[pinterbanget]

Summary

This adds research/pr4338-b2-chain-check/, an independent recomputation of the arithmetic in #4338 (Ross Richardson). #4338 is the optional ordinary B2 stage split out of #4270. At BIT coupling c = 1/577 it claims:

• the ordinary saving a2 = 57697923247/33292900000000;
• the bound T_B2 ≤ 4283584·A·V·e^(1−a2);
• a2 > C, where C is the pooled complex endpoint.

Claim type: an independent exact check of a written arithmetic chain, including a certified moment enclosure. No new κ. None of #4338's source-relative physical contracts is checked.

Result

Every link of PROOF.md §1, §3 and §4 holds, recomputed with exact rationals. The inputs are read from main: H is the selected BIT supplier's nine.profile, a1 is PR2899's ordinary_saving, and C is staged-fourth-mixture-ceiling's root.

Link	Result
a2 = c(1−c) + c·a1, and a2 − C	exact as stated (a2 − C ≈ 2.06·10⁻⁶)
§1: bootstrap at the complex rate	digits match. It falls short of 0.001727989140903569 by 5.84263·10⁻⁸
F and μ_1	exact. μ_1 = 0.99435… < 199/200
μ_(576/577)	enclosure width < 10⁻³³, inside the stated 10⁻³⁰ interval. 1 − μ = 1.0614·10⁻⁶
Fit comparisons, exponent algebra, coefficient 4283584	all hold
Gap table	exact. The minimum is c − a2 = 6.24·10⁻⁸

Control. Dropping the fallback weight εF moves μ_(576/577) out of the stated interval.

Tightest margin. The 10⁶ power coefficient needs 1 − μ_(576/577) > 10⁻⁶. The true value is 1.06·10⁻⁶, a 6% margin.

Evidence

• Standard library only; runs in under a second.
• Imports nothing from Extract optional ordinary B2 bootstrap with canonical-source replay #4338. The enclosure code is my own: ln by atanh after reducing by powers of two, exp by Taylor with a Lagrange remainder.
• Extract optional ordinary B2 bootstrap with canonical-source replay #4338's PROOF.md is vendored byte-identically, SHA256-checked, with vendor/NOTICE.md, because its head is not reachable from main. The verifier checks 28 of its phrases.

python3.12 -B scripts/research_package.py --package research/pr4338-b2-chain-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4338-b2-chain-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4338-b2-chain-check outcome=completed

Head: 890a37de5e4dc410bbb2e552091a4ef9c76d2f3d.

Not covered

• The B1/C1/B2 factory composition, restoration, the 1,123-chart registry and the fit predicates beyond the stated comparisons.
• The production factory and any complex caller.
• The source of the legacy target 0.001727989140903569, which is not on main.

Task and overlap

• Card: independent-moment, refined, priority revision 7.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244.
• Extract optional ordinary B2 bootstrap with canonical-source replay #4338 was opened about an hour before this check. No PR or discussion references it.

Credit

The B2 construction and arithmetic are #4338's (Ross Richardson with OpenAI Codex assistance), composing Jose Manuel's sources, Rohan Arun's PR185/387 argument and the PR589 BIT profile. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code