[pinterbanget]

Summary

This adds research/pr4326-bit-root-check/, the first independent check of #4326 (ai-nanachi). #4326 claims a surcharged BIT moment root strictly inside [1744853764761145849274, …275]·10⁻²⁴, which is 0.41562% above PR4183, together with the majorant T ≤ 200Cn + 10⁷C·n^(1−b)·w at b = 0.00174481. No other PR or discussion references #4326.

Claim type: an independent certified finite check. No new κ. It does not accept #4326's construction or caller premises.

Result

All four claims hold, checked with exact rational enclosures (ln by atanh after reducing by powers of two, exp by Taylor with a remainder):

• Root bracket. The moment μ(a) = Σ n_r(r/64)^(1−a)/W + (32·64²/10¹⁶)Σn·(1/64)^(1−a)/W with W = 28416 is < 1 at the bracket's lower end and > 1 at its upper end.
• 200C prefactor. μ_1 = 0.9943517737 < 199/200.
• 10⁷C prefactor. μ_(1−b) < 1 − 10⁻⁷. It holds, but tightly: the margin is 1.42·10⁻⁷ against the required 10⁻⁷.
• Gain over PR4183. It is exactly 0.415620%, the recorded gain_lower. The root is 0.66% above the selected BIT saving. The selected κ is complex-bound, so κ does not change.
• Profile. It sums to 900,416 queries and has rank mass 1,808,352, both equal to RECORD.json.
• Control. Crediting the nine private families to W (Retire two BIT helpers and bind the compact caller at c > 0.00174485376 #4326's own rejected variant) moves the root above the bracket.

Evidence

The verifier uses only the standard library and runs in under a second. vendor/RECORD.json is byte-identical to #4326's record and SHA256-checked. The profile is transcribed from #4326's independent_price.py at the same head. The selected BIT saving comes from the pinned research/e8-bit-p111-tuned/tune/EXPECTED.json. The registered replay and committed-byte preflight both pass at 49e899e9601afa5aa5223e39dceac1c9099db3a5.

Not covered

• Rebuilding the profile from Retire two BIT helpers and bind the compact caller at c > 0.00174485376 #4326's word and remainders. This is the open question, given the 1.42·10⁻⁷ margin.
• The logical supplier, fixed tapes and caller.
• No proof-kernel check.

Task and overlap

• Card: independent-moment, priority revision 7. Main is unchanged at 12fa8c5c844be21bfefb38a19503fbd867a11244 as of 10:34 UTC.
• Overlap was checked at 10:40 UTC: nothing else references Retire two BIT helpers and bind the compact caller at c > 0.00174485376 #4326.

Credit

The construction is ai-nanachi's #4326, building on Ross Richardson's PR4183 and PR4021 and the retained BIT lineage. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code