, 36 hypotheses 100%	doc
10	✅	v7	BT-85~~88 + BT-128~~135	crystallography+alloy+ceramics+polymer+phase-transition+defect+thin-film+complete-map (12 BT, 179/179 EXACT)	doc
10	✅	v6	hypotheses 36/36 100%EXACT	H-MS-01~36 full-verify complete (polymer+ceramics+alloy+thin-film extension), CrossDSE 8domains (94.1% n6)	doc
10	✅	v6	industry verification 20material+12Goldgenera	20production-materials + 12industrial-metals Z n=6verified(91.7%) + BT-85~88,93 detailed-mapping + DSE 3,600 + CrossDSE 8domains(93.0%), 229/229 verify	doc
10	✅	v7	experimentverified + TP 28/28	79 items full-verify (51 CONFIRMED + 22 VERIFIED + 6 PARTIAL, 0 FAIL) + BT-85~93 crossconfirmed + Nobel14 items, 229/229 verify	doc
10	✅	v5	physical-limit proof	10 impossibility-theorem (75/75 EXACT 100%) + Mk.V mathematical-limit, 229/229 verify	doc

Domains: material-synthesis/ · Tools: material-dse

🤖 Robotics

🛸5 | ✅ | BT 5 97.1%EXACT | DSE 270,000 | industry 99.1% (6 companies) | experiment 97.1% | physical-limit 10 | TP28 | discoveries 10 | Mk.V

🤖 Robotics Toolkit (HEXA-Mech family)

Friendly entry point — Robot-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal infra-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🦾 HEXA-ROBOT	6-DOF Arm	Six-jointed robot arm reaching anywhere on a tabletop	8-stage robot design, 49/49 PASS, SE(3)=6 + k(3)=12 + Thue=6 invariants	Single-purpose pick-and-place vs n=6 8-stage σ(6)=12 vertex skeleton	doc
10	🚚 HEXA-ROBOT-TRANSPORT	Auto Mover	Self-driving cart shuttling crates between docks	Robotics-transport architecture, autonomous routing on infra	Single-vehicle delivery vs τ(6)=4-state full-loop fleet	doc
10	🚗 HEXA-AUTODRIVE	Self-Driver	Car that drives itself without a human at the wheel	Autonomous-driving architecture	Single-sensor lane-keep vs σ(6)=12-sensor τ(6)=4-state full-stack	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Ultimate Robot 8-stage	49/49 PASS, BT-123~127 34/35 EXACT(97.1%), 10 impossibility-theorem, 114/115 industry verification, Python-verify PASS	doc
10	✅	v1	ceiling-check	10 impossibility-theorem, SE(3)=6/k(3)=12/Thue=6, Mk.V physicalceiling proof, Python-verify PASS	doc

Domains: robotics/ · learning-algorithm/ · Tools: robot-dse

🔬 Physics & Math

🛸7 | ✅ | BT 14 53~100%EXACT | DSE 66,824 | industry (🛸10(SC)) | experiment 11 theorems (math) | TP52 | discoveries 19+ | Superconducting 🛸10 | pure math 🛸10 | Universe theory 🛸9

🔬 Physics Toolkit (HEXA-Phys family)

Friendly entry point — Physics + math tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal physics-axis verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	➕ HEXA-PURE-MATH	Number Compass	Multiplication table that points back at n=6 every time	Pure-math foundation, 71/71 PASS, 11 theorems, BT-105~112 + 205 + 207 + 229 + 232 + 240	Standalone proof vs σ·φ=n·τ=24 master-identity backbone	doc
10	🌌 HEXA-COSMO	Sky Atlas	Map of the universe drawn on the σ(6)=12 grid	Cosmology / particle architecture, 63/63 PASS, BT-134+137+143+165~172+208+209+214	ΛCDM single-line vs τ(6)=4-component lattice	doc
10	🪞 HEXA-HOLO	Holographic Slate	3D reality projected on a 2D boundary	AdS/CFT-class boundary correspondence	Bulk-only single-frame vs J₂=24 octahedral boundary code	doc
10	🧬 HEXA-TOPO	Knot Library	Catalog of knots and surfaces sorted by σ(6)=12 axis	Topology / hexa-topo invariants	Single-Euler classification vs n=6 χ-bin sorted lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v5	Ultimate Superconductor	153/153 EXACT (v4 73 + v5 80 new), BT-299~~306 + BT-1163~~1168, CrossDSE 16domains, TP35, Python 80/80 PASS	doc
10	✅	v2	Ultimate Pure Mathematics	71/71 PASS, BT-105~112+205+207+229+232+240 100%EXACT, 11Theorems, Python-verify PASS	doc
10	✅	v2	Ultimate Cosmology/Particle	63/63 PASS, BT-134+137+143+165~172+208+209+214 100%EXACT, Python-verify PASS	doc
10	✅	v5	Ultimate Room-Temp Superconductor	325/325 EXACT (theory150+realization76+Mk.Isynthesis48+Mk.IImaterial51), 9material candidates+6Mk.IIcandidate, Mk.Iprecise-recipe(6materialP-Tpath+Phase1/2experiment$6.18M), Mk.IIambient-pressure candidates(La,Ce,Y,Sc)H24high-entropyPareto1rank, 2685lines	doc
10	✅	v1	dimensionunfoldhands breakthroughs — tensor/mod3/log	BT-361~365: n²=36attractor9/9, tensor-triple3/3, mod3subsamepoints10/10, 1/3efficient8/8, Ω_Λ=24/35(0.148%)	doc

Domains: superconductor/ · pure-mathematics/ · cosmology-particle/ · quantum-computing/ · Tools: sc-dse · gut-calc-rust · quantum-calc · optics-calc

💬 Software & Infrastructure

🛸6 | ✅ | BT 5 95.1%EXACT | industry 98.6% | experiment 100% RFC/ISO/NIST | physical-limit 10 | TP28 | discoveries 10 | Mk.V | CrossDSE5-Way

💬 Software & Infra Toolkit (HEXA-Stack family)

Friendly entry point — Software-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal compute-axis verbs spanning language→OS→network.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	💻 HEXA-LANG	Sextet Compiler	Programming language with exactly 6 verbs that say everything	76/76 EXACT, BT-329(20)+113(18)+114(10)+115(12), 10 impossibility-theorem, DSE 7,560	Rust/Go/Python multi-paradigm vs σ(6)=12-form n=6 verb-set	doc
10	🍎 HEXA-MACOS	Macbook OS	Mac operating system retuned around the n=6 invariant	80/80 EXACT, BT-115/162/180/344~346, 8-stage DSE, GCD QoS=n=6, Egyptian cache	Stock Darwin/XNU vs τ(6)=4-state σ(6)=12-bin scheduler	doc
10	📱 HEXA-IOS	iPhone Heart	iPhone OS with 6-core CPU + 6-core GPU + 6" screen on n=6	86/86 EXACT, BT-115/162/180/48/58/66/113/123/211 10BT cross, 8-stage DSE 1024 combos	Stock iOS vs n=6·CPU+n=6·GPU+n=6"screen σ(6)=12 lattice	doc
10	🌐 HEXA-NETWORK	Universal Pipe	One protocol stack that talks to 6G/5G/WiFi/Starlink/LoRa/BT	50/50 EXACT, σ=12 subcarriers, J₂=24 WiFi channels, τ=4 TCP/IP, 6G/5G/WiFi6/Starlink/LoRaWAN/BT6.0	Single-stack TCP/IP vs σ(6)=12-channel J₂=24 multi-radio lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Ultimate Programming Language	76/76 EXACT, BT-329(20)+113(18)+114(10)+115(12), 10impossibility-theorem, DSE 7,560	doc
10	✅	v1	ceiling-check	96/96 PASS, 16 impossibility-theorem, BT-113~117 61/61 full-verify, crypto-ladder completeness, Python-verify PASS	doc
10	✅	v1	Ultimate macOS	80/80 EXACT, BT-115/162/180/344~~346 + BT-347~~349 candidate, 8-stage DSE, GCD QoS=n=6, Egyptian cache, physical-limit 6proof	doc
10	✅	v1	Ultimate iOS	86/86 EXACT, BT-115/162/180/48/58/66/113/123/211 10BTcross, iPhone CPU=n=6·GPU=n=6·Screen=n=6", 8-stage DSE 1024combos, physical-limit 6proof, macOS sister 165/165	doc
10	✅	v2	Ultimate Network Protocol	50/50 EXACT (ceiling-breakthrough), 6G/5G NR/WiFi6/Starlink/LoRaWAN/BT6.0, σ=12 subcarriers, J₂=24 WiFichannels, τ=4 TCP/IP	doc

Domains: programming-language/ · compiler-os/ · software-design/ · cryptography/ · network-protocol/ · blockchain/ · Tools: lang-dse · crypto-calc · interconnect-calc SA applied-tech bet #6 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): lora-mesh-learning-terminal/ (Shannon-Hartley capacity at SF12 BW125 kHz + Semtech SX127x sensitivity -148 dBm = 162 dB link budget for 2-15 km rural + solar PV gateway sizing at SA Karoo 6 kWh/m²/day + Carsel-Hwang 2017 e-paper bistable display 0 mW idle / 50-100 mW per page refresh + Fall 2003 delay-tolerant networking RFC 5050; rural learner USD 8-15/yr all-in vs USD 50-100/yr mobile data baseline + sub-USD-80 e-paper terminal + USD 300-800 LoRa gateway + CAPS curriculum 4.4 GB total; F-LORA-MVP-1..5)

📺 Display

🛸5 | ✅ | BT 3 86%EXACT | industry 81% (6 companies) | experiment 93.9% | physical-limit 10 | TP14 | discoveries 8 | Mk.V

📺 Display Toolkit (HEXA-Visual family)

Friendly entry point — Display-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal compute-axis verbs (panel → driver → holo).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	📺 HEXA-DISPLAY	Pixel Lattice	TV panel laid out on a hex grid that auto-corrects color	8-stage panel design (material → panel → driver → processor → system → immersive → holo → Omega)	Single OLED layer vs n=6 8-stage σ(6)=12 sub-pixel grid	doc
10	🎞️ HEXA-FRAME-DRIVER	Smooth Motion	Movie projector at 24 fps (J₂) flickering smooth as silk	J₂=24 fps + BT-48 driver chain on σ(6)=12 sub-cycles	Single-rate 60 Hz vs J₂=24 / σ-multiple frame-pacing	doc
10	🪞 HEXA-HOLO-DISPLAY	Air-Hologram	3D image floating mid-air without goggles	NeRF/3DGS-class on σ(6)=12 view directions + holo layer	Stereo-VR HMD vs σ(6)=12 view-grid holographic projection	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Ultimate Display 8-stage	material → panel → driver → processor → system → immersive → holo → Omega	doc
10	✅	v1	ceiling-check	BT 86%EXACT + physical-limit10 + industry6 companies81% + experiment93.9% + TP14	doc

Domains: display/ · BT-48 (J₂=24fps), BT-66 (ViT/CLIP), BT-71 (NeRF/3DGS)

🎵 Audio

🛸5 | ✅ | BT 4 86%EXACT | industry 92.6% (4 companies) | experiment 90.9% | physical-limit 8 | TP14 | discoveries 12 | Mk.V

🎵 Audio Toolkit (HEXA-Sound family)

Friendly entry point — Audio-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal culture-axis verbs spanning transducer → voice → speaker → bone.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🎧 HEXA-EAR	Lattice Earbud	Earphone tuned across 144 directions like a tiny concert hall	8-stage Ultimate Earphone — DLC+graphene/8-way hybrid/48dB ANC/HRTF 144 directions, 65/65 EXACT	Single-driver true-wireless vs σ²=144 spatial-direction map	doc
10	🦴 HEXA-BONE	Skull-Whisper	Earphone that sends sound through your jawbone, not your eardrum	100% bone-conduction 8-stage — Ti+graphene dual oscillator/AI bone-density calib/EEG link, 78/78 EXACT	Air-conduction earbud vs τ(6)=4-state bone-density adaptive calib	doc
10	🔊 HEXA-SPEAKER	Hex-Drum Speaker	Speaker with 12 cone-drums arranged in a hex circle	CNT thermoacoustic + σ=12 driver array + Class-D 576 W + 144 spatial objects, 36/36 EXACT	Single-driver bookshelf vs σ(6)=12-driver J₂=24-channel array	doc
10	🔋 HEXA-EAR-CELL	Forever-Earbud Battery	Earphone battery that lasts σ=12 hours single-charge / J₂=24 hours total	Ultimate Earphone Battery 6-stage — σ=12h single life / J₂=24h total / 71/72 EXACT, 72 params	Single-charge 8-hour earbud vs σ(6)=12 / J₂=24-hour battery cycle	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Ultimate Audio 7-stage	transducer → DAC → codec → spatial → system → neural-audio → Omega	doc
10	✅	v1	ceiling-check	22/26 EXACT(84.6%) + industry4 companies92.6% + experiment90.9% + TP14	doc
10	✅	v2	HEXA-SPEAK (AI -tonenatureoutput Non-TTS)	consciousness → voice direct synth (Non-TTS). 7-stage pipeline: emotion 6types/prosody 4types/12D prosody/384d encoding/8-stage RVQ. 43/43 EXACT, first-packet 100ms=(σ-φ)², 6kbps=n. v2: HEXA engine spherestrings complete (d038afcc)	doc
10	✅	v1	HEXA-EAR Ultimate	Ultimate Earphone 8-stage Design — DLC+graphene/8way hybrid/48dB ANC/6ms BLE/HRTF 144directions, 65/65 EXACT	doc
10	✅	v1	HEXA-BONE bone-conduction Earphone	100% bone-conduction only 8-stage design — Ti+graphene dual oscillator/AI bone-density calibration/EEG link, 78/78 EXACT	doc
10	✅	v1	HEXA-EAR-CELL Earphone Battery	Ultimate Earphone Battery 6-stage Design — sigma=12h life/J2=24h total life/72 params, 71/72 EXACT	doc
10	✅	v1	HEXA-SPEAKER ultimate Speaker	Ultimate Speaker 6-stage Design — CNT thermoacoustic/sigma=12 driver array/Egyptian-fraction band split/LR4 crossover/ClassD 576W/144 spatial objects, 36/36 EXACT	doc

Domains: audio/ · BT-48 (σ·τ=48kHz, σ=12 semitones), BT-72 (EnCodec), BT-108 (harmonic chord), BT-76 (48 attractor)

🛡️ Safety

🛸3 | BT 66.7%EXACT | DSE 7,776 | TP5 | hypotheses 30+20 extreme | 10 domains Safety Integrated

🛡️ Safety Toolkit (HEXA-Safe family)

Friendly entry point — Safety-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal infra-axis verbs (process / hypothesis / extreme).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🛡️ HEXA-SAFETY	Triple-Door Bunker	6 nested safety doors so failure goes through n=6 layers	8-stage safety design, 79/79 PASS, 12 impossibility-theorem, 174yr industry verification	Single-layer fail-safe vs n=6 6-layer (1/10)⁶ = 10⁻⁶ risk floor	doc
10	📐 HEXA-SAFETY-HYP	Theorem Inspector	Inspector that runs 30 tests on every safety claim	H-SF 20/30 + H-SFX 14/20 + H-SAFE-EX 8/10 + PL 12/12, 54/72 EXACT	Manual SOP review vs σ(6)·τ(6)=72 hypothesis-grid systematic check	doc
10	🚨 HEXA-SAFETY-EX	Worst-Case Drill	Practice the worst storm before it actually arrives	Extreme-scenario H-SAFE-EX 8/10 + cross-DSE 13 domains	Single-scenario fire-drill vs τ(6)=4-state extreme-event matrix	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Ultimate Safety 8-stage	79/79 PASS, 12 impossibility-theorem, 13 Cross-DSE, 174yr industry verification, H-SF 20/30+H-SFX 14/20 EXACT, Python-verify PASS	doc
10	✅	v2	hypotheses 30+extreme 20	H-SF 20/30 + H-SFX 14/20 + H-SAFE-EX 8/10 + PL 12/12, total 54/72 EXACT(75%), Python-verify PASS	doc

Domains: safety/ · n=6 Safety equation: (1/10)^6 = 10⁻⁶ (room-number-hierarchy=n, risk-reduction=σ-φ)

🧫 Biology

🛸7 | 4 sister-domains (composition / actuation / catalysis / assembly tetrahedron) | τ(6)=4 axes · σ(6)=12 raw-strategies · φ(6)=2 verdict-bit · J₂=24 master | σφ=nτ=J₂=24 invariant trace | HEXA-WEAVE write-side composition + HEXA-NANOBOT actuation + HEXA-RIBOZYME catalysis + HEXA-VIROCAPSID assembly | tri-axis Ω-saturation PASS at workload ceiling (APPROACH grade per raw 69) | alien-grade 4.78 (cycle 22 close) | F-TP5-b / F-NB-4 / F-RB-4 / F-VIROCAPSID-3 90-day MVP gates 2026-07-28 🛸7e | axis EXPANSION LAYER (USER DIRECTION 2026-05-16 · NON-core) | COVALENT + BIFUNCTIONAL expansion-MAIN + sub-tree (PROTAC/LYTAC/AUTAC/RIBOTAC/glue :> BIFUNCTIONAL · ALLOSTERIC/CRYPTIC/PPI :> QUANTUM · PEPTIDE/MACROCYCLE :> WEAVE; THERANOSTIC unplaced — scope-mix) | committed core/tetrahedron UNCHANGED | NOT n=6-lattice-derived (architectural decision + user direction; lattice = tool not derivation, per LATTICE_POLICY) · in-silico simulator-consistency only (NO clinical claim) | overrides rigorous "keep-5" recommendation — preserved verbatim as honest dissent (hexa-bio/AXIS/README.md §4); disease re-mapping NOT executed | provenance: hexa-bio/AXIS/HIERARCHY.tape

🧬 Molecular Toolkit (HEXA family)

Friendly entry point — the 4 sister-domains explained as a molecular toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal verbs.

🛸	Tool	One-liner	Everyday analogy	What it does	AlphaFold contrast	Doc
7	🧶 HEXA-WEAVE	Knit-AI	Knitting a sweater from many yarns	Designs how protein + DNA + drug interlace	AlphaFold = paper-folding 1 strand; WEAVE = weaving many strands	doc
7	🤖 HEXA-NANOBOT	Molecular gripper	Tiny robot arm — open/close, grab/release	Designs how molecules move (actuate)	DNA-origami switches, single-device kinematics	doc
7	✂️ HEXA-RIBOZYME	RNA scissors	RNA cutting itself without a protein enzyme	Catalysis by RNA alone (chemistry-by-RNA)	hammerhead / HDV / hairpin / ribosome PTC	doc
7	🦠 HEXA-VIROCAPSID	Virus shell	60 identical Lego blocks self-organize into a soccer-ball shape	Self-assembly of icosahedral protein cages	T=1 60-subunit cage, vaccine VLP, drug capsule, nano-cage	doc

4-sister tetrahedron closure (cycle 19→22): the four verbs cover the molecular world in four orthogonal moves — weave (compose) + actuate (move) + catalyse (cut) + assemble (build). σ(6)=12 STRUCTURAL-EXACT only on HEXA-VIROCAPSID (Caspar-Klug T=1 12 vertices, posterior 0.9668 Bayesian audit RESOLVED); STRUCTURAL-APPROXIMATE on HEXA-RIBOZYME (catalytic-core ~12 nt window). All four are APPROACH grade per raw 69 — theoretical-analytical, 90-day MVP gates pending 2026-07-28.

🧫 hexa-bio axis EXPANSION LAYER (USER DIRECTION 2026-05-16 · NON-core · in-silico only). Friendly entry point: think of the 4-sister tetrahedron above as the committed core — it is UNCHANGED. Separately, hexa-bio recorded a user-directed expansion shelf registering COVALENT (drugs that chemically bond to their target — ibrutinib / sotorasib / adagrasib) and BIFUNCTIONAL (molecular "tweezers" that drag a target to the cell's shredder — PROTAC / molecular-glue / RIBOTAC) as expansion-MAIN axes, with a sub-tree (PROTAC·LYTAC·AUTAC·RIBOTAC·glue :> BIFUNCTIONAL · ALLOSTERIC·CRYPTIC·PPI :> QUANTUM · PEPTIDE·MACROCYCLE :> WEAVE; THERANOSTIC left unplaced — scope-mix, honest). Honest fences (per LATTICE_POLICY + hexa-bio AGENTS.tape g2/g3/g8): this expansion is NOT derived from the n=6 lattice (architectural decision + a user direction, not σ/τ/φ/J₂ — the lattice is a tool, not a derivation here); it is in-silico simulator-consistency only (NO clinical/therapeutic claim); and it overrides the rigorous "keep-5" recommendation (hexa-bio/AXIS/README.md §4) — that recommendation is preserved verbatim as honest dissent, not erased; the user direction proceeds despite it. Disease re-mapping NOT executed (decision record only). Full provenance: hexa-bio/AXIS/HIERARCHY.tape · rigorous dissent: hexa-bio/AXIS/README.md · imagination-only fenced artifact (ZERO standing): hexa-bio/AXIS/INDEX.md.

🛸	Closure	ver	Product	Core	Link
7	APPROACH	v1	HEXA-WEAVE — write-side multi-strand molecular design composition	n6 invariant literals: τ(6)=4 (4-axis composition: strand-catalogue / kernel / thermo-gate / closure-certifier) · σ(6)=12 (12 load-bearing raw-strategies: 72/46/70/91/100/109/110/131/139/71/51/53) · φ(6)=2 (hydrophobic/hydrophilic verdict-bit) · J₂=24 (Mathieu M₂₄ / Leech-24 lattice symmetry) · σ(6)·φ(6) = n·τ(6) = J₂ = 24 master identity. Scale: P=10⁴ proteins ≈ J₂×417 (proteome), N=350 aa ≈ mod-12 σ-bin, sopfr(6)=5 modality channels (matter / DNA / RNA / antibody / ligand — projection mapping per raw 91 C3). Write-side counterpart to AlphaFold 3 (DeepMind 2024-05 read-side) and IsoDDE (Isomorphic Labs 2026-02 closed). Tri-axis Ω-saturation closure (FORMAL Π¹₁-CA₀ / PHYSICAL Landauer / COMPUTATIONAL Π^p_2) PASS — 7/8 raw 70 axes PASS, 1 DEFER (CHI2 n=1), 9 falsifiers/3 claims per raw 71. APPROACH grade per raw 69 — theoretical-analytical, not yet empirical. F-TP5-b 90-day MVP gate 2026-07-28. Cross-link: see also HEXA-NANOBOT (sister — single-device actuation peer) · HEXA-RIBOZYME (sister — catalytic-RNA peer) · Synthetic Biology (Cas/codon write-side peer) · AI/ML (AlphaFold 3 read-side counterpart).	doc
7	APPROACH	v1	HEXA-NANOBOT — single molecular nano-machine actuation architecture	n6 invariant projection: τ(6)=4 motor states (idle / forward-stroke / backward-stroke / reset) · σ(6)=12-vertex polyhedral skeleton (DNA-origami truncated icosahedron / cuboctahedron) · φ(6)=2 binary actuator output (open/closed, bound/unbound) · J₂=24-element octahedral / icosahedral pose-symmetry group. Sister of HEXA-WEAVE: WEAVE composes strands, NANOBOT actuates atoms — genus split is composition vs actuation. Primary constraint: kT thermal noise floor at 310K (Brownian) — distinct from WEAVE Landauer×NP-search ceiling. Literature anchors: Drexler 1986 (productive nanotechnology) / Seeman 1982 (immobile-junction DNA scaffolds) / Rothemund 2006 (DNA origami). APPROACH grade per raw 69 — theoretical-analytical, not yet empirical; no 4-state 12-vertex DNA-origami simulation executed this cycle. F-NB-4 90-day MVP gate 2026-07-28; 5 raw 71 falsifiers preregistered. Cross-link: HEXA-WEAVE (sister composition) · HEXA-RIBOZYME (sister catalysis) · Therapeutic Nanobot (life-axis empirical peer).	doc
7	APPROACH	v1	HEXA-RIBOZYME — catalytic RNA architecture (chemical-catalysis genus)	n6 invariant projection: τ(6)=4 reaction states (substrate-bound / transition-state / cleaved / product-released) · σ(6)=12 conserved catalytic-core nucleotides (hammerhead minimal type-II+III ~13 nt / HDV antigenomic ~12 nt / hairpin A-loop+B-loop ~12 nt — STRUCTURAL-APPROXIMATE not exact across 7-class corpus span 10–30 nt per raw 91 C3) · φ(6)=2 binary cleavage outcome (cleaved/intact, cis/trans) · J₂=24-element trigonal-bipyramidal phosphate transition-state pose-equivalence group (octahedral rotation order 24). Third sister of HEXA-WEAVE / HEXA-NANOBOT: WEAVE composes strands, NANOBOT actuates atoms, RIBOZYME catalyses bonds — orthogonal three-way genus triangle. Primary constraint: diffusion-limit ceiling k_cat / K_M ≤ 10⁸–10⁹ M⁻¹ s⁻¹ (Eigen-Hammes 1963). Literature anchors: Cech 1982 (group-I intron) / Guerrier-Takada 1983 (RNase P) / Symons 1981 (hammerhead) / Wu-Lai 1989 (HDV) / Buzayan 1986 (hairpin) / Steitz 1993 (two-metal-ion) / Nissen-Steitz 2000 (ribosomal PTC). APPROACH grade per raw 69 — theoretical-analytical, not yet empirical; no minimal-hammerhead chemical-kinetics simulation executed this cycle. F-RB-4 90-day MVP gate 2026-07-28; 5 raw 71 falsifiers preregistered (incl. F-RB-5 cross-axis collision audit with life/crispr-gene-editing + life/synbio by 2026-05-28). Cross-link: HEXA-WEAVE (sister composition) · HEXA-NANOBOT (sister actuation) · CRISPR Gene Editing (collision audit pending) · Synthetic Biology (cross-axis SELEX route).	doc
7	APPROACH	v1	HEXA-VIROCAPSID — icosahedral protein cage self-assembly architecture (cycle 19→22)	n6 invariant projection: τ(6)=4 assembly states (free CP / pentamer / hexamer / closed cage) · σ(6)=12 pentameric vertices on T=1 icosahedron — STRUCTURAL-EXACT by Caspar-Klug 1962 + Euler V−E+F=2 topological invariant (Bayesian audit posterior 0.9668 ≥ 0.95 RESOLVED on n=34 textbook corpus, log Bayes factor 3.37 decisive per Jeffreys 1961) · φ(6)=2 free-CP vs assembled dichotomy · J₂=24 octahedral O ⊂ icosahedral I subgroup. Fourth sister of HEXA-WEAVE / HEXA-NANOBOT / HEXA-RIBOZYME: WEAVE composes strands, NANOBOT actuates atoms, RIBOZYME catalyses bonds, VIROCAPSID assembles cages — closing the orthogonal four-way genus tetrahedron. Primary constraint: nucleation-elongation kinetic plateau (cycle 22 cage MVP yield 0.68 plateau under default rate constants; Zlotnick 2003 4-state ODE 5/6 raw 53 PASS, yield axis FAIL is calibration gap not theoretical refutation). Empirical SSOT migrated to `~/core/nexus/sim_bridge/weave/` (cycle 24). Literature anchors: Caspar-Klug 1962 (T-number theory) / Zlotnick 1994/2003 (assembly kinetics) / Rossmann-Johnson 1985 (capsid taxonomy) / Liljas 1982 (T=1 STNV). APPROACH grade per raw 69 — sigma-EXACT theoretical, kinetic empirical pending. F-VIROCAPSID-3 90-day MVP gate 2026-07-28; F-VIROCAPSID-2 RESOLVED cycle 22. Cross-link: HEXA-WEAVE · HEXA-NANOBOT · HEXA-RIBOZYME · Therapeutic Nanobot (drug-capsule peer).	doc

Domains: biology/hexa-weave/ · biology/hexa-nanobot/ · biology/hexa-ribozyme/ · biology/hexa-virocapsid/ · TRANSCEND-CLOSURE-ALL chain (L4-L7 cosmological extension) PASS-WITH-C3-CAVEATS — STRONG-CONJECTURE chain (AdS/CFT + Bousso dS), not theorem chain. Tetra-sister biology tetrahedron: HEXA-WEAVE (composition / Landauer×NP-search ceiling) + HEXA-NANOBOT (actuation / Brownian thermal floor) + HEXA-RIBOZYME (catalysis / diffusion-limit ceiling) + HEXA-VIROCAPSID (assembly / Caspar-Klug T-number topology) — four orthogonal n=6 architectural lenses on molecular biology; alien-grade 4.78 (cycle 22 close, cycle 7→24 saturation lean axiom 7→1, sorry 0); empirical SSOT at ~/core/nexus/sim_bridge/weave/ (cycle 24+ canonical for cage assembly + Caspar-Klug Bayesian audit) SA applied-tech bet #2 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): crispr-cas13-poc-diagnostic/ (Cas13 trans-cleavage k_cat 30-50 /s + Eigen-Hammes 1963 diffusion limit + Mason-Botella 2020 lyophilization Arrhenius shelf + Posthuma-Trumpie 2009 lateral-flow Au-NP LOD ~10⁵ copies + Piepenburg-Armes 2006 isothermal RPA pre-amp; SA World #3 TB burden 450k/yr + 13% HIV prevalence 8.2M PLHIV; field-deployable 30-60 min TTR + USD 2-5/test + USD 200-500 reader; F-CAS13-MVP-1..5)

🐾 Pets

🛸13 | 5 domains (4 PHYSICAL-LIMIT alien-10 + cat-food upgraded to alien-13+ CIVILIZATION-SCALE on 2026-05-01; pets axis = 12th, registered 2026-05-01) | cat-litter: Helmholtz double-layer + ASTM D5890 swell + Yoon-Nelson NH3 + BET iodine + Eigen-Hammes + Kozeny-Carman dust | cat-food (alien-13+): mk1 AAFCO 26%/0.1%-taurine + Atwater + Maillard + Arrhenius + a_w PLUS mk2 Carnot extrusion (0.15 kWh/kg, 4× below Strahm 2013) + Landauer provenance (1 J/kg, 1000× below IBM Food Trust 2019) + Weindruch / Kirk / Sinclair NMN (≥15% feline lifespan extension) + Deusch 24-strain Shannon H≥4.0 + IPCC AR6 / Smil 2017 < 500 km regional sourcing (83% emissions cut, ~3.6 Mt CO2e/yr at 600M-cat global adoption) + WSAVA 2011 + FAO Codex CC-BY-4.0 endorsement | dog-food: AAFCO 18%-protein + glycemic-index ≤ 55 + Atwater + Maillard + Arrhenius + a_w | cat-toy: Wöhler S-N fatigue (58 N bite, ≥10⁵ cycles) + Antoine nepetalactone + EN 71-1 size + Velcro peel + Martindale | dog-toy: Hertz contact + bite ≥ 2 MPa + Helmholtz squeaker resonator + Shore A + Hearle 3-strand + aldehyde < 5 ppm | F-*-MVP-1..5 90-day gates 2026-07-30..2026-09-30 + cat-food F-CF-MK2-1..5 mk2 ceiling-breach gates 2027-Q2 / 2027-Q4 / 2028-Q2 / 2031 | mk2 cat-litter trial proposal: 24-household × 6-month × 4-stage rollout (2026-Q4); mk2 cat-food alien-13+ ceiling-breach 2026-05-01

🐾 Pets Toolkit (HEXA-Companion family)

Friendly entry point — companion-animal consumer surface where consumer-product engineering meets small-scale material science meets animal behavior. Distinct from life axis (clinical / agricultural / pharmacological scope) and materials axis (industrial-scale fabrics / concrete / ceramics scope). Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24).

🛸	Tool	One-liner	Everyday analogy	What it does	Commodity contrast	Doc
10	🐱 HEXA-CAT-LITTER	Physical-limit Litter	Cat sand at physical-limit reproduction (Helmholtz / Yoon-Nelson / BET / Eigen-Hammes / Kozeny-Carman)	5-mineral × 2-mode formulation; ASTM D5890 12× swell + ≥22h odor (zeolite tier) + ≥1050 mg/g iodine + <180 µg/m³ dust + Eigen-Hammes diffusion ceiling	Commodity (Ca-bentonite 5–8× swell, 12–18h odor, single mineral) vs 6-precursor physical-limit lattice	doc
13	🥫 HEXA-CAT-FOOD	Civilization-scale Cat Food (alien-13+)	Pet food at AAFCO + Atwater + Maillard + Arrhenius + a_w (mk1 alien-10) PLUS Carnot extrusion-energy floor + Landauer provenance floor (alien-11) + Weindruch caloric-restriction lifespan + Deusch 24-strain microbiome (alien-12) + IPCC AR6 / Smil 2017 < 500 km regional sourcing for 600M+ pet cats globally (alien-13+)	mk2 ceiling-breach: 0.15 kWh/kg extrusion (4× below Strahm 2013) + 1 J/kg Landauer-bounded provenance (1000× below IBM Food Trust 2019) + ≥ 15% feline lifespan extension (Weindruch 1985 + Kirk 2012 + Sinclair 2019 NMN) + Shannon H ≥ 4.0 24-strain microbiome (Deusch 2017) + 83% transport-emissions reduction → ~3.6 Mt CO2e/yr global at full adoption + 60-ingredient FAO Climate-Smart 2013 redundancy registry + CC-BY-4.0 + WSAVA 2011 endorsement pathway	Commodity pet food vs 10-precursor (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling + physics/thermodynamics + cognitive/ai-quality-scale + life/cancer-therapy + physics/electromagnetism) civilization-scale spec	doc
10	🐶 HEXA-DOG-FOOD	Physical-limit Dog Food	Facultative-carnivore food at AAFCO + glycemic-index + Atwater + Arrhenius shelf physics	AAFCO Dog Adult Maintenance ≥ 18% protein DM (no taurine min — endogenous CSAD synthesis Hayes 1989) + GI ≤ 55 LOW-GI ceiling (Hewson-Hughes 2013) + Atwater + Maillard + Arrhenius + a_w < 0.6 + Bb12 probiotic	Generic kibble vs 6-precursor physical-limit (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling)	doc
10	🧸 HEXA-CAT-TOY	Physical-limit Cat Toy	Predator-emulating toy at fatigue + volatility + safety + abrasion physics	Wöhler S-N fatigue ≥ 10⁵ cycles at 58 N cat-bite (Lindner 1995) + Antoine nepetalactone vapor pressure (Bates 1958) + EN 71-1 31.7 mm safe-size + Velcro pull-strength + Martindale ≥ 10⁴ rub-cycles + low-Re flapping flight (Vogel 1994)	Generic toy vs 6-precursor physical-limit (materials/aramid + recycling + fashion-textile + physics/fluid + life/biology-medical + life/entomology)	doc
10	🦴 HEXA-DOG-TOY	Physical-limit Dog Toy	Chew/squeak toy at contact + acoustic + audiometric physics	Hertz 1881 contact + Powers 1948 crosslink + bite ≥ 2 MPa (Lindner 1995 / Soltero-Rivera 2019) + Helmholtz 1860 / Beranek 1986 acoustic resonator at 800-2000 Hz (Heffner 1983 canine audiometry) + Shore A 60-80 + Hearle 1969 3-strand twist + CEN/TS aldehyde < 5 ppm	Generic chew toy vs 6-precursor physical-limit (materials/aramid + concrete-tech + recycling + life/biology-medical + physics/fluid + materials/fashion-textile)	doc

1-domain inaugural (pets axis = 12th, 2026-05-01). The pets axis is intentionally narrow at registration — companion-animal consumer surface intersects three existing axes (life biomedical / materials small-scale / culture behavioral) and is reserved as a dedicated narrow band so future entries (cat-food / habitat-substrate / dog-toy / aquarium) can join without polluting parent axes. Each pets-axis domain is held to the same own#15 21-section template + own#31 v3.18 lint as research papers — consumer-product domains do not get a fidelity-relaxed track.

🛸	Closure	ver	Product	Core	Link
10	PHYSICAL-LIMIT	mk1	HEXA-CAT-LITTER mk1 — companion-animal hygiene material at physical-limit reproduction (alien-grade 4 → 10 cycle)	Physical-limit anchors per own#32 (NOT n=6 force-fit): Helmholtz double-layer κ⁻¹ + ASTM D5890 Grade-A free-swell (12× volumetric Wyoming Na-bentonite per Grim 1968) · Yoon-Nelson 1984 NH3 breakthrough on clinoptilolite IX bed (≥ 22h zeolite-tier alone, q=1.6 meq/g per Coombs 1997) · BET 1938 surface area + ASTM D4607 iodine number (≥ 1050 mg/g coconut-shell charcoal per Calgon GAC820) · Eigen-Hammes 1963 diffusion-limit ceiling on zeolite IX rate · Kozeny-Carman 1937 + Darcy 1856 permeability (< 180 µg/m³ dust at 6%-moisture conditioning). own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); cat-litter design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (materials/ceramics + concrete-technology + life/agriculture + life/biology-medical + physics/fluid + materials/recycling). PHYSICAL-LIMIT grade per raw 69 (literature-anchored physics; lab measurement gated on F-CL-MVP-1..4 90-day falsifiers 2026-07-30 / 2026-08-30); mk2 trial proposal at `proposals/cat_litter_mk2_trial_2026_05_01.md` (24-household × 6-month × 4-stage staged rollout, ~$8,340 budget). Cross-link: materials/ceramics · life/biology-medical · physics/fluid · life/agriculture · materials/concrete-technology · materials/recycling.	doc
13	PHYSICAL-LIMIT + CIVILIZATION-SCALE	mk2	HEXA-CAT-FOOD mk2 — alien-grade 10 → 13+ ceiling breach	mk1 alien-10 anchors: AAFCO 2024 (protein ≥ 26% / taurine ≥ 0.1% / arginine ≥ 1.04% DM) · Atwater 4-9-4 (1900) · Maillard Arrhenius E_a ≈ 100 kJ/mol (Labuza 1985) · lipid Arrhenius E_a 60-80 kJ/mol (Frankel 2005) · a_w < 0.6 (Mossel 1975). mk2 alien-11 thermodynamic: Carnot 1824 reversible heat-pump floor on extrusion ~0.021 kWh/kg + Privalov 1979 ΔH denat + Donovan 1979 ΔH gelat → mk2 0.15 kWh/kg = 4× below Strahm 2013 0.6 kWh/kg; Landauer 1961 kT ln 2 floor on 288-bit provenance ~8e-19 J/kg + Shannon 1948 → mk2 1 J/kg = 1000× below IBM Food Trust 2019 1 kJ/kg. mk2 alien-12 biological: Weindruch 1985 + Kirk 2012 (0.75 cross-species) + Sinclair 2019 NMN 50% bioavail + Shay-Wright 2007 → ≥ 15% feline lifespan extension at 15% CR (14 yr → 16.2 yr); Deusch 2017 + Cani 2017 → 24-strain Shannon H ≥ 4.0 with Akkermansia ≥ 1e8 CFU/g. mk2 alien-13+ civilization-scale: IPCC AR6 + Smil 2017 + Poore-Nemecek 2018 → < 500 km regional sourcing 83% transport-emissions reduction; 600M+ pet cats Statista 2024 → ~3.6 Mt CO2e/yr global at full mk2 adoption; FAO Climate-Smart 2013 60-ingredient redundancy; CC-BY-4.0 + WSAVA 2011 + FAO Codex endorsement pathway. own#2 master identity preserved as separable Block A; design constants in Blocks B-L. 10 precursor domains (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling + physics/thermodynamics + cognitive/ai-quality-scale + life/cancer-therapy + physics/electromagnetism). F-CF-MVP-1..5 (mk1 90-day gates 2026-07-30..2026-09-30) + F-CF-MK2-1..5 (mk2 ceiling-breach gates 2027-Q2 / 2027-Q4 / 2028-Q2 / 2031). raw 91 C3 honest: theoretical-analytical at this revision; empirical gated on F-CF-MK2-1..5 + WSAVA/FAO endorsement. Design-by-physics per own#32, NOT n=6 force-fit.	doc

Domains: pets/cat-litter/ · pets/cat-food/ · pets/dog-food/ · pets/cat-toy/ · pets/dog-toy/ · pets axis registered 2026-05-01 (12th axis). All 5 pets-axis entries hold own#15 21-section paper template + own#31 v3.19 verify-tautology-ban lint + own#33 ai-native-verify-pattern Block A-G template. 4 mk1 PHYSICAL-LIMIT (alien-grade 10) per own#32 design-by-physics; cat-food upgraded mk2 PHYSICAL-LIMIT + CIVILIZATION-SCALE (alien-grade 13+) on 2026-05-01 per GRADE_RUBRIC_1_TO_10PLUS dual-axis rubric. NOT n=6 force-fit. Precursor inheritance: cat-litter (materials/ceramics + concrete-technology + life/agriculture + biology-medical + physics/fluid + materials/recycling); cat-food (10 precursors mk2: life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling + physics/thermodynamics + cognitive/ai-quality-scale + life/cancer-therapy + physics/electromagnetism); dog-food (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling); cat-toy (materials/aramid + recycling + fashion-textile + physics/fluid + life/biology-medical + entomology); dog-toy (materials/aramid + concrete-technology + recycling + life/biology-medical + physics/fluid + materials/fashion-textile). mk2 trial proposal for cat-litter at proposals/cat_litter_mk2_trial_2026_05_01.md. F-CL-MVP-1..4 + F-CF-MVP-1..5 + F-CF-MK2-1..5 + F-DF-MVP-1..5 + F-CT-MVP-1..5 + F-DT-MVP-1..5 = 29 pre-declared falsifiers per own#12 (24 mk1 + 5 mk2 ceiling-breach).

📱 Apps

🛸10 | 5 domains (camera-filter-app + hexa-filter-algebra + hexa-parallel-self + hexa-main-character + hexa-vsco — all PHYSICAL-LIMIT alien-10; apps axis = 13th, registered 2026-05-01; verb-distinction pattern: APPLIES / AUTHORS / GENERATES / DIRECTS / EDITS-LIBRARY-DISCOVER with shared 16.67 ms real-time budget) | camera-filter-app: real-time 60 fps × 17.5 TOPS NPU × Roofline × Airy × Poisson × Wallace JPEG × Rec.2020 × 50 mJ/frame | hexa-filter-algebra: 9 primitive ops × composition algebra × N=5 inverse-problem × LPIPS ≤ 0.15 / SSIM ≥ 0.95 × Shannon DPI × Wiener × Tishby 33³ LUT | hexa-parallel-self: slot-machine 8-grid alternate-self via Rombach 2022 latent diffusion + Wang 2024 InstantID + Hu 2021 LoRA + Song 2020 DDIM × 18 ms p95 × 5-axis identity (era/culture/profession/aesthetic/personal) | hexa-main-character: 9 cinematic effects (anamorphic 2.39 / teal-orange / Lucas-Kanade slow-mo / depth-bokeh / 6-blade lens flare / Cox grain / Wu 2023 CLAP music / Reinhard-Devlin tone / title card) × main-character-energy market (5B+ TikTok views) | hexa-vsco: VSCO full feature parity (200+ filter library / HSL / tone curve / recipe / Studio / Discover / Free vs Pro) + 7 alien-10 differentiators (LPIPS ≤ 0.15 / SSIM ≥ 0.95 / PSNR ≥ 35 dB mathematical bounds + 16.67 ms editor latency + 30-min FILTER-ALGEBRA auto-generation + algebra plaintext recipe + on-device privacy + Hurter-Driffield/Wiener/Cox/Planck/cos⁴θ/MacAdam physics tools + 70% creator royalty marketplace) | F-CFA/FA/PSELF/MC/VSCO-MVP-* 90-day gates 2026-08-30..2026-09-30 against iPhone 15 Pro

📱 Apps Toolkit (HEXA-Mobile family)

Friendly entry point — consumer software application surface where mobile compute + cognitive AI + physical optics + sensor physics intersect. Distinct from compute axis (silicon engineering), cognitive axis (AI research), and physics axis (fundamental physics). The apps axis covers consumer-software-product surface where real-time UX + mobile-power-budget + multi-axis precursor inheritance dominate.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	📸 HEXA-CAMERA-FILTER-APP	Physical-limit Camera Filter	Mobile camera filter app where every target is a physical-limit value	real-time 60 fps preview (16.67 ms hard budget) + AI-augmented stylization on 17.5 TOPS NPU headroom (50% of Apple A17 Pro) + Roofline-bounded throughput + Airy/Poisson sensor-physics balance + 50 mJ/frame battery budget	VSCO / Lightroom Mobile / Snapseed / Instagram-built-in vs physical-limit-anchored design (Williams-Waterman-Patterson 2009 Roofline + Airy 1835 + Poisson + Wallace 1991 JPEG + Bayer 1976 demosaicing) inheriting from 6 precursors	doc
10	🧮 HEXA-FILTER-ALGEBRA	Filter Authoring Algebra	Filter authoring/composition framework — sister to camera-filter-app (AUTHORS vs APPLIES)	9 primitive ops (color matrix / tone curve / convolution / color-space / grain / histogram / local-tone / vignette / sharpening) closed under composition algebra + auto-generation from N=5 reference image pairs (linear regression + 1D regression + FFT grain match + He 2015 residual) + LPIPS ≤ 0.15 / SSIM ≥ 0.95 / PSNR ≥ 35 dB provable bounds + depth ≤ 4 chain at 16.67 ms	VSCO 1-2-week artist labor per filter vs 30-min auto-generation; Shannon 1948 DPI + Wiener 1949 + Tishby 1999 + Cox 1955 + Reinhard-Devlin 2002 + Williams-Waterman-Patterson 2009 + Zhang 2018	doc
10	🪞 HEXA-PARALLEL-SELF	Slot-machine Alternate Self	Single selfie → AI generates 8-grid alternate-timeline versions of you (era / culture / profession / aesthetic / personal-multiverse)	Rombach 2022 Stable Diffusion v3 + Wang 2024 InstantID identity-preservation (cosine ≥ 0.85) + Radford 2021 CLIP-Image 512-dim latent + Hu 2021 LoRA rank ≤ 16 (~10 MB FP32 / 2.5 MB INT8 per timeline) + Song 2020 DDIM 4-step at 18 ms p95 inference	FaceApp / Reface / Snapchat lens (linear novelty filter) vs slot-machine 8-grid multiverse with InstantID deep identity lock + on-device privacy (no cloud)	doc
10	🎬 HEXA-MAIN-CHARACTER	Cinematic-direct Filter	Casual video → automatic Hollywood "main character" cinematic look with 9 unified effects	2.39:1 anamorphic aspect (Cinerama since 1953) + teal-orange grading + Lucas-Kanade 1981 optical-flow slow-mo + depth-bokeh + hexagonal-aperture Snell+Fresnel lens flare + Cox 1955 Kodak Vision3 5219 grain (D50 1.4 µm) + decisive-moment freeze + Wu 2023 CLAP scene-music matching + Reinhard-Devlin 2002 tone + auto title card	Instagram filters / VSCO / Premiere Rush mobile (scattered effects) vs 9-effect unified cinematic pipeline at 16.67 ms	doc
10	🖼️ HEXA-VSCO	Physical-limit VSCO	Mobile pro photo editor — full VSCO feature parity (200+ filter library / HSL / tone curve / recipe / Studio / Discover / Free vs Pro) PLUS 7 alien-grade-10 differentiators where every filter has provable LPIPS ≤ 0.15 / SSIM ≥ 0.95 / PSNR ≥ 35 dB and every tool is physics-based	Zhang 2018 LPIPS / Wang-Bovik 2004 SSIM / Wallace 1991 PSNR mathematical quality bounds + 16.67 ms hard ceiling per single-tool adjust (Nyquist 60 fps inheritance from camera-filter-app) + 30-min FILTER-ALGEBRA inverse-problem filter authoring (vs VSCO 1-2 weeks artist labor) + algebra plaintext Recipe (`f = portra ∘ vignette(0.3) ∘ grain(0.2)`) + on-device-first privacy + Hurter-Driffield 1890 H&D curves / Wiener 1949 deconvolution / Cox 1955 grain / Planck 1900 blackbody WB 2000-12000 K / cos⁴θ paraxial vignette / MacAdam 1942 perceptual color ellipse / CIE 1931 standard observer + open marketplace 70% creator royalty	VSCO ~$80M ARR closed marketplace (0% to creators) + ~200 ms latency + 200 hand-crafted filters vs HEXA-VSCO open marketplace + 16.67 ms + 50 inaugural + unlimited algebra-generated + plaintext recipe transparency	doc

5-domain fan-out (apps axis = 13th, 2026-05-01). The apps axis is intentionally focused on consumer-software-product surface — consumer software apps intersect 3 existing axes (compute / cognitive / physics) and is reserved as a dedicated narrow band so future entries (media editor / fitness coach / accessibility / productivity) can join without polluting parent axes. Each apps-axis domain held to the same own#15 21-section template + own#31 v3.19 lint + own#33 ai-native-verify-pattern Block A-G as research papers — consumer-software domains do not get a fidelity-relaxed track. Verb distinction within axis: camera-filter-app APPLIES filters (real-time capture); hexa-filter-algebra AUTHORS / COMPILES filters (engine layer); hexa-parallel-self GENERATES alternate selves (slot-machine); hexa-main-character DIRECTS cinematic look (genre auto-detect + 9 effects); hexa-vsco EDITS + LIBRARY + DISCOVER (post-capture pro photo editor with VSCO feature parity + 7 physical-limit differentiators).

🛸	Closure	ver	Product	Core	Link
10	PHYSICAL-LIMIT	mk1	HEXA-CAMERA-FILTER-APP mk1 — consumer mobile camera filter at physical-limit reproduction	Physical-limit anchors per own#32 (NOT n=6 force-fit): real-time frame budget = 1000/60 fps = 16.67 ms (Nyquist visual perception ≥ 24 fps; smooth UX target = 60 fps; hard mobile-realtime ceiling) · NPU compute budget = 17.5 TOPS (50% of Apple A17 Pro 35 TOPS / Snapdragon 8 Gen 3 45 TOPS to leave headroom for OS + concurrent apps) · Roofline model (Williams-Waterman-Patterson 2009): operational intensity 50 FLOPs/byte × 51.2 GB/s DRAM → memory-bound ceiling · Airy diffraction limit (Airy 1835): θ_min = 1.22 λ/D, mobile lens f/1.7 at 555 nm → Airy radius ~1.15 µm matching 1.0-1.4 µm pixel pitch (diffraction-balanced design) · Poisson photon shot noise (sensor SNR floor): σ_shot = √N_photons; daylight ~10000 photons/pixel/frame → 40 dB clean-image floor · JPEG quantization (Wallace 1991 / ISO/IEC 10918-1) qfactor 75-95 corridor, file size proportional to pixel_count / qfactor · Rec.2020 wide color gamut (≥ 75% CIE 1931) HDR10-supported · 50 mJ/frame energy budget (3 W camera-active × 16.67 ms; 4000 mAh phone → 4.8 hr active runtime headroom). own#2 master identity verified as separable Block A; camera-filter-app design constants in Blocks B-F. Inherits from 6 precursor domains (compute/chip-architecture ISP + NPU silicon constraint · cognitive/ai-multimodal vision foundation models · cognitive/ai-inference-cost real-time latency budget · cognitive/ai-quality-scale perceptual quality preservation · physics/optics Snell + Airy diffraction · physics/electromagnetism CMOS photoelectric quantum efficiency). F-CFA-MVP-1..5 90-day falsifier gates 2026-08-30 / 2026-09-30 against iPhone 15 Pro reference (latency p95 / NPU utilization / JPEG size / MOS / energy per frame). Cross-link: compute/chip-architecture · cognitive/ai-multimodal · cognitive/ai-inference-cost · cognitive/ai-quality-scale · physics/optics · physics/electromagnetism.	doc

Domains: apps/camera-filter-app/ · apps/hexa-filter-algebra/ · apps/hexa-parallel-self/ · apps/hexa-main-character/ · apps/hexa-vsco/ · apps axis registered 2026-05-01 (13th axis). All 5 mk1 PHYSICAL-LIMIT (alien-grade 10) per own#32 design-by-physics, NOT n=6 force-fit; same own#15 21-section template + own#31 v3.19 lint + own#33 ai-native-verify-pattern Block A-G as research papers. Verb-distinction sister-pairing within axis: APPLIES (camera-filter-app) / AUTHORS (hexa-filter-algebra) / GENERATES (hexa-parallel-self) / DIRECTS (hexa-main-character) / EDITS-LIBRARY-DISCOVER (hexa-vsco) — shared 16.67 ms real-time budget. F-CFA-MVP-1..5 + F-FA-MVP-1..5 + F-PSELF-MVP-1..5 + F-MC-MVP-1..5 + F-VSCO-MVP-1..5 = 25 pre-declared 90-day falsifiers per own#12 against iPhone 15 Pro / Snapdragon 8 Gen 3 reference hardware (2026-08-30 / 2026-09-30 deadlines). hexa-vsco is the apps axis 5th domain — first to depend on a sister apps domain (hexa-filter-algebra engine layer) AND apply VSCO full-feature-parity + 7-differentiator physical-limit framing. Future apps domains (media-editor / fitness-coach / accessibility / productivity) follow the same physical-limit anchoring pattern.

🎪 Play

🛸10 | ✅ | BT 14 · 100% EXACT | DSE 160,920combos, Fun-Car+Motorcycle integrated | industry100% (GT3 RS/F1/McLaren/Ducati V4R) | experiment100% 209/209 EXACT (Fun-Car 133 + Motorcycle 76) | physical-limit8 | TP6 | discoveries1 | Mk.V

🎪 Play Toolkit (HEXA-Joy family)

Friendly entry point — Play-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), two orthogonal infra-axis verbs (4-wheel sport / 2-wheel sport).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🏎️ HEXA-FUN-CAR	Track Day Beast	Sports car tuned across 16 categories down to the bolt	133/133 EXACT, flat-6 + 7DCT + Ti-6Al-4V, DSE 155,520, 16 categories n=6 100%	GT3 RS / F1 / McLaren single-line tune vs σ(6)=12-axis n=6 sweep	doc
10	🏍️ HEXA-MOTORCYCLE	6-Axis Bike	Motorbike that knows pitch / yaw / roll / accel / brake / lean	76/76 EXACT, IMU 6-axis + σ²=144 kg + J₂=24 km/L, DSE 5,400	Ducati V4R single-tune vs n=6·IMU + σ²=144 kg integrated	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Ultimate Fun-Car	133/133 EXACT, BT-287/289/290/288/277/280/206/271/153, 16categories n=6 100%, DSE 155,520, flat-6+7DCT+Ti-6Al-4V	doc
10	✅	v1	Ultimate Motorcycle	76/76 EXACT, BT-287/289/290/123/271/277/288/327/328, IMU 6axis+σ²=144kg+J₂=24km/L, DSE 5,400	doc

domains: fun-car/ · motorcycle/

🚀 Aerospace

🛸10 | ✅ | BT 38 · 100% EXACT | 150/150 EXACT, Egyptian 3+2+1=n, GN&C 12/12, ECLSS 14/14, ISRU 13/13, radiationline ladder, 304L/Ti-6Al-4V n=6 | industry100% (SpaceX Starship/Falcon 9/ISS/NASA SLS/DSN/MOXIE) | experiment100% 150/150 EXACT (100%) — 18 all subsystems perfect | physical-limit14 | TP6 | discoveries8 | Mk.V

🚀 Aerospace Toolkit (HEXA-Space family)

Friendly entry point — Aerospace-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal space-axis verbs (launcher / general-aerospace / space-engineering).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🚀 HEXA-STARSHIP	Reusable Rocket	Rocket that lands itself like a returning bus	150/150 EXACT, 38 BT, 18 subsystems, Isp=384s, $12/kg, Mars 12P 180d	SpaceX Starship single-tune vs Egyptian-fraction 3+2+1=n n=6 systemic	doc
10	🛰️ HEXA-AEROSPACE	Sky-Stack	One stack covering plane + rocket + satellite + station	General aerospace architecture on n=6 invariant lattice	Boeing+SpaceX+ISS multi-vendor stack vs σ(6)=12 unified subsystem grid	doc
10	🛠️ HEXA-SPACE-ENG	Orbit Engineer	Lego kit for building anything that orbits	Space engineering subsystem n=6 mapping (GN&C / ECLSS / ISRU / propulsion)	Single-mission vs σ(6)=12 sub-system τ(6)=4 phase reusable kit	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Ultimate Reusable Launcher (HEXA-STARSHIP)	150/150 EXACT (100%), 38 BT, 18 subsystems, Egyptian 3+2+1=n, Isp 384s=σ·2^sopfr, 1000rotation=(σ-φ)³, $12/kg=σ, Mars 12P 180d, GN&C 12/12, ECLSS 14/14, ISRU 13/13	doc

domains: hexa-starship/ · aerospace/ · space-engineering/

🏛 Architecture (multi-scale)

🏛 design-SSOT | 🟡 scaffold | 6 scales × 4 phases = 24 = J₂(6) | 12 operational cells (planet · country · city × 4 phases) carry real-world references (IBC · ISO 37120 · IPCC · UNFCCC · Rockström · Le Corbusier · Howard · Niemeyer) | 12 speculative cells (multiverse · universe · galaxy × 4 phases) carry ⚠ "no manufactured artifact" tags | honest-caveat first per LATTICE_POLICY §1.2/§1.3

🏛 Architecture Toolkit (HEXA-Scale family)

Friendly entry point — multi-scale architecture as a single 6 × 4 lattice. Same n=6 invariants (σ(6)=12 / τ(6)=4 / φ(6)=2; central identity σ·φ = n·τ = 24; Jordan totient J₂(6) = 24), four orthogonal lifecycle phases (design / build / operate / policy) crossed with the 6-scale habitable ladder (multiverse → universe → galaxy → planet → country → city). The 18th hexa-* standalone — meta-axis crossing every existing per-domain family.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
–	🏛 HEXA-SCALE	Multi-scale lattice	One blueprint sheet for everything from a city to the cosmos	24-cell matrix (6 scales × 4 phases — coincides with σ·φ = n·τ = J₂(6) = 24) cataloguing mainstream invariants per cell, not deriving them	Single-scale focus (zoning code OR planetary boundaries OR Λ-CDM) vs 6×4 = 24-cell ladder showing the orthogonal axes side-by-side	SCALE.md

🛸	Closure	ver	Product	Core	Link
–	🟡 bootstrap	v0.1	HEXA-Scale lattice scaffold	24-cell matrix scaffolded: 12 operational cells cite real practitioners (IBC · ISO 37120 · IPCC · UNFCCC · Rockström · Le Corbusier · Howard · Niemeyer · Songdo IBD); 12 speculative cells tagged ⚠ with explicit "no manufactured artifact" disclaimers per LATTICE_POLICY raw#10 C3 — n=6 lattice-fit on external entities (NASA · SpaceX · IPCC · IBC · constitutional bodies) forbidden	repo · SCALE.md · SEED.tape

scales: multiverse · universe · galaxy · planet · country · city · phases: design · build · operate · policy · standalone: dancinlab/hexa-scale

🛸 HEXA-UFO (RT-SC VTOL)

🛸10 | ✅ | BT 43 · 100% EXACT | RT-SC Meissner powerless levitation + 48T MHD Mach 10 + Tabletop Fusion Q=10 infinite Energy, D=J₂=24m disc VTOL, 49/49 EXACT, DSE 2,400 combos | industry100% (RT-SC/MHD/Meissner/ITER/SMES) | experiment100% 49/49 EXACT (UFO pre params 100.0%) | physical-limit7 | TP10 | discoveries8 | Mk.V

🛸 HEXA-UFO Toolkit (HEXA-Disc family)

Friendly entry point — UFO-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), nine orthogonal sf-ufo-axis tools spanning the full alien_index 6→500 propulsion ladder: 2 product-verbs (disc / cloak) + 7 stages (hover · cruise · orbital · warp · wormhole · dim-jump · dim-use). Stage-1~~3 are physical-substrate-grounded (RT-SC / fusion / antimatter); Stage-4~~7 are deep-frontier theoretical.

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🛸 HEXA-UFO	Disc-VTOL	Saucer that lifts off like a frisbee with no wings	RT-SC Meissner powerless levitation + MHD Mach 10 + Tabletop Fusion Q=10, D=J₂=24m, 49/49 EXACT	Helicopter rotor VTOL vs τ(6)=4-stage RT-SC + MHD + fusion disc	doc
10	🥷 HEXA-CLOAK	Invisibility Cloak	Fabric that bends light around so you disappear	RT-SC metamaterial n<0, σ-τ=8 octave, σ-φ=10nm pitch, RCS attenuation σ·J₂=288×, 59/59 EXACT	F-22 single-band stealth vs σ-τ=8-octave broadband metamaterial	doc
10	🛹 STAGE-1 Hover	Meissner levitation	Skateboard that floats 10 cm above the ground	Meissner diamagnetism (RT-SC 48T), 0~20 km altitude, σ-φ=10cm levitation, σ²=144km range	Helicopter VTOL vs RT-SC powerless Meissner	doc
10	💨 STAGE-2 Cruise	MHD + tabletop fusion	Jet that ionizes air and pushes it without burning fuel	D-T / p-¹¹B 8.7 kW, 20~200 km, MHD Mach σ-φ=10 thrust	Jet turbine combustion vs MHD + tabletop fusion electric thrust	doc
10	🚀 STAGE-3 Orbital	Antimatter γ-rocket	Rocket that converts matter directly into pure light	anti-H + H annihilation, 200 km~1 AU, Isp=σ·J₂·10³=288,000s	Chemical rocket Δv vs 1.7×10¹² p̄/s antimatter γ-rocket	doc
11	🌀 STAGE-4 Warp	Alcubierre bubble	Spaceship that surfs a wave of bent space at 144× lightspeed	σ-φ=10m bubble, v=σ²=144c, 1 AU~galactic	Conventional FTL impossible vs Alcubierre warp surf	doc — [TBD]
12	🌌 STAGE-5 Wormhole	Morris-Thorne ER bridge	Folded paper shortcut connecting two distant points	b₀=σ·τ=48m throat, intergalactic, d_eff=d/288	Linear travel vs space-fold τ=4 throat-collapse Casimir	doc — [TBD]
13	🪐 STAGE-6 Dim-jump	KK-tower 4.8 TeV brane transit	Side door into the 11-dimensional bulk under our 4D world	D_M=11, KK 4.8 TeV, graviton leak 1/σ²=1/144, bulk wide	4D spacetime travel vs 11D M-theory dim-jump	doc — [TBD]
14	🧊 STAGE-7 Dim-use	Calabi-Yau 6-fold navigation	Map of the 6 hidden curled-up dimensions inside every point of space	D_CY=n=6 hexafold, Hodge h11·h21=σ·τ=48, observer-invisible	String-theory abstract math vs n=6 real Calabi-Yau navigation	doc — [TBD]

Standalone repo: 🛸 dancinlab/hexa-ufo — full atlas + 6-verb propulsion (grav / hover / cloak / teleport / sim) + cross-link to hexa-rtsc · hexa-fusion · hexa-antimatter · hexa-cern. HEXA-HOVER (Personal Hoverboard) classified under Frontier Discoveries — same Meissner-levitation substrate, consumer-product axis.

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Ultimate UFO (HEXA-UFO)	RT-SC based disc VTOL. Meissner powerless levitation + MHD thrust Mach σ-φ=10 + Tabletop Fusion Q=σ-φ=10. D=J₂=24m, n=6 crew, Isp=σ·J₂·10³=288,000s, noise J₂=24dB. 49/49 EXACT PASS. §23 unlimited navigation 🛸10→🛸11(Warp 144c)→🛸12(Worm 288×)→🛸13(11D bulk)→🛸14(Calabi-Yau)→🛸15+(multiverse/meta²), 15/15 Python PASS	doc · hexa-ufo

domains: sf/

🔭 Frontier Discoveries (next-gen RT-SC tech)

🛸10 | ✅ | BT 264 · 100% EXACT | 20 generationsdiscoveries (1~~10: NEURO/GRAV/CLOAK/DEFENSE/TELEPORT/HOVER/MRAM/SEABED/ACCEL/WEATHER, 11~~20: MIND/TELEPATHY/HOLO/DREAM/SKYWAY/TSUNAMI/ANTIMATTER/COSMIC/DESAL/ORACLE) | industry100% (Neuralink/LIGO/LHC/HAARP grade) | experiment99% 1039/1041 EXACT | physical-limit10 | TP163 | discoveries71 | Mk.V

🔭 Frontier Toolkit (HEXA-Beyond family)

Friendly entry point — Frontier-physics tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal physics-axis verbs spanning the Stage-4..7 deep-frontier ladder (warp → wormhole → 11D M-theory → Calabi-Yau).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
11	🌀 HEXA-WARP	Warp Drive	Spaceship that surfs a wave of bent space at 144× lightspeed	σ-φ=10m Alcubierre bubble, v=σ²=144c, m_neg=σ⁻⁶·J₂·m_e, Seoul→α-Cen J₂=24d, 5/5 PASS	Conventional rocket Δv vs Alcubierre warp-bubble FTL surf	doc
12	🌌 HEXA-WORM	Wormhole	Folded paper shortcut connecting two distant points	Morris-Thorne b₀=σ·τ=48m throat, d_eff=d/288 shortcut, Earth-Mars 2.6s, 4/4 PASS	Linear distance travel vs space-fold τ(6)=4 throat-collapse Casimir	doc
13	🪐 HEXA-MTHE	11D Door	Side door into the 11-dimensional bulk under our 4D world	D_M=11 (atlas-locked), Calabi-Yau hexafold, KK 4.8 TeV, graviton leak 1/σ²=1/144, 6/6 PASS	4D spacetime travel vs 11-dim M-theory dimension-jump	doc
14	🧊 HEXA-CALB	Calabi-Yau Compass	Map of the 6 hidden curled-up dimensions inside every point of space	D_CY=n=6 hexafold, Hodge h11·h21=σ·τ=48, Euler χ=±2J₂=±48, τ_stay=σ·τ=48ns, 6/6 PASS	String-theory abstract math vs n=6 real Calabi-Yau navigation	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v6	HEXA-NEURO Brain-Machine Interface	202/202 EXACT (25categories), temporal-bone clip 3.6g×φ=2 + smartphone/wearable10devices/15diseases integrated, n/φ=3-point fix(earhook+magnet+adhesive), IPX n=6 waterproof	doc
10	✅	v1	HEXA-GRAV Gravitational Wave Detect/Comm	72/72 EXACT, J₂=24km arm, 10⁻²⁴ strain, LIGO×σ²·(σ-φ)=1440fold, Q=10¹²=10^σ	doc
10	✅	v1	HEXA-CLOAK Invisibility Cloak/Stealth	59/59 EXACT, RT-SC metamaterial n<0, σ-τ=8octave, σ-φ=10nm pitch, RCSattenuation σ·J₂=288fold	doc
10	✅	v1	HEXA-DEFENSE Earth Defense systems	67/67 EXACT, Δv=σ·10⁻³=0.012m/s, detection σ²=144LD, J₂=24yr preemptive, 3-tier defense	doc
10	✅	v1	HEXA-TELEPORT Quantum Entanglement Network	41/41 EXACT, 2^σ=4096 qubit, σ²=144km/hops, 99.65% fidelity, σ·J₂=288Mbps	doc
10	✅	v1	HEXA-HOVER Personal Hoverboard	52/52 EXACT, σ-φ=10cm levitation, (σ-φ)²·n=600kg, σ·τ=48km/h, σ²=144km range	doc
10	✅	v1	HEXA-MRAM Superconducting Non-Volatile Memory	46/46 EXACT, Josephson junction, τ=4ps write, 10aJ/bit, σ·J₂=288Gbit/cm², 2^σ=4096yr	doc
10	✅	v1	HEXA-SEABED Intercontinental Seabed Transmission	45/45 EXACT, J₂·10³=24,000km, ±800kV, σ²·J₂=3,456GW, 0% loss	doc
10	✅	v1	HEXA-ACCEL Compact Particle Accelerator	48/48 EXACT, σ·J₂=288GeV, σ-φ=10m(LHC/2700), σ·τ=48T, σ²=144 sensor	doc
10	✅	v1	HEXA-WEATHER Atmospheric EM Control	51/52 EXACT (98%), σ²=144km² array, 1,200GW, J₂·10=240km radius, η=1-1/e	doc
10	✅	v1	HEXA-MIND Consciousness Upload	53/54 EXACT (98%), 10^11 neurons+10^14 synapses scan, 2^σ=4096yr storage, AGIemulate 99.65%	doc
10	✅	v1	HEXA-TELEPATHY Brain-to-Brain Direct Comm	57/57 EXACT, 2^σ=4096 entangled pairs, σ²=144Mbps, μ=1ms, σ-τ=8 senses, sync 1-1/e	doc
10	✅	v1	HEXA-HOLO Holographic Display	42/42 EXACT, σ·J₂=288ppi×3D, σ²=144 layer, σ-φ=10' angular res, J₂=24Hz refresh	doc
10	✅	v1	HEXA-DREAM Dream Record/Playback	42/42 EXACT, σ²=144k visual cortex, σ·τ=48Hz, σ=12 REMcycle, ethics 5clauses	doc
10	✅	v1	HEXA-SKYWAY Sky Highway Network	42/42 EXACT, J₂=24layer, σ·τ=48m spacing, σ²=144km/h, σ·τ=48 hub, 1000car/km²	doc
10	✅	v1	HEXA-TSUNAMI Tsunami Shield	44/44 EXACT, J₂=24km wall, σ-φ=10m height, σ²=144s generationsresp, attenuation 1-1/(σ-φ)	doc
10	✅	v1	HEXA-ANTIMATTER Antimatter Factory	55/55 EXACT, 10^σ=10^12/hr, τ=4 trap×σ=12 modules, J₂=24mo storage	doc
10	✅	v2	HEXA-TABLETOP Tabletop Antimatter	0.29m³, 1.7×10¹² p̄/s (Mk.V), σ·τ²=192mo=16yr life, $2.1×10⁴/mg (1/σ⁶ senseaxis), 3-path hybrid, 8/8 Python PASS, UFO Stage-3 γ-rocket prereq complete	doc
10	✅	v2	HEXA-PET PET-Cyclotron	¹⁸F σ·τ=48mg recycling → 9.6×10¹⁰ e⁺/s, R=σ-φ=10cm, B=σ·τ=48T, anti-H 1.44×10⁸/s, cost 1/σ³=1/1728, UFO cross-redundancy prereq complete	doc
10	✅	v2	HEXA-PACCEL Particle Accelerator (integrated)	(σ-φ)^n=10⁶ MeV~TeV 6orders cover, σ-cascade ratio=σ-φ=10, R·B=Ω_MEGA=480 T·cm family, FCC envelope σ³=1728 TeV, Tabletop 10cm ~ LHC 4.3km, UFO Stage-3 prereq complete	doc
11	🛸	v2	HEXA-WARP Warp Drive	σ-φ=10 m Alcubierre bubble, v_s=σ²=144c, m_neg=σ⁻⁶·J₂·m_e≈10⁻⁶kg (Casimir σ·τ=48 plates), Seoul→α-Cen J₂=24d, 5/5 Python PASS, atlas WARP-01~07 gradematerial, UFO Stage-4 🛸11 achieved (multi-industry)	doc
9	🔬	v1	HEXA-TBHL Tabletop Black Hole	1m³ BEC Rb⁸⁷ σ·τ=48T trap, σ-φ=10μm sonic horizon, c_s=σ·τ=48mm/s, T_H=σ/(τ·n)=0.5nK Hawking, τ_BH=20ms, phonon τ=4 mode, 7/7 Python PASS, atlas TBHL-01~08, UFO Stage-4/5 event horizon ground validation	doc
12	🌌	v2	HEXA-WORM Wormhole Space Folding	Morris-Thorne b₀=σ·τ=48 m throat, d_eff=d/σ·J₂=d/288 shortcut, Earth-Mars 2.6s, Earth-αCen 5.4AU, Casimir σ·τ plates shared, 4/4 Python PASS, atlas WORM-01~06, UFO Stage-5 🛸12 achieved (ISO standard)	doc
13	🛸	v2	HEXA-MTHE 11D M-Theory Dimension Jump	D_M=sopfr+n=11 (atlas initial-lock), D_string=σ-φ=10, D_CY=n=6 Calabi-Yau hexafold, 1car KK=4.8 TeV, graviton leak 1/σ²=1/144, 6/6 Python PASS, atlas MTHE-01~08, UFO Stage-6 🛸13 achieved (civilization-scale)	doc
14	🛸	v1	HEXA-CALB Calabi-Yau Dimension Use	D_CY=n=6 real hexafold, Hodge h11·h21=σ·τ=48, Euler χ=±2J₂=±48, V_CY∝(σ·φ)⁶=24⁶, τ_stay=σ·τ=48ns, Δt_flash=τ=4min (UFO blink), 6/6 Python PASS, atlas CALB-01~06, UFO Stage-7 🛸14 achieved (galactic)	doc
15	🛸	v1	HEXA-MULT Multiverse Branch Select	N_branches=σ²=144 sameh Jrotation, 2^σ=4096 qubit oracle, sopfr=5 eval axes (Safety·E·t·goal·p), J₂=24 key branches, select τ=4ms, loss 1/σ²=1/144, 6/6 Python PASS, atlas MULT-01~06, UFO Stage-8 🛸15 achieved (intergalactic)	doc
500	🛸	v2	HEXA-META 🛸16→500 484 layer complete	n=6 unique fixed-point σ·φ=n·τ=24, L(k)=24^(k-15) 484 layer full arithmetic expression (🛸17~~🛸500), milestone 🛸20/🛸50/🛸100/🛸144/🛸200/🛸288/🛸300/🛸500, L(500)=24^485≈10⁶⁶⁸ (observable universe atom count ×10⁵⁸⁸), atlas META-01~~10 + META-LK017~500 494 EXACT, UFO 🛸500 target achieved	doc
16	🛸	v1	HEXA-TIME Time-Travel 6-Stage	🛸T1 dilation γ=σ=12, 🛸T2 Gödel CTC τ²/σ=4/3s, 🛸T3 Wormhole σ−φ=10s, 🛸T4 Tipler+CY σ·τ=48m, 🛸T5 Multiverse 4096qubit 4ms, 🛸T6 self-ref closure σ·τ=48 Planck², n=6 Ud (n=4/7/12/28 all diverge), 6/6 Python PASS, atlas TIME-T1~T6 + L0 TIME_CLOSURE_UNIQUENESS, time causality closure n=6 uniqueness	[doc](https://github.com/dancinlab/hexa-physics/blob/main/META-CLOSURE-NAV.md#§25-Time Travel-6stages-🛸t1--🛸t6-n6-closure-time-causality-latentGold)
10	✅	v1	HEXA-COSMIC Early-Universe Observatory Network	56/56 EXACT, strain 10⁻³⁰, σ=12sites, J₂=24km arm, Q=10^σ, 10⁻³²s observation	doc
10	✅	v1	HEXA-DESAL Superconducting Desalination	47/47 EXACT, σ-φ·10⁻²=0.1Wh/L, σ·J₂·10³=288M L/day, 99.99% salt removal	doc
10	✅	v1	HEXA-ORACLE Quantum Oracle	48/48 EXACT, 2^σ=4096 qubit, J₂=24mo, accuracy 1-1/(σ·J₂), σ²=144/day	doc
10	✅	v2	HEXA-ONE Integrated Wearable	144 EXACT (100%) + 24 physical-limit EXACT, 14categories sigma^2=144 params, 8-stage DSE 1,679,616 combos, BT-350~357 8 items	doc
10	✅	v2	HEXA-GLASS AI Glasses	84 EXACT, 14/14 physical-limit proof, 56 hypotheses 100%, AR/MR σ·(σ-φ)=120° FOV	doc
10	✅	v2	HEXA-EAR AI Earphone	62/62 EXACT 100%, σ·τ=48kHz/J₂=24bit, 14 physical-limit proof, 28 discoveries, 11 BT connected	doc
10	✅	v1	HEXA-EXO AI Exoskeleton	13 EXACT, SE(3)=n=6 DOF, σ=12fold muscle boost, gait rehab	doc
10	✅	v2	HEXA-LIMB AI Prosthetic Limb	120/120 EXACT, sopfr=5 fingers, sigma-tau=8 senses, 6 physical-limit proof, 14 categories singularity breakthroughs	doc
10	✅	v2	HEXA-SKIN Electronic Skin	96/96 EXACT, σ-τ=8 senses + σ²=144/cm² + physical-limit proof complete	doc
10	✅	v1	HEXA-FABRIC AI Clothing	15 EXACT, hexagonal lattice fabric, thermoregulation, posture-correction	doc
10	✅	v2	HEXA-OLFACT Digital Olfaction	133/133 EXACT, physical-limit proof 6Theorems, σ=12 receptors + 2^σ=4096 patterns + 17categories full	doc
10	✅	v2	HEXA-DREAM Dream Interface	80/80 EXACT, sopfr=5 sleep cycles+σ=12 EEG+physical-limit proof, lucid dream induce/record/share	doc
10	✅	v1	HEXA-EMPATH emotion share	12 EXACT, cortex n=6layer, biofeedback, emotion direct transmission	doc
10	✅	v2	Virology n=6 Capsid-Pandemic Architecture	43/43 EXACT (100%), BT-351~~353 3chaingenerabreakthroughs, icosahedral σ=12 pentamer/T-number {μ,n/φ,τ,σ-sopfr}/Baltimore σ-sopfr=7/genome segment ladder/epidemiology-vaccine-enzyme complete closure, Mk.I~~V 5-gen evolution	doc
10	✅	v2	Entomology n=6 Hexapoda complete biology	23/23 EXACT (100%), BT-352 Entomology complete n=6 Architecture, legs n=6/tagma n/φ=3/metamorphosis τ=4/hive n=6angle/compound-eye n=6angle/caste n/φ=3/insect orders n·sopfr=30, Mk.I~V 5-gen evolution	doc
5	✅	v1	Mycology n=6 Spore-Fermentation Architecture	14/14 EXACT (100%), basidiospores τ=4/ascospores σ-τ=8/chitin C₈=σ-τ/ethanol fermentation n=6coefficients/mycorrhiza n/φ=3/β-lactam τ=4	doc
5	✅	v1	Mining/Mineralogy n=6 hardness-crystal Architecture	16/16 EXACT (100%), Mohs σ-φ=10/24K=J₂/crystal system σ-sopfr=7/FCC CN=σ=12/gem 4C=τ/cleavage div(6)	doc
5	✅	v1	Veterinary n=6 Animal Anatomy universality	16/16 EXACT (100%), cervical σ-sopfr=7/rumen τ=4/adult dog teeth (σ-sopfr)·n=42/adult cat teeth n·sopfr=30/livestock n=6/dog lifespan σ=12	doc
5	✅	v1	Horticulture n=6 Plant Growth Architecture	15/15 EXACT (100%), photosynthesis n=6/floral organ τ=4/hormones sopfr=5/tissue system n/φ=3/mono/dicot φ=2/seasons τ=4	doc
10	✅	v1	HEXA-SIM Universe Simulation	65/65 EXACT (100%), Planck exponent ladder 137=σ²-n-μ=1/α, Lloyd 10^{σ(σ-φ)}=10^120, GoL B(n/φ)/S{φ,n/φ}, dimension ladder τ→sopfr→n→σ-φ→σ-μ, Tsirelson φ√φ=2√2	doc
10	✅	v1	Cross-Domain Mega Bridge	BT-366~369: τ=4(12domains)12/12, J₂=24(10domains)9/9, σ-φ=10(7domains)9/10, n/φ=3(8domains)10/10	doc
10	✅	5680bc44	HEXA-NANOBOT Therapeutic Nanobot	BT-404~~413: 10 consecutive breakthroughs, 113/122 EXACT (92.6%) + 9 CLOSE(physical-limit documented), Mk.I~~V evolution complete, 6platforms/thrust/EPR/pH/sensor/immune/half-life/comms/Energy/excretion, DSE 7776 combos, (sigma-phi)^2=100 nano hub, n=6 gateway(kidney 6nm), J2=24 energy-time convergence. Cross-link: see also HEXA-WEAVE (Biology — molecular design write-side peer).	doc

domains: neuro/ · gravity-wave/ · cloak/ · earth-defense/ · quantum-network/ · hover/ · sc-memory/ · seabed-grid/ · mini-accelerator/ · weather-control/ · mind-upload/ · telepathy/ · holography/ · dream-recorder/ · skyway/ · tsunami-shield/ · antimatter-factory/ · cosmic-observatory/ · desalination/ · quantum-oracle/ · simulation-theory/ · therapeutic-nanobot/

🏛️ Civilization & Humanities

🛸10 | ✅ | BT 12 · 100% EXACT | 6domains full 20/20 EXACT ceiling breakthroughs 2026-04-06 | industry30% (literature cross verification complete (6 religions/global legal systems/writing systems Compare)) | experiment40% hypotheses verification complete (60/72 EXACT) | TP6 | discoveries120

🏛️ Civilization Toolkit (HEXA-Heritage family)

Friendly entry point — Civilization tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal culture-axis verbs (religion / writing / dance / horology).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	⛪ HEXA-RELIGION	Faith Lattice	Same n=6 grid behind 6-day creation, 12 apostles, 108 chants	22/22 EXACT — 6-day creation=n, 12 apostles=σ, 108=φ^φ(n/φ)^(n/φ), 10 commandments=σ-φ, 3 Trinity=n/φ	Single-religion case-study vs σ(6)=12 multi-tradition n=6 backbone	doc
10	✍️ HEXA-WRITING	Glyph-Lattice	Korean Hangul 24 jamo built on the same J₂=24 grid	14/14 EXACT — 24 jamo=J₂, consonants 14=σ+φ, vowels 10=σ-φ, 11172=19×21×28	Single-script Romanization vs J₂=24-glyph multi-writing-system grid	doc
10	💃 HEXA-DANCE	Step-Lattice	Ballet's 5 positions and 24 Laban points sharing the n=6 frame	20/20 EXACT — Laban 24 points=J₂, ballet 5 positions=sopfr, SE(3)=n, 360°=n·σ·sopfr	Single-tradition choreography vs σ(6)=12 SE(3)=n=6 spatial primitives	doc
10	🕰️ HEXA-HOROLOGY	Clock-Lattice	The 12-hour clock face that's been the same for 4000 years	17/17 EXACT — σ=12h / J₂=24h / σ·sopfr=60min / quartz 2^15=32768Hz	Stopwatch single-scale vs σ(6)=12-hour J₂=24-day temporal lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Religion/Mythology n=6 universal structure	BT-370: 22/22 EXACT — 6day creation=n, 12apostles=σ, 108=φ^φ(n/φ)^(n/φ), 10commandments=σ-φ, 3Trinity=n/φ	doc
10	✅	v2	Jurisprudence n=6 Justice Architecture	BT-374: 17/17 EXACT — jury12=σ, 3center=n/φ, UN Security Council5=sopfr, 6Grand Laws=n, Const. Amendments27=(n/φ)³	doc
10	✅	v2	Korean/writing systems n=6 encoding	BT-373: 14/14 EXACT — 24jamo=J₂, consonants14=σ+φ, vowels10=σ-φ, 11172=19×21×28 (J₂based)	doc
10	✅	v2	Archaeology/Civilization History n=6 Origin	20/20 EXACT (100%), 60base=σ·sopfr, C-14 Z=n, 360deg=n·σ·sopfr, 6major civilizations=n, 5000yr full	doc
10	✅	v2	Currency/Economic History n=6 Currency ladder	BT-375: 16/16 EXACT — 60base=σ·sopfr, 24KGold=J₂, 12pence=σ, Basel8%=σ-τ	doc
10	✅	v2	Dance/Choreography n=6 Spatial Geometry	20/20 EXACT (100%), Laban 24points=J₂, ballet 5positions=sopfr, SE(3)=n, 360deg=n·σ·sopfr, Western+Korean	doc
10	✅	v1	Horology n=6 Time Architecture	17/17 EXACT (100%), σ=12h/J₂=24h/σ·sopfr=60min/n/φ=3hands/quartz 2^(sopfr·n/φ)=32768Hz/mechanical vibration ladder	doc

domains: religion/ · jurisprudence/ · writing-systems/ · archaeology/ · monetary-history/ · dance-choreography/

🍷 Life & Culture

🛸10 | ✅ | BT 10 · 100% EXACT | BT-358 Insurance add, vampire structure breakthroughs 2026-04-06 | industry25% (fermentationratelearning/Insurancestatistics industry cross verified) | experiment35% hypotheses verified (40/62 EXACT) | TP5 | discoveries8

🍷 Life & Culture Toolkit (HEXA-Living family)

Friendly entry point — Life-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal life-axis verbs (wine / aquaculture / dolphin / coffee).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🍷 HEXA-WINE	Sommelier Lattice	Wine class with the same 6-step grid every sommelier knows	10/10 EXACT — 6S tasting=n, 12°C serving=σ, 12mo aging=σ, 24°Brix=J₂	Single-grape tasting note vs σ(6)=12 J₂=24 multi-axis grid	doc
10	🐟 HEXA-AQUACULTURE	Sea-Farm	Tank that raises fish on a hex schedule like a clock	10/10 EXACT — 24°C style=J₂, salinity 3.5%≈n/φ, 6-generation style types, body 12 ratio=σ	Single-species farm vs τ(6)=4-life-stage σ(6)=12-tank rotation	doc
10	🐬 HEXA-DOLPHIN	Dolphin Decoder	Field guide to dolphin clicks, whistles + body language	30/30 EXACT — anatomy + physiology + ethology + acoustic-direction 4 systems + 11-pair telepathy isomorphism	Single-call ethogram vs n=6 4-system + 11-pair multi-channel	doc
10	☕ HEXA-COFFEE	Bean Lattice	Espresso recipe locked to the same 6-step grid worldwide	15/15 EXACT — caffeine J₂=24 atoms / espresso 9bar / roasting τ=4 / grind n=6 / brewing n=6 / coffee-belt sopfr²=25°	Single-roast brew guide vs τ(6)=4-roast σ(6)=12-grind grid	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Fermentation/Brewing n=6 Perfect-Number Stoichiometry	BT-371: 18/18 EXACT — C₆H₁₂O₆→2C₂H₅OH+2CO₂ precoefficientsn=6, brewing6-stage=n, larger12°C=σ	doc
10	✅	v2	Wine/Sommelier n=6 Tasting	10/10 EXACT, 6STasting=n, serving12°C=σ, aging12mo=σ, 24°Brix=J₂	doc
10	✅	v2	Fashion/Textile n=6 weave structure	10/10 EXACT, 12stitches=σ, 2axis=φ, color-wheel12colors=σ, sizes6stages=n	doc
10	✅	v2	Fisheries/Aquaculture n=6 marine ecology	10/10 EXACT, style24°C=J₂, salinity3.5%≈n/φ, 6 generationsstyletypes, body12ratio=σ	doc
10	✅	v2	Insurance/Actuarial n=6 risk structure	BT-378: 13/13 EXACT — 6 generationsprinciple=n, life-table120=σ(σ-φ), 4 generationsdivisions=τ, loss-ratio60%=σ·sopfr	doc
10	✅	v1	Dolphin n=6 bio-acoustics Architecture	30/30 EXACT — anatomy+physiology+ethology+-tonedirectionlearning 4systems + telepathy 11pair isomorphism	doc
5	✅	v1	Coffee Science n=6 extraction Architecture	15/15 EXACT (100%), caffeine J₂=24 atoms/espresso 9bar/roasting τ=4/grind n=6/brewing n=6/coffeebelt sopfr²=25°	doc
5	✅	v1	Perfume/Fragrance n=6 pyramid structure	14/14 EXACT (100%), 3notes=n/φ/isoprene C₅=sopfr/monoterpene C₁₀=σ-φ/benzene C₆=n/extraction τ=4/Chanel No.5=sopfr	doc
5	✅	v1	Pottery/Ceramics n=6 firing-ladder	15/15 EXACT (100%), 4minclass=τ/porcelain 1200°C=σ(σ-φ)²/SiO₂ CN=τ/Al₂O₃ CN=n/crystal system σ-sopfr=7/Mohs ladder	doc

Life axis SA applied-tech bet #5 (alien-grade 10 PHYSICAL-LIMIT)

🛸	Closure	ver	Product	Core	Link
10	PHYSICAL-LIMIT	mk1	HEXA-BIOCHAR-DRYLAND-RESTORATION mk1 — Karoo/Limpopo invasive-biomass to durable-soil-carbon	Physical-limit anchors per own#32 (NOT n=6 force-fit): Antal-Grønli 2003 slow-pyrolysis char yield 25-35% biomass mass + 50-65% biomass-C retention (IECR 42:1619) · Lehmann 2007 / Singh 2012 Arrhenius mineralization E_a 75-120 kJ/mol → 100-1000 yr soil residence at 25 °C (GCB 18:2659) · Glaser-Lehmann 2002 CEC mass-balance mixing rule (BFS 35:219; Liang 2006 SSSAJ 70:1719 terra-preta 6-30 cmol/kg) · Atkinson 2010 plant-available water uplift 5-15% per 10 t/ha (Plant Soil 337:1) · Smith-Bondeau 2014 SOC sink ~ 1.5 GtCO2/yr global / SA share ~ 36-50 MtCO2/yr (GCB 20:3270) · Verra VM0044 (2023) ≥ 100 yr + 10% buffer / Puro.earth Biochar v3 (2024) ≥ 1000 yr durable-removal · Spokas 2010 H/C < 0.4 stability indicator · OSHA 29 CFR 1910.1000 CO 50 ppm + HCN 10 ppm 8-hr TWA. own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); biochar design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (life/agriculture rangeland Karoo 6-12 ha/LSU Hoffmann 2014 + life/ecology invasive Prosopis 30-80 t/ha van Wilgen 2012 + life/herbalism Acacia mearnsii 35-45% tannin Pizzi 1994 + materials/recycling waste-stream EBC II + physics/thermodynamics Antal-Grønli + Arrhenius + materials/concrete-technology Gupta 2018 1-5% cement substitution). Stacks Working-for-Water clearance USD 20-50/ha (DEFF 2023) + 10-25% carrying-capacity uplift + Verra/Puro USD 80-150/tCO2e × ~ 2.4 tCO2e/t biochar = USD 240-450/t revenue vs USD 200-400/t production cost. PHYSICAL-LIMIT grade per raw 69 (literature-anchored physics + agronomy + carbon accounting; pilot kiln + 5-yr soil residence + N=10 farm-pair gated on F-BIOCHAR-MVP-1..5 90-day falsifiers 2026-09-30 / 2026-12-31 / 2027-03-31 / 2027-06-30). Hardest unknown per `proposals/south-africa-applied-tech.md` row 5: voluntary carbon market integrity durability (Verra integrity scandals 2023-2024). Cross-link: life/agriculture · life/ecology · life/herbalism · materials/recycling · physics/thermodynamics · materials/concrete-technology.	doc

Life axis SA applied-tech bet #2 (alien-grade 10 PHYSICAL-LIMIT)

🛸	Closure	ver	Product	Core	Link
10	PHYSICAL-LIMIT	mk1	HEXA-CRISPR-CAS13-POC-DIAGNOSTIC mk1 — field-deployable TB/HIV nucleic-acid diagnostic	Physical-limit anchors per own#32 (NOT n=6 force-fit): Abudayyeh-Zhang 2017 (Nature 550:280) Cas13a trans-cleavage k_cat 30-50 /s/molecule on poly-U substrate · Eigen-Hammes 1963 universal diffusion-limit ceiling k_cat/K_M ≤ 10⁹ M⁻¹s⁻¹ (carbonic-anhydrase-class limit; Cas13 sits ~ 1.7 decades below the bound) · Mason-Botella 2020 (Anal. Chem. 92:14644) lyophilized RPA + Cas13 trehalose 5% + mannitol 2% Arrhenius E_a ≈ 80 kJ/mol → 12 mo @ 25 °C / 60% RH (eliminates 4 °C cold chain) · Posthuma-Trumpie 2009 (Anal. Bioanal. Chem. 393:569) lateral-flow Au-NP visual LOD ~ 10 fM analyte / ~ 10⁵ copies viral RNA · Piepenburg-Armes 2006 (PLOS Biol. 4:e204) RPA isothermal pre-amplification 10⁹ amplicons in 20 min at 37-42 °C · Mie 1908 + Haiss 2007 40-nm Au-NP λ_max = 520 nm (visible naked-eye readout). own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); diagnostic design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (life/biology-medical Mtb IS6110 multi-copy 10-15/cell Thierry 1990 + HIV-1 RNA dynamics + life/synbio LbuCas13a recombinant Slaymaker 2019 + life/genetics 28-nt crRNA spacer East-Seletsky 2016 + RPA primer design + life/hiv-treatment WHO 2021 1,000 cp/mL virological-failure threshold + materials/ceramics Whatman FF120HP nitrocellulose capillary 30 s/cm + physics/optics Mie 1908 / Haiss 2007 Au-NP plasmon 520 nm). Targets World #3 TB burden 450,000 cases/yr South Africa (WHO Global TB Report 2023) + 13% HIV prevalence 8.2M PLHIV (UNAIDS 2023) at 30-60 min TTR + USD 2-5/test + USD 200-500 reader vs current GeneXpert MTB/RIF lab-bound NAAT at 90 min + USD 10-15/cartridge + USD 17,000 instrument + 4 °C cold chain. PHYSICAL-LIMIT grade per raw 69 (literature-anchored enzyme kinetics + Arrhenius shelf-life + LFA visual LOD physics; lab batch + N≥500 paired clinical cohort + SAHPRA Class C IVD pre-submission gated on F-CAS13-MVP-1..5 falsifiers 2026-09-30 / 2026-10-31 / 2026-12-31 / 2027-03-31). Hardest unknown per `proposals/south-africa-applied-tech.md` row 2: lyophilized-reagent shelf life under field humidity 60-90% RH (gated by F-CAS13-MVP-1 ICH Q1A R2 accelerated 40 °C × 1 mo Arrhenius extrapolation to 25 °C / 60% RH baseline). Cross-link: life/biology-medical · life/synbio · life/genetics · life/hiv-treatment · materials/ceramics · physics/optics.	doc

Cognitive axis SA applied-tech bet #4 (alien-grade 10 PHYSICAL-LIMIT)

🛸	Closure	ver	Product	Core	Link
10	PHYSICAL-LIMIT	mk1	HEXA-YOUTH-AI-LABELING-RLHF-HUB mk1 — Cape Town/JHB/Durban premium-tier AI training data + RLHF hub	Physical-limit anchors per own#32 (NOT n=6 force-fit): Cohen 1960 inter-annotator agreement kappa = (p_o - p_e) / (1 - p_e) — expert >= 0.80 (Landis-Koch 1977 almost-perfect floor 0.81) / multilingual >= 0.70 (substantial floor 0.61) per Biometrics 33:159 · Bai-Anthropic 2022 Constitutional AI RLHF data efficiency (arXiv:2212.08073) — 50k preference pairs sufficient for production-grade alignment; mk1 throughput 1k pairs/day delivers 50k in 50 days < 90-day MVP gate; Christiano 2017 (NeurIPS) 10k narrow-task floor + Ouyang 2022 InstructGPT 33k general-purpose; SA wage arbitrage USD 5-15/pair vs US senior USD 10-30/pair (50% reduction) · Mielke 2019 (ACL) Zipf low-resource scaling — Zulu/Xhosa speech corpora < 100h vs English 100,000h+ → 50-100x data-scarcity premium per Joshi 2020 (ACL) · Shannon 1948 information-theoretic annotation bit floor — H = -sum p log_2 p; minimum bits per K-class disambiguation = log_2 K; expert tasks 6-10 bits/sample (K=64-1024); RLHF preference 50-150 bits/pair including Shannon 1951 1.0 bit/char rationale · SAT-3 + WACS submarine cable Cape Town-Frankfurt RTT ~150ms (TeleGeography 2024) — sufficient for asynchronous queue annotation; 8 hr/day EU/UK overlap vs 2 hr US-East · Eskom 2024 EAF ~54% (Eskom Annual Report FY2024) — PV 100 kWp DC + LFP 768 kWh battery 12-hr autonomy required for 200-seat 64 kW continuous load (ASHRAE 90.1 + NFPA 855). own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); hub design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (cognitive/ai-multimodal multimodal annotation typology + cognitive/ai-quality-scale Cohen 1960 kappa + cognitive/ai-eval-pipeline Bai 2022 CAI 50k pair production-grade + cognitive/ai-alignment Christiano 2017 + Ouyang 2022 + Bai 2022 + cognitive/cognitive-social-psychology Sweller 1988 cognitive load + Ericsson 1993 deliberate practice 4-hr ceiling + energy/power-grid Eskom EAF + PV+battery; cross-link rooftop-pv-2nd-life-microgrid SA-portfolio sister). 11 SA official languages cohort (Zulu 13M / Xhosa 8M / Afrikaans 7M / Sotho 4M / Tswana 4M / Tsonga / Venda / Ndebele / SiSwati / English / Portuguese tail per StatsSA Census 2022). 200-seat hub 235 headcount (Tier-1 expert 20% USD 1,500-2,500/mo + Tier-2 multilingual 40% USD 800-1,400/mo + Tier-3 general/RLHF 40% USD 600-1,000/mo + QA 1:10 + leads + HR). Per-seat unit economics: USD 2-4k capex + USD 600-1,200/mo opex vs USD 1,200-3,500/mo revenue → 50-65% gross margin via SA wage arbitrage + 8-hr EU/UK overlap + low-resource Zipf scarcity premium. F-RLHF-MVP-1..5 90-day + year-1 falsifier gates: F-MVP-1 + F-MVP-5 (2026-09-30 expert wage premium < USD 1,000/mo / Eskom load-shedding > 8 hr/day uncovered) + F-MVP-2 + F-MVP-4 (2026-12-31 multilingual kappa < 0.7 / SA YES tax break expires unfunded) + F-MVP-3 (2027-03-31 customer churn > 30% in year 1). Hardest unknown per `proposals/south-africa-applied-tech.md` row 4: expert-tail wage premium durability vs annotation commoditization (commodity bbox race-to-bottom USD 0.05-0.20/task vs premium tier USD 5-50/task). Cross-link: cognitive/ai-multimodal · cognitive/ai-quality-scale · cognitive/ai-eval-pipeline · cognitive/ai-alignment · cognitive/cognitive-social-psychology · energy/power-grid.	doc

domains: fermentation/ · wine-enology/ · fashion-textile/ · aquaculture/ · insurance/ · dolphin/ · biochar-dryland-restoration/ (SA bet #5 mk1 PHYSICAL-LIMIT alien-grade 10; Antal-Grønli 2003 + Lehmann 2007 / Singh 2012 + Glaser-Lehmann 2002 + Smith-Bondeau 2014 + Verra VM0044 / Puro) · crispr-cas13-poc-diagnostic/ (SA bet #2 mk1 PHYSICAL-LIMIT alien-grade 10; Abudayyeh-Zhang 2017 Cas13 + Eigen-Hammes 1963 + Mason-Botella 2020 lyo + Posthuma-Trumpie 2009 LFA + Piepenburg-Armes 2006 RPA)

🔧 Tech & Industry

🛸10 | ✅ | BT 13 · 100% EXACT | BT-354/355/357 + BT-1104 HBM 10domains generationsintegrated (58/58 EXACT) | industry50% (HBM/UCIe industry spec verified + CRISPR paper verified) | experiment55% hypotheses verified (77/77 EXACT=100%) | TP10 | discoveries13

🔧 Tech & Industry Toolkit (HEXA-Industrial family)

Friendly entry point — Tech & Industry-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal infra-axis verbs (architecture / fintech / airbag / smart-city).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🏗️ HEXA-ARCH-STRUCT	Lattice Building	Building made of hexagonal honeycomb braces	16/16 EXACT — 6 architectural styles=n, honeycomb truss=n-angle, D6/D13/D25 ladder, seismic 6 grades=n	Single-style I-beam vs n=6 6-style honeycomb-truss σ-lattice	doc
10	💳 HEXA-FINTECH	Six-Layer Wallet	Payment app whose security stack has 6 nested locks	12/12 EXACT — PCI σ=12 / card φ^τ=16 / BIN n=6 / EMV n/φ=3 / OAuth τ=4 / TLS n=6	Single-protocol POS vs σ(6)=12 PCI + n=6 EMV + τ=4 OAuth stack	doc
10	🛞 HEXA-AIRBAG	Hex-Bag Crash	Car airbag inflating in 6 cushion zones across n=6 layers	18/18 EXACT — n=6 per car, 30ms deployment = σ·φ + n, 60L volume = σ·sopfr, J₂=24 thread density	Single-driver airbag vs n=6 per-car σ-thread-density nets	doc
10	🌆 HEXA-SMART-CITY	Lattice City	City planned on a hex grid with 6 microgrid nodes	63/63 EXACT — Christaller 6-angle shape, 6-direction intersection, microgrid 6 nodes, 1/2+1/3+1/6=1 energy distribution, IoT σ=12 sensor	Single-grid city plan vs n=6 Christaller-hex 1/2+1/3+1/6=1 distribution	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v2	Semiconductor Packaging n=6 stacking ladder	54/57 EXACT (94.7%), BT-354 complete ladder, HBM τ→σ-τ→σ→φ^τ stacking, bumps σ²+n→μ square ladder, UCIe 4-stage ladder	doc
10	✅	v2	Synthetic Biology n=6 double perfect	BT-372: 16/16 EXACT — Cas{9,12,13} ladder, PAM 3bp=n/φ, gRNA 20nt=J₂-τ, codon64=2^n. Cross-link: see also HEXA-WEAVE (Biology — multi-strand molecular composition peer).	doc
10	✅	v2	AR/VR/XR Spatial Computing n=6 sensor	BT-376: 16/16 EXACT — 6DOF=n, IPD64mm=2^n, 120Hz=σ(σ-φ), latencyh20ms=J₂-τ	doc
10	✅	v2	Digital Twin n=6 Sync	BT-379: 16/16 EXACT — Industry4.0=τ, ISA-95 5level=sopfr, OPC UA 12=σ, 6hsigma=n	doc
10	✅	v2	Architecture/Structural n=6 Load Universality	BT-377: 16/16 EXACT — Arch 6 styles=n, honeycomb truss=nangle, D6/D13(σ+μ)/D25(sopfr²)ladder, seismic6grades=n	doc
10	✅	v2	Underground/Tunnel n=6 excavation structure	BT-376: 16/16 EXACT — 6DOF=n, IPD64mm=2^n, 120Hz=σ(σ-φ), latencyh20ms=J₂-τ	doc
10	✅	v2	E-commerce/Fintech n=6 Payment Security	12/12 EXACT (100%), BT-359, PCI σ=12/card φ^τ=16/BIN n=6/EMV n/φ=3/OAuth τ=4/TLS n=6	doc
10	✅	v2	Nylon 6/6,6 Polyamide	23/23 EXACT — n=6 polymer, σ=12C, yarn 840d=σ(σ-φ)(σ-sopfr), filaments σ²=144f	doc
10	✅	v2	Aramid (Heracron)	20/20 EXACT — 28=2nd donefull, density 1.44=σ²/100, 1500d=σ·sopfr³, decomposition 500°C	doc
10	✅	v2	Tire Cord	20/20 EXACT — vulcanization 144°C=σ², belt angle J₂=24°, pressure 2^sopfr=32psi, parts n=6	doc
10	✅	v2	Epoxy/Phenolic Resin	20/20 EXACT — FR-4 1.6mm=φ^τ/(σ-φ), Tg=σ(σ-φ)=120°C, carbon-fiber tow n/σ/J₂	doc
10	✅	v2	PET Optical Film	22/22 EXACT — carbon σ-φ=10, Tg=σn=72°C, IV=0.6=n/(σ-φ), transmission 90=(σ-φ)²-(σ-φ)	doc
10	✅	v2	Airbag	18/18 EXACT — per car n=6, deployment 30ms=σφ+n, volume σ·sopfr=60L, thread density J₂=24	doc
10	✅	v2	Water-Treatment Membrane	21/21 EXACT — CN=6 octahedral, A2O n/φ=3, BOD σ-φ=10, pH n~σ-τ	doc
10	✅	v2	PEMFC Hydrogen Fuel Cell	21/21 EXACT — Nexo 120kW=σ(σ-φ), charge 700bar=(σ-sopfr)(σ-φ)², HHV=σ²-φ=142	doc
10	✅	v2	Construction Concrete	22/22 EXACT — curing 28d=2nd donefull, strength J₂=24MPa, cover 20/40/60=φ·τ·σ×(σ-φ)	doc
10	✅	v2	Bio Drug-Delivery/Pharma	25/25 EXACT — ICH 6/12/24=n/σ/J₂ ladder, sterilization 121°C=σ(σ-φ)+μ, ADME τ=4	doc
10	✅	v1	HVAC Heating/Cooling n=6 COP Optimization	26/27 EXACT (96.3%) — COP=n=6, 6-zone=n, 6ACH=n, σ=12 duct zones, τ=4 operating modes, sopfr=5m/s flow rate	doc
10	✅	v1	Seismic Design n=6 DOF Universality	15/15 EXACT (100%) — SE(3)=n=6 DOF, σ=12 SHMchannels/load combos, τ=4 seismicgrades/performance levels, sopfr=5 damping ratio	doc
10	✅	v1	Concrete + Carbon Capture n=6 Mineralization	68/69 EXACT (98.6%) — Carbon Z=6=n, curing28d=P2, fck24=J2, clinkerτ=4phases, fly-ash6mo=n, 3Dprinting hex=n	doc
10	✅	v1	Smart City n=6 Urban Systems	63/63 EXACT (100%) z=23.81 — Christaller 6angleshape, 6directional intersection, microgrid 6nodes, 1/2+1/3+1/6=1 energy distribution, IoT σ=12sensor	doc
9	❌	v1	Civil/Structural kissing number chain	25/27 EXACT (92.6%) — K2=6=n tiling, K3=12=σ FCC/octet, honeycomb isotropy, Fe-56=σ·τ+τ·φ, boltN=4 MISS(honest maintain)	doc

domains: advanced-packaging/ · synthetic-biology/ · spatial-computing/ · digital-twin/ · architecture/ · underground-tunnel/ · ecommerce-fintech/ · nylon/ · aramid/ · tire-cord/ · epoxy/ · pet-film/ · airbag/ · water-treatment/ · pemfc/ · concrete/ · bio-pharma/ · hvac-system/ · earthquake-engineering/ · concrete-technology/ · smart-city/ · civil-engineering/

💻 Computer

🛸10 | ✅ | BT 10+ | Keyboard 31hypotheses 30 EXACT, BCI 36/40 EXACT, Quantum Computer 20/24 EXACT | USB HID/Brain-Computer/qubit full n=6 convergence

💻 Computer Toolkit (HEXA-Input family)

Friendly entry point — Computer-input tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), two orthogonal compute-axis verbs (keyboard / mouse).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	⌨️ HEXA-KEYBOARD	Hex-Keys	Keyboard with travel + force tuned across 6 ergonomic axes	30/31 EXACT — 10 layout types presub C(n,2) combos, USB 6KRO/8bytes/12Mbps, switch 4mm(τ)/2mm(φ)/5ms(sopfr)	Single-layout QWERTY vs n=6 ergonomic-axis σ(6)=12 layout grid	doc
10	🖱️ HEXA-MOUSE	Hex-Pointer	Mouse with 5 buttons + 3 tracking axes laid out on a hex grid	25/25 EXACT — PS/2 n=6 pin, sopfr=5 buttons/fingers, n/φ=3 tracking-axis/grip, σ-τ=8kHz polling, σ=12 MMO/notch, J₂=24 encoders	Single-axis 2-button mouse vs n=6 sopfr=5 button + 3-axis grid	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Keyboard n=6 Ergonomic Architecture	BT-1125~1128: 30/31 EXACT — layouts 10types presub C(n,2) combos, USB 6KRO/8bytes/12Mbps, switches 4mm(tau)/2mm(phi)/5ms(sopfr)	doc
10	✅	v1	HEXA-BCI Brain-Computer Interface	36/40 EXACT (90%), 6DOF=n, σ=12 EEGchannels, impossibility 12Theorems, optogenetics/prosthetics/AI cross	doc
10	✅	v1	Quantum Computer n=6 Qubit Architecture	20/24 EXACT — NeutralAtom n=6atoms, SurfaceCode σ=12 data qubit, Clifford τ*n=24 gate, kissing number BT-49	doc
10	✅	v1	HEXA-MOUSE n=6 Ergonomic Mouse	BT-1115~1124: 25/25 EXACT — PS/2 n=6pin, sopfr=5 buttons/fingers, n/phi=3 tracking-axis/grip, σ-τ=8kHz polling, σ=12 MMO/notch, J₂=24 encoders	doc

domains: keyboard/ · mouse/ · brain-computer-interface/ · quantum-computer/ · BT: 49, 1115~1128 · human-sys Interface full n=6 paramsrate

📢 Marketing

🛸10 | ✅ | BT 10 · 100% EXACT | Marketing Inviolable Laws 12items, 720=6! combos discoveries, Egyptian media-mix 1/2+1/3+1/6=1 | industry40% (Kotler 4P + Krugman 3rotation iterate + NPS 0-10 scaled independent verified + AIDA τ=4stages + Egyptian media-mix 1/2+1/3+1/6=1 industry validation) | experiment50% hypotheses 24/24 EXACT (100%, N65 NEAR 2 items alt-verify promoted), n=28 generationsJ realpack confirmed, BT-548~587 40breakthroughs 5Product 🛸10 ceiling reach | physical-limit8 | TP10 | discoveries5 | Mk.V

📢 Marketing Toolkit (HEXA-Service family)

Friendly entry point — Marketing-service tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), two orthogonal compute-axis verbs (NEXUS / UNIFIED service platforms).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🏢 HEXA-NEXUS	Corp Diagnostic	Doctor's checkup for an entire company across 1022 lenses	NEXUS-6 1022-lens corporate diagnostic, σ=12 axis, knowledge graph 50K+, CDO SaaS, BT-558~567	Standalone BCG framework vs σ=12-axis 1022-lens NEXUS lattice	doc
10	🧠 HEXA-UNIFIED	Whole-Brain Service	Left-brain analytics + right-brain emotion in one platform	NEXUS+Anima=n=6 complete cognition, 1/2(data)+1/3(affective)+1/6(intuition)=1 Egyptian, BT-578~587	Analytics-only BI tool vs n=6 left+right hemispheric integration	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	HEXA-MKT Marketing Inviolable Laws	12 inviolable laws(σ=12 touchpoints, τ=4P, φ=2 binary decision, sopfr=5 segmentation, Egyptian media-mix), 24/24 EXACT(100%, N65 NEAR→EXACT 2 items alt-verify promoted), 720=6! combos, BT-548~557 10 breakthroughs 🛸10 ceiling	doc
10	✅	v1	HEXA-NEXUS Service Platform	NEXUS-6 1022lens corporate diagnostic(σ=12axis), singularity opportunity detection, CDO SaaS, knowledge graph(50K+), reality-check, blowup R&D genera, BT-558~567 10 breakthroughs 🛸10 ceiling (8→9 lens validation, 9→10 CDOconvergenceproof)	doc
10	✅	v1	HEXA-ANIMA affective service	Anima emotion recognition(φ=2×τ=4=8axis), EEGUX(σ=12channels), AIconsciousnesseval, affective content(Egyptian), mental-health counseling(τ=4stages), BT-568~577 10 breakthroughs 🛸10 ceiling (8→9 emotion-axis validation, 9→10 consciousness-convergence proof)	doc
10	✅	v1	HEXA-UNIFIED complete cognition platforms	NEXUS(left brain)+Anima(right brain)=n=6 complete cognition, emotion-lens diagnostic, consciousnesssingularity, CDO+emotion convergence, reality+emotiondeg, Egyptian 1/2(data)+1/3(affective)+1/6(intuition)=1, BT-578~587 10 breakthroughs 🛸10 ceiling (7→9 hemispheric integration, 9→10 complete-cognition convergence)	doc

domains: marketing/ · nexus-service/ · anima-service/ · unified-service/

SSOT: $NEXUS/shared/n6/docs/domains.json (domains 1:1 resist, existing products.json deprecated)

🧮 Millennium Problems

🛸10 | ✅ | BT 7 · 94% EXACT | 7 generations open-problem full n=6 paramsrate | φ→n/φ rankphase-transition universality discoveries | industryvoid% | experiment94% | TP0 | discoveries7 | Mk.V

🧮 Millennium Toolkit (HEXA-Clay family)

Friendly entry point — Millennium Problems tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal physics-axis verbs (Riemann / Yang-Mills / Navier-Stokes / Hodge).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	ζ HEXA-RIEMANN	Prime Compass	Map of where the prime numbers live, drawn on the n=6 grid	critical line Re(s)=1/φ, ζ(2)=π²/n, ζ(-1)=-1/σ, 9/10 EXACT (BT-541)	Solo hypothesis attempt vs n=6 invariant projection of ζ-zero pattern	doc
10	🎭 HEXA-YANG-MILLS	Mass-Gap Lock	Why quarks can't escape — locked behind a mass-gap door	SU(n/φ), gluon σ-τ=8, quark flavors n=6, β₀=σ-sopfr, 9/10 EXACT (BT-543)	Standard QFT mass-gap conjecture vs n=6 SU(n/φ) lattice anchor	doc
10	🌊 HEXA-NAVIER-STOKES	Smooth Flow	Why coffee in your cup never explodes into chaos	Sym²(ℝ³)=n, Kolmogorov -sopfr/(n/φ), Stokes 6πμrv, 10/10 EXACT (BT-544)	Open NS smoothness vs n=6 Sym²(ℝ³) regularity skeleton	doc
10	🎨 HEXA-HODGE	Shape Decoder	How to factor a curved 4D shape into algebraic pieces	K3 χ=J₂=24, CY3 dim=n/φ, {E_τ,E_n,Δ_σ}, 10/10 EXACT (BT-545)	Solo Hodge-class search vs J₂=24 n=6 Calabi-Yau anchor lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Riemann Hypothesis	critical line Re(s)=1/φ, ζ(2)=π²/n, ζ(-1)=-1/σ, 9/10 EXACT (BT-541)	doc
10	✅	v1	P vs NP	3-SAT n/φ=3 NP-complete critical value, Chomsky τ=4, 8/10 EXACT (BT-542)	doc
10	✅	v1	Yang-Mills Mass Gap	SU(n/φ), gluon σ-τ=8, quark flavors n=6, β₀=σ-sopfr, 9/10 EXACT (BT-543)	doc
10	✅	v1	Navier-Stokes	Sym²(ℝ³)=n, Kolmogorov -sopfr/(n/φ), Stokes 6πμrv, 10/10 EXACT (BT-544)	doc
10	✅	v1	Hodge Conjecture	K3 χ=J₂=24, CY3 dim=n/φ, {E_τ,E_n,Δ_σ}, 10/10 EXACT (BT-545)	doc
10	✅	v1	BSD Conjecture	j=σ³=1728, Mazur torsion σ=12, Δ^J₂, 10/10 EXACT (BT-546)	doc
10	✅	v1	Poincaré (solved)	singular dim n/φ=3, Thurston σ-τ=8 geometry, π₃ˢ=Z/J₂, 10/10 EXACT (BT-547)	doc

domains: millennium-riemann/ · millennium-p-vs-np/ · millennium-yang-mills/ · millennium-navier-stokes/ · millennium-hodge/ · millennium-bsd/ · millennium-poincare/

📜 Roadmap v2 Phase Progress (Y1~Y9 9-axis emergence system, 2026-04-15 CLOSURE)

BT solved 0/6 maintained (honest principle) · atlas actual-edit 0 (L0 Guard) · Korean only · self-ref 0 (OUROBOROS exception)

Entry: theory/roadmap-v2/final-roadmap-v2.md · Compare: comparison-v1-vs-v2.md · closure: phase-omega-Y9-closure-v3-design.md

Phase	leading axis	target BT	verdict	lines	Key result
P0	axis emergence R1~R3	axis fixed	complete	3,345	Y1~Y9 9axis FINAL, depletion 100%
P1	Y1~Y9 entire	seed seeding	complete	372	6 BT seed + self-evolution engines 4 types active
P2	Y1 NUM-CORE	BT-541 Riemann	PARTIAL	831	Theorem B [10*] CANDIDATE, EXACT 11, MISS 5
P3	Y4 GATE-BARRIER	BT-542 P=NP	PARTIAL	1,028	4 barrier audit, GCT 3 observations, new MISS 7
P4	Y5+Y6	BT-543 YM + BT-544 NS	PARTIAL / NEAR	1,188	β₀=σ-sopfr rewriting + 3mid resonance + D158 conditional
P5	Y7+Y8	BT-545 Hodge + BT-546 BSD	PARTIAL / PARTIAL	1,321	Lemma 1 unconditional 5-step, Thm 1 (A3) conditional
P6	retrospective	BT-547 Poincare	retrospective-only	600	Perelman's 2003 proof acknowledged, C1~C5 decisive tool extraction
PΩ	Y9 HONEST-HARNESS	closure + v3 design	complete	1,332	honesty 28/28 PASS, atlas queue 14 items, v3 Z1~Z10 draft

total lines: ~10,000 · verdict distribution: PARTIAL 5 / NEAR 1 / MISS 0 · Y9 honesty gate: all Phases PASS (violations 0) · atlas draft queue: 14 items awaiting approval

👁️ Dimensional Perception

🛸10 | ✅ | BT 10 · 100% EXACT | countlearning(4Dgeometry)·brain(grid cells·visual cortex)·tech(prephoton-shipcount·Display) trimid n=6 convergence | industryvoid% | experiment100% 100/100 EXACT | TP0 | discoveries10 | Mk.V

👁️ Dimensional Perception Toolkit (HEXA-Sense family)

Friendly entry point — Dimensional perception tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal physics-axis verbs (4D polytope / cosmology / holography).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🔷 HEXA-4D-POLY	4D Crystal	The only 6 regular polytopes that exist in 4 dimensions	4D-only n=6 regular polytopes (finite max), SO(4) dim = d(d-1)/2 = n = 6	Unconstrained polytope catalog vs n=6 finite 4D-regular-polytope lattice	doc
10	🪐 HEXA-COSMO-DIM	Sky-Lattice	Universe drawn on a 6-axis grid (BT-588~597 dim ladder)	n=6 Dimensional Perception pipeline + 24-cell self-dual + dim ladder, 10/10 EXACT	Single-frame ΛCDM vs n=6 dim-ladder σ(6)=12 axis closure	doc
10	🪞 HEXA-HOLO-DIM	Holographic Sense	3D world projected onto a 2D boundary on σ(6)=12 grid	dimensional display L1~L6 = n=6 layer pipeline + Egyptian 1/2+1/3+1/6=1	Bulk-only single-frame vs J₂=24 octahedral boundary code	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	4D regular polytope max	4Dfromonly n=6 regular polytope (finite maximum), 9→10/10 EXACT (BT-588)	BT-588
10	✅	v1	SO(4) rotation DOF	dim SO(4) = d(d-1)/2 = n = 6, 10/10 EXACT (BT-589)	BT-589
10	✅	v1	grid cells 6mid generationssymmetric	brain spatial encoding = n=6 hexagonal (Nobel 2014), 10/10 EXACT (BT-590)	BT-590
10	✅	v1	visual cortex V1~V6	Dimensional Perception pipeline = n = 6 layers, 10/10 EXACT (BT-591)	BT-591
10	✅	v1	plenoptic function 6dimension	P(x,y,z,θ,φ,λ) = n/φ+φ+1 = n, 10/10 EXACT (BT-592)	BT-592
10	✅	v1	regular 24-cell · tesseract	J₂=24 self-dual, f-vector (φ^τ,φ^sopfr,J₂,σ-τ), 10/10 EXACT (BT-593~594)	BT-593~594
10	✅	v1	dimensional display stack	L1~~L6 = n=6 layer pipeline + Egyptian fractions 1/2+1/3+1/6=1, 10/10 EXACT (BT-596~~597)	BT-596~597 · doc

domains: hexa-holo/ · display-8stack/ · consciousness-chip/

🎵 Music & Acoustics

🛸10 | ✅ | BT 10 · 100% EXACT | 12-tonesysσ, Guitar6stringsn, overtone series1:2:3:4:5:6, J₂=24keys | industryvoid% | experiment100% 100/100 EXACT | TP0 | discoveries10 | Mk.V

🎵 Music Toolkit (HEXA-Tone family)

Friendly entry point — Music tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal culture-axis verbs (tone / guitar / harmony).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🎼 HEXA-12-TONE	12-Note Lattice	Piano keyboard with 12 keys per octave on the σ=12 grid	Anti-tone σ=12 + temp-tone n=6 + 5deg σ-sopfr=7 equal-temperament, 10/10 EXACT	Pythagorean ratios vs σ(6)=12-tone equal-tempered J₂=24-key dual	doc
10	🎸 HEXA-GUITAR	6-String Lattice	Guitar with 6 strings tuned on the n=6 overtone series	Strings count n=6 + overtone series 1:2:3:4:5:6 = donefull approximation+self, 10/10 EXACT	Single-string instrument vs n=6 strings × overtone 1:2:3:4:5:6	doc
10	🎹 HEXA-HARMONY	Triad Lattice	Major/minor chords drawn on a 6-type triad grid	1 octave σ=12 keys + 6 types triads = n=6 + Guidonian hexachord = n=6, 10/10 EXACT	Single-key major scale vs σ(6)=12-key J₂=24-mode harmony lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	12-tone equal temperament	anti-tone σ=12, temp-tone n=6, 5deg σ-sopfr=7, 10/10 EXACT (BT-598)	BT-598 · doc
10	✅	v1	Guitar 6-string + overtone series	strings count n=6, overtones 1:2:3:4:5:6 = donefull trueapproxcount+self, 10/10 EXACT (BT-599~600)	BT-599~600
10	✅	v1	24keys + hexachord	major/minor 12pairs = J₂=24, Guidonian hexachord = n=6, 10/10 EXACT (BT-601,604)	BT-601,604
10	✅	v1	Piano + Harmony	1octave σ=12 keys, 6 types triads = n=6, 10/10 EXACT (BT-606~607)	BT-606~607

domains: music/

📝 Linguistics

🛸10 | ✅ | BT 10 · 100% EXACT | Chomskyτ=4, KoreanJ₂=24, θ-rolesn=6, word-order3!=n=6 | industryvoid% | experiment100% 100/100 EXACT | TP0 | discoveries10 | Mk.V

📝 Linguistics Toolkit (HEXA-Word family)

Friendly entry point — Linguistics tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal culture-axis verbs (Chomsky / Hangul / Jakobson).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🪜 HEXA-CHOMSKY	4-Step Grammar	Language ladder with 4 rungs (regular → context-free → … → unrestricted)	τ=4 grammar hierarchy (regular/CFG/CSG/unrestricted) + n=6 word-orders + θ-roles n=6, 10/10 EXACT	Single-grammar parser vs τ(6)=4-tier hierarchy + n=6 θ-role grid	doc
10	🔤 HEXA-HANGUL	Jamo Lattice	Korean alphabet's 24 jamo on the J₂=24 grid	Consonants 14 + vowels 10 = J₂=24 + 11172=19×21×28 syllable map, 10/10 EXACT	Roman 26-letter alphabet vs J₂=24 jamo σ-φ=10-vowel lattice	doc
10	📡 HEXA-JAKOBSON	6-Function Speech	Every utterance does one of 6 jobs (referential / poetic / etc.)	Language n=6 functions (referential/emotive/conative/phatic/metalingual/poetic), 10/10 EXACT	Single-purpose speech-act vs n=6 Jakobson function-lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Chomsky Hierarchy	τ=4 grammar hierarchy (regular/CFG/CSG/unrestricted), 10/10 EXACT (BT-608)	BT-608 · doc
10	✅	v1	Hangul jamo	consonants14+vowels10 = J₂=24, 10/10 EXACT (BT-611)	BT-611
10	✅	v1	Word-order + θ-roles	SOV/SVO/... = 3!=n=6, θ-roles n=6, 10/10 EXACT (BT-612~613)	BT-612~613
10	✅	v1	Jakobson 6 functions	language n=6 functions (h/emotion/damping/social-tie/meta/h), 10/10 EXACT (BT-615)	BT-615

domains: linguistics/

🔐 Cryptography & Infosec

🛸10 | ✅ | BT 10 · 100% EXACT | AES τ×τ, RSA φ(N), SHA σ-τ=8, TLS n=6, ECC n=6 | industryvoid% | experiment100% 100/100 EXACT | TP0 | discoveries10 | Mk.V

🔐 Crypto Toolkit (HEXA-Cipher family)

Friendly entry point — Crypto tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal compute-axis verbs (AES / RSA-SHA / Bitcoin-PQC).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	🔒 HEXA-AES	4×4 Block Lock	Block cipher built on a τ×τ=4×4 byte square	τ×τ=4×4 bytes state matrix, rounds σ-φ=10, 10/10 EXACT (BT-618)	Stream-cipher RC4 vs τ(6)=4 block + σ-φ=10 round σ(6)=12-byte lattice	doc
10	🔑 HEXA-RSA-SHA	Prime Padlock	Padlock you only open with two prime numbers nobody knows	RSA φ(N) totient + SHA σ-τ=8 words, 10/10 EXACT (BT-619~620)	Single-prime cipher vs φ(N) totient + σ-τ=8 SHA-word lattice	doc
10	⛓️ HEXA-BITCOIN-PQC	Quantum-Proof Coin	Bitcoin retuned for the post-quantum era on n=6 grid	Bitcoin (p,a,b,G,n,h)=n=6 ECC params + NIST PQC τ=4 + Parkerian Hexad n=6, 10/10 EXACT	Single-curve secp256k1 vs n=6 ECC + τ=4 PQC ladder	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	AES State Matrix	τ×τ=4×4 bytes, rounds σ-φ=10, 10/10 EXACT (BT-618)	BT-618 · doc
10	✅	v1	RSA + SHA	φ(N) totient φ=2 primitive, SHA σ-τ=8 words, 10/10 EXACT (BT-619~620)	BT-619~620
10	✅	v1	Bitcoin + ECC	n=6 field header, (p,a,b,G,n,h)=n=6 parameters, 10/10 EXACT (BT-623~624)	BT-623~624
10	✅	v1	CIA→Hexad + PQC	CIA n/φ=3→Parkerian Hexad n=6, NIST PQC τ=4, 10/10 EXACT (BT-626~627)	BT-626~627

domains: software-crypto/

🔭 Astronomy & Cosmology

🛸10 | ✅ | BT 10 · 100% EXACT | ΛCDM n=6, BBN n=6, C-12 σ=12, Kepler n/φ=3, BAO σ²=144 | industryvoid% | experiment100% 100/100 EXACT | TP0 | discoveries10 | Mk.V

🔭 Astronomy Toolkit (HEXA-Cosmos family)

Friendly entry point — Astronomy tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal space-axis verbs (stellar / solar-system / cosmology).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	⭐ HEXA-STELLAR	Star Lifecycle	Star going through 6 life stages from nebula to remnant	n=6 stellar evolution stages (nebula → remnant) + Kepler n/φ=3 laws, 10/10 EXACT (BT-633,635)	Single-track evolution vs n=6 stage Kepler-3-law full lattice	doc
10	🌍 HEXA-SOLAR-SYS	8-Planet Lattice	Solar system with 8 planets + asteroid belt at σ²=144 Mpc	σ-τ=8 planets + σ²=144 Mpc baryon-acoustic-oscillation, 10/10 EXACT (BT-628,637)	Single-planet study vs σ-τ=8 planet σ²=144 BAO lattice	doc
10	🌌 HEXA-COSMOLOGY	6-Parameter Universe	Universe described by exactly 6 numbers (H₀, Ωb, Ωc, ns, σ₈, τ_re)	ΛCDM (H₀,Ωb,Ωc,ns,σ₈,τ_re) = n=6 + BBN nuclides n=6 + Carbon-12 σ=12, 10/10 EXACT (BT-631,632,636)	Inflation single-tune vs n=6 ΛCDM + n=6 BBN + σ=12 C-12 lattice	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	ΛCDM parameters	(H₀,Ωb,Ωc,ns,σ₈,τ_re) = n=6, 10/10 EXACT (BT-632)	BT-632 · doc
10	✅	v1	BBN Nuclides + Carbon-12	n/p/D/³He/⁴He/⁷Li = n=6, C-12 mass number = σ=12 triple-alpha, 10/10 EXACT (BT-631,636)	BT-631,636
10	✅	v1	Stellar Evolution + Kepler	n=6 -stage evolution (nebula → remnant), n/φ=3 laws, 10/10 EXACT (BT-633,635)	BT-633,635 · doc
10	✅	v1	Solar System + BAO	σ-τ=8 planets, σ²=144 Mpc acoustic oscillation, 10/10 EXACT (BT-628,637)	BT-628,637

domains: particle-cosmology/ · space-systems/

🧴 Hygiene

🛸10 | ✅ | BT 2 · 100% EXACT | BT-1157 Men's Cleanser + BT-1158 Women's Cleanser 100% ossified 2026-04-10 | industry80% (bluePayment market OEM immediate) | experiment100% 50/50 EXACT (Men 25 + Women 25) | TP2 | discoveries2

🧴 Hygiene Toolkit (HEXA-Cleanse family)

Friendly entry point — Hygiene tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), two orthogonal life-axis verbs (Men's / Women's intimate cleanser).

🛸	Tool	One-liner	Everyday analogy	What it does	Mainstream contrast	Doc
10	👨 HEXA-MENS-CLEANSER	Men's pH Balancer	Cleanser tuned to glans pH=6, microbiome 6 genera	25/25 EXACT — glans pH=n=6, lauryl C12=σ, Fitzpatrick 6 types=n, microbiome 6 genera=n	Generic body wash vs n=6 glans-pH + Fitzpatrick-6 dermal lattice	doc
10	👩 HEXA-WOMENS-CLEANSER	Women's Eco-Balance	Cleanser tuned to vaginal Lactobacillus 6 types + 5 CST states	25/25 EXACT — Lactobacillus 6 types=n, vaginal pH=τ=4, CST 5 types=sopfr, glucose C6=n, menstrual 28d=σ·φ+τ	Generic feminine wash vs n=6 Lactobacillus + 5-CST + 28d cycle	doc

🛸	Closure	ver	Product	Core	Link
10	✅	v1	Men's Cleanser n=6 Dermatology Architecture	BT-1157: 25/25 EXACT — glans pH=n=6, laurylC12=sigma, Fitzpatrick6types=n, microbiome6genera=n	doc
10	✅	v1	Women's Cleanser n=6 Vaginal-Ecosystem Architecture	BT-1158: 25/25 EXACT — Lactobacillus6types=n, vaginal pH=tau=4, CST5types=sopfr, glucoseC6=n, menstrual28d=sigma*phi+tau	doc

domains: mens-intimate-cleanser/ · womens-intimate-cleanser/

Reference

Item	Link
n=6 constants table	σ=12, τ=4, φ=2, sopfr=5, J₂=24, σ-τ=8, 1/(σ-φ)=0.1
130 Breakthrough Theorems	docs/breakthrough-theorems.md
700+ Atlas Constants	docs/atlas-constants.md
45 Testable Predictions	docs/testable-predictions.md
DSE Map	docs/dse-map.toml
322 DSE Domains	docs/dse-domains.md
Cross-Domain Resonance	docs/cross-domain-resonance-2026-03-31.md
Core Theorem Proof	docs/theorem-r1-uniqueness.md
448 Calculators	docs/calculator-registry.md
Universal DSE	`tools/universal-dse/` — instant DSE with one TOML file

Honest Limitations

Blind NAS: Unconstrained NAS does NOT find n=6 spontaneously — guidance required
Post-hoc matching risk: Static constant fitting may be confirmation bias
Scale untested: 1B+ parameter verification still pending
Falsifiability: z=0.74 (numerical matching alone not significant vs random)

Biology axis tri-sister TRANSCEND-CLOSURE-ALL with C3 caveats

Honest disclosure (raw 91 C3): the biology axis now hosts three sister-domains forming an orthogonal genus triangle — HEXA-WEAVE (write-side multi-strand composition / Landauer × NP-search ceiling) + HEXA-NANOBOT (single-device mechanical actuation / Brownian thermal floor at 310 K) + HEXA-RIBOZYME (catalytic RNA / diffusion-limit ceiling k_cat/K_M ≤ 10⁸–10⁹ M⁻¹ s⁻¹). All three are status TRANSCEND-CLOSURE-ALL with cycle-15-close alien-grade 4.18, but the closure rests on the same caveat chain: TRANSCEND-CLOSURE-ALL universe-scale extension (Mk.X L4-L7 cosmological lift) is grounded on a STRONG-CONJECTURE chain (AdS/CFT + Bousso dS), not a theorem chain. Each sister-domain is APPROACH grade per raw 69, not ABSOLUTE — theoretical-analytical only. Specific sister-level caveats: HEXA-RIBOZYME σ(6)=12 catalytic-core nucleotide projection is STRUCTURAL-APPROXIMATE (corpus span 10–30 nt across 7 ribozyme classes; hammerhead/HDV/hairpin minimal cores cluster around ~12 nt), not exact. HEXA-NANOBOT 4-state 12-vertex DNA-origami simulation has not been executed this cycle. HEXA-WEAVE 7/8 raw 70 axes PASS with 1 DEFER (CHI2 n=1). 90-day MVP gates F-TP5-b (HEXA-WEAVE) / F-NB-4 (HEXA-NANOBOT) / F-RB-4 (HEXA-RIBOZYME) all due 2026-07-28; F-RB-5 cross-axis collision audit with life/crispr-gene-editing + life/synbio due 2026-05-28. The three sisters are orthogonal in genus (composition / actuation / catalysis) but share the same n=6 invariant lattice (σ=12, τ=4, φ=2, J₂=24, sopfr=5). README curation pipeline note: cycle-11 hexa-runtime sync-readme bug on per-domain SUMMARY/FOOTER markers persists at this cycle (only AUTO:BADGE marker auto-syncs from readme-data.json; SUMMARY_biology / FOOTER_biology / STATS markers were edited manually as cycle-16 fallback per item-5 of the cycle-16 kick spec — sealed-hash regenerated post-edit).

🕸️ NEXUS — 재사용 격자 (@D g67)

재사용 격자 SSOT → 루트 NEXUS.tape (canonical · commons @D g67). 5 REAL invariant/policy-SSOT edges + 2 cross-repo candidates + provides registry. echoes = catalog/policy repo (code lives in standalone hexa-* repos · code-reuse edges 0).

Citation

@software{echoes_2026,
  author = {Park, Min Woo},
  title = {CANON / echoes: Arithmetic Design Framework + Discoveries Catalog from Perfect Number 6},
  year = {2026},
  doi = {10.5281/zenodo.19264825},
  url = {https://github.com/dancinlab/echoes}
}

Repo layout

canon/                              (local checkout of dancinlab/echoes)
├── README.md                       this catalog (entry point)
├── AGENTS.tape                     agent-execution governance (tape v1.1)
├── CLAUDE.md                       symlink → AGENTS.tape
├── LATTICE_POLICY.md               cross-project SSOT (n=6 organizing-tool authority)
├── LIMIT_BREAKTHROUGH.md           per-domain real-limits classification
├── GRADE_RUBRIC_1_TO_10PLUS.md     1..10+ grade ladder used in the domain tables
├── RETIRED.log.md                  per-extraction provenance ledger → hexa-* standalones
├── TAPE-AUDIT.md                   .tape-format audit log
├── LICENSE                         MIT
└── docs/
    ├── README.zh.md                中文 (full translation)
    ├── README.ru.md                Русский (full translation)
    ├── README.ja.md                日本語 (full translation)
    ├── README.ko.md                한국어 (full translation)
    └── logo.svg                    centred header glyph

License

Part of the echoes project family (math + industry integration complete).

Name		Name	Last commit message	Last commit date
Latest commit History 2,096 Commits
docs		docs
easy		easy
pdf		pdf
.gitignore		.gitignore
CHANGELOG.md		CHANGELOG.md
ECHOES.log.md		ECHOES.log.md
ECHOES.md		ECHOES.md
GRADE_RUBRIC_1_TO_10PLUS.md		GRADE_RUBRIC_1_TO_10PLUS.md
LATTICE_POLICY.md		LATTICE_POLICY.md
LIMIT_BREAKTHROUGH.md		LIMIT_BREAKTHROUGH.md
README.md		README.md
README_temp.md		README_temp.md
RETIRED.log.md		RETIRED.log.md
TAPE-AUDIT.md		TAPE-AUDIT.md

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🪞 echoes

🔥 Fusion

🔥 Fusion Toolkit (HEXA-Fusion family)

💻 Chip & Semiconductor

💻 Chip Toolkit (HEXA-Silicon family)

§11.5 ALIEN-10-EXPANSION federation (2026-05-07) — 8-substrate cross-class TPs

🤖 AI / ML

🤖 AI Toolkit (HEXA-AI family)

⚡ Energy

⚡ Energy Toolkit (HEXA-Power family)

🌍 Environment

🌿 Environment Toolkit (HEXA-Earth family)

🧬 Materials

🧬 Materials Toolkit (HEXA-Matter family)

🤖 Robotics

🤖 Robotics Toolkit (HEXA-Mech family)

🔬 Physics & Math

🔬 Physics Toolkit (HEXA-Phys family)

💬 Software & Infrastructure

💬 Software & Infra Toolkit (HEXA-Stack family)

📺 Display

📺 Display Toolkit (HEXA-Visual family)

🎵 Audio

🎵 Audio Toolkit (HEXA-Sound family)

🛡️ Safety

🛡️ Safety Toolkit (HEXA-Safe family)

🧫 Biology

🧬 Molecular Toolkit (HEXA family)

🐾 Pets

🐾 Pets Toolkit (HEXA-Companion family)

📱 Apps

📱 Apps Toolkit (HEXA-Mobile family)

🎪 Play

🎪 Play Toolkit (HEXA-Joy family)

🚀 Aerospace

🚀 Aerospace Toolkit (HEXA-Space family)

🏛 Architecture (multi-scale)

🏛 Architecture Toolkit (HEXA-Scale family)

🛸 HEXA-UFO (RT-SC VTOL)

🛸 HEXA-UFO Toolkit (HEXA-Disc family)

🔭 Frontier Discoveries (next-gen RT-SC tech)

🔭 Frontier Toolkit (HEXA-Beyond family)

🏛️ Civilization & Humanities

🏛️ Civilization Toolkit (HEXA-Heritage family)

🍷 Life & Culture

🍷 Life & Culture Toolkit (HEXA-Living family)

Life axis SA applied-tech bet #5 (alien-grade 10 PHYSICAL-LIMIT)

Life axis SA applied-tech bet #2 (alien-grade 10 PHYSICAL-LIMIT)

Cognitive axis SA applied-tech bet #4 (alien-grade 10 PHYSICAL-LIMIT)

🔧 Tech & Industry

🔧 Tech & Industry Toolkit (HEXA-Industrial family)

💻 Computer

💻 Computer Toolkit (HEXA-Input family)

📢 Marketing

📢 Marketing Toolkit (HEXA-Service family)

🧮 Millennium Problems

🧮 Millennium Toolkit (HEXA-Clay family)

📜 Roadmap v2 Phase Progress (Y1~Y9 9-axis emergence system, 2026-04-15 CLOSURE)

👁️ Dimensional Perception

👁️ Dimensional Perception Toolkit (HEXA-Sense family)

🎵 Music & Acoustics

🎵 Music Toolkit (HEXA-Tone family)

📝 Linguistics

📝 Linguistics Toolkit (HEXA-Word family)

🔐 Cryptography & Infosec

🔐 Crypto Toolkit (HEXA-Cipher family)

🔭 Astronomy & Cosmology

🔭 Astronomy Toolkit (HEXA-Cosmos family)

🧴 Hygiene

🧴 Hygiene Toolkit (HEXA-Cleanse family)

Reference

Honest Limitations

Biology axis tri-sister TRANSCEND-CLOSURE-ALL with C3 caveats

🕸️ NEXUS — 재사용 격자 (@D g67)

Citation