[pinterbanget]

Summary

This adds research/pr4100-bit-moment-enclosure/, an independent certified check of the two finite inequalities behind Cinna Davis's #4100 BIT.md §3 recurrence at the retuned c = 8667/5,000,000. They are μ_1 < 1 and μ_(1−c) < 1, where μ_x = (Σ_r H_r(r/64)^x + ηF(1/64)^x)/W.

Before this, they were checked only by #4100's own check_composition.py, through a vendored engine. #4171 reproduces a1 and a2 from c, but not these moments. #4311's coverage map listed this as open.

Claim type: an independent certified finite check, plus exact algebra. No new κ.

Result

• μ_1 is exact. It equals 2874298095721977/2890625000000000, which is Propose unconditional κ = 0.00173097911567079247276057 via batched CRT #4100's ledger value bit_linear_moment.
• μ_(1−c) is certified below 1. It is < 0.99999991163325597, so the margin exceeds 8.836·10⁻⁸. The enclosure is narrower than 10⁻³⁰: ln comes from an atanh series after reducing by powers of two, with a geometric tail bound, and exp from Taylor with a Lagrange remainder.
• Headroom. The root c* lies in (0.0017334270, 0.0017334271), so c sits at least 2.7·10⁻⁸ below it.
• Sensitivity. One extra rank-1 child in H makes μ_(1−c) > 1 at this c. The proof needs H exactly as printed.
• Stage algebra. a1 = c(1−c) and a2 = c(1−c²) equal the printed constants. The exponent identity (1−c)² + c(1−a) = 1 − a_next holds exactly at a = 0 and a = a1.
• Body word. The six printed states of D−=H; F_I; D+=H; F_I; D=−D; D+=H are checked in Z/7³ on 200 random instances.

Update: H and W bound to the selected supplier (head b5b72817d7b3a85a1125d5b203e0922fcf4930b3)

This answers the package's open question.

• The chain. certificates/selected-result.json leads, through its SHA256-pinned certificate research/community-frontier1094-audit/ASSEMBLY.json, to bit_supplier = research/e8-bit-p111-tuned/tune/EXPECTED.json (Git blob checked). There nine.profile = H and nine.bit.live = W = 28416.
• The surcharge. The certificate marks the BIT moment as surcharged, and Propose unconditional κ = 0.00173097911567079247276057 via batched CRT #4100's ηF term is that surcharge. With it, the root of μ_(1−a) = 1 reproduces the selected bit_lower = 0.001733427039589844234749 inside a 10⁻²⁰ window. Without it, the root moves by about 2·10⁻¹².
• So Propose unconditional κ = 0.00173097911567079247276057 via batched CRT #4100's μ_x is exactly the selected BIT moment, and c sits at least 2.7·10⁻⁸ below the selected BIT saving.

Evidence

The verifier uses only the standard library, runs in under a second, and imports nothing from the audited package. Source pins of BIT.md and composition-controls.json, plus 8 exact BIT.md phrases.

python3.12 -B scripts/research_package.py --package research/pr4100-bit-moment-enclosure --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4100-bit-moment-enclosure
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4100-bit-moment-enclosure outcome=completed
python3.12 -B scripts/check_research_commit.py --package research/pr4100-bit-moment-enclosure --check-source-history
  PASS_RESEARCH_COMMIT_BYTES {... "files": 7, ...}

Not covered

• Rebuilding H from the word itself, which is the selected record's existing cold replay. This package binds H to the pinned supplier data.
• η's bad-packet rate (Prove exact extreme-rank BIT header densities #4227 and Prove exact intermediate-rank BIT header densities #4228).
• BIT.md's stock, tape and header-route constructions.
• No proof-kernel check.

Task and overlap

• Card: uniform-transfer-audit, refined to these moments (recorded in TASK.json), priority revision 7.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244. Propose unconditional κ = 0.00173097911567079247276057 via batched CRT #4100 is pinned at 337d04939571a637aeab54a0f58f54fde811663a.
• Overlap: refreshed at 09:50 UTC. Only my own map mentions this moment.
• No advance claim: this was a short session, as the procedure allows.

Credit

The construction and constants are Cinna Davis's #4100 (OpenAI Codex assistance). The profile comes from the selected PR589 lineage. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code