[pinterbanget]

Summary

This adds research/pr4554-outer-recount-check/, an independent check of two documents from Dugongue's #4554 (head 4f46c6a9):

• NATIVE-OUTER-ASSEMBLY.md, the caller-tolerance theorem that would carry any faster native transform to multiplication;
• NATIVE-RECOUNT.md, the Gaussian-map recount.

With #4556–#4560, this covers every constructive component of #4554 except NATIVE-STABILITY.md and PHASE-TABLES.md §2. All checked claims are confirmed. No new κ.

Both texts are vendored (blobs b9c54968 and 300188c8, SHA256-pinned).

Checks

• Caller tolerance, exact. For L ≤ 2^64 and b ≤ 16 (1,024 cases), 2L2^bδ + δ² + δ < 1/16 holds, along with the L^4 2^(4b) domain and the 1/8 budget.
• Perturbed assemblies. 16 runs up to 65,534 bits, with every forward, product and inverse output perturbed by δ within the contract, coherently or randomly. All products are exact, with carries ≤ B2^b. These are samples; the analytic worst case rests on the exact inequalities.
• Lattice tail. The two-sided tail ≤ 4e^(−a(R−1)²)/(1−e^(−a(2R−1))) holds for 4,000 random real centres, with worst ratio 0.26.
• Radius selection. Doubling with rational squared comparisons meets both conditions and lands within a factor 2 of the least admissible radius. The second condition binds only when α exceeds about √P, outside the source regime.
• Cost exponents. h ~ p^(1/4−ε/2), dh ~ p^(1/4+ε/2), dp/α² ~ p^(1/2) and direct forward p^(3/4+3ε/2), in exact exponent arithmetic.
• Metadata lemma. next = (current−M)&M enumerates every submask, checked for all M < 2^11. The odometer makes at most 2T+d changes.

python3.12 -B scripts/research_package.py --package research/pr4554-outer-recount-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4554-outer-recount-check outcome=completed   (~5 s, stdlib only)

Limitations:

• The faster cyclic-transform hypothesis is not supplied, here or in Native Word RAM Gaussian adapters: chirp blocks and reusable banded inverse #4554.
• The perturbation runs are samples.
• NATIVE-STABILITY.md is left open.

Head: 30ce22be2dd737791d40318bd90928042db40ee3. Base: canonical main f626db5c.

Credit: Dugongue (#4554). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code