Separate dynamic circuit integers and streamline integer kernels

[wangxiao1254]

Summary

Separate fixed-width and dynamic circuit integers, reduce integer circuit costs, and remove pointer-sort staging copies.

Changes

Integer representations

• require N > 0 for fixed UInt_T<Ctx,N> and Int_T<Ctx,N>;
• add explicit DynamicUInt_T<Ctx> and DynamicInt_T<Ctx> types with private positive-width vector storage;
• retain unbound default construction as an assignment target;
• validate runtime codecs and session boundaries;
• add to_dynamic() / to_fixed<M>() conversions and signed/unsigned reinterpretation;
• remove UInt_T::mod_exp;
• preserve internal BitVec_T<Ctx,0> use while excluding zero-width frontend/session bundles.

Circuit kernels

• reduce equality from N to N-1 AND gates;
• remove the discarded difference vector from unsigned comparison;
• seed multiplication from its first partial row;
• avoid materializing a quotient for remainder-only calls and remove the per-bit quotient branch;
• seed fixed and dynamic popcount from the first input bit;
• preserve existing aliasing and division-by-zero semantics.

Sorting and ownership checks

• run pointer-backed Batcher sorting directly over caller storage;
• check signed secret-shift operands belong to the same context before building the barrel shifter.

Source migration

Replace both old runtime-width spellings:

UInt_T<Ctx, 0>              -> DynamicUInt_T<Ctx>
Int_T<Ctx, 0>               -> DynamicInt_T<Ctx>
UInt_T<Ctx, runtime_width>  -> DynamicUInt_T<Ctx>
Int_T<Ctx, runtime_width>   -> DynamicInt_T<Ctx>

UInt_T::mod_exp has no replacement in this PR. A future modular exponentiation API should use a full-width modular multiplication rather than an N-bit wrapping product.

Tests

• clean Apple Clang 17 Release/Ninja build: 100/100 build steps;
• full CTest suite: 77/77 passed;
• focused dynamic/fixed integer, sorting, and foreign-context shift suite: 6/6 passed;
• fresh Debug ASan+UBSan focused build: 16/16 build steps and 6/6 tests passed.

Fixed/dynamic parity is checked at widths 1, 2, 7, 8, 31, 32, 63, 64, and 65, including values, gate counts, output wires, and structural digests. Additional tests cover exhaustive small-width arithmetic, exact gate counts, codecs, unbound/moved states, conversions, pointer sorting, empty ranges, and foreign-context secret shifts.

Stack

This is PR 6 of 6 and targets audit/ir-foundations.