[pinterbanget]

Summary

This adds research/stage-zero-forced-translation/. It is an independent check of mihir-s-05's #4464, which answers #4457's open question 1: the stage-zero [D0, Q] = 0 premise for the actual complex caller, with the required translation. It also gives a closed form showing that the recorded translations are forced.

Claim type: an independent exact check plus a closed form. No new κ.

Results

• All 112 ports, separately written code.
  • [q; B] is orthonormal.
  • |ξ| − q·ξ ≡ Σ b_j·ξ + 2t·ξ (mod 4) holds for all 512 characters, i.e. D0 = T_t G_B.
  • [D0, Q] = 0 by exact ℚ(i) XOR convolution, at two ports.
  • The port-0 witness (D0 − G_B)[0,0] = −1/16 holds exactly.
  • The weight profiles 77/35 match research: certify the actual stage-zero Gaussian commutation premise #4464.
• New: the translation is forced. Evaluating at ξ = e_i gives t_i = [c_i ≡ 3 (mod 4)], where c_i is the odd column count of the orthogonal matrix. This equals the recorded translation_after at all 112 ports, and the same formula reproduces all 2,016 non-empty recorded idle normalizations (ranks 8–48). The translation is never optional, which explains research: certify the actual stage-zero Gaussian commutation premise #4464's "every rank-eight normalization needs its nonzero translation".

Evidence

python3.12 -B scripts/research_package.py --package research/stage-zero-forced-translation --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/stage-zero-forced-translation
  PASS_REGISTERED_RESEARCH_PACKAGE research/stage-zero-forced-translation outcome=completed   (~1 s, stdlib only)

The only input is the pinned DATA-PHASES.json. Head: 496a7d6bd053b7019935529ce5b5c3eb3dc664ed. Base: canonical main 2a13eb18.

Not covered

• research: certify the actual stage-zero Gaussian commutation premise #4464's bindings to the native cover, the canonical word and the Conditional κ = 0.00296 via query-thinned productive controllers (+10.18%) #4440 controller.
• Native realization, rounding, BIT and cost.

Credit: mihir-s-05 (#4464) and Matarener (#4457). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code