[thakrarsagar]

Status: independent verification. No new κ; the selected result is unchanged.

Track 75–84 (independent verification), assignment seed 76 (OS CSPRNG via Python secrets). Base commit 2921874911956718fcaaaf9396fe8267b3cfa9f0.

What this adds

PR991 replayed the selected T37 package and states that its replay is not code-disjoint, because it uses both retained moment engines. This package rechecks the arithmetic chain of the selected record, from the hosted payload to κ, without importing or reading moment.py, base_two_moment.py or outer.py:

1. Profile from the payload. 333 calls times the local paid profile, plus idle children, recomputed from the hosted template. It equals the record's complex_profile, with deficit 11,840.

2. Endpoints. All three endpoints certify: native complex, conservative complex, and the PR589 bit endpoint with the inherited surcharge. The moment is below one at the endpoint and above one at the next 10⁻²⁴ grid point.

   Model	G − 1 at the endpoint	G − 1 at endpoint + 10⁻²⁴
   native complex, 0.001664727258740678855772	≤ −3.362e−25	≥ +2.612e−24
   conservative complex, 0.001664727255848707292019	≤ −1.533e−24	≥ +1.414e−24
   bit, 0.001733427039589844234749	≤ −1.599e−24	≥ +1.669e−24

3. Independent arithmetic.

   • Logarithms come from prime decompositions, using atanh(1/3), atanh(1/5), atanh(1/9), atanh(1/15) and atanh(1/145) with explicit tails.
   • Exponentials come from Taylor polynomials with a Lagrange remainder.
   • Intervals are exact rationals rounded outward to 2⁻³²⁰.

4. Consistency with the record. All 12 recorded retained-engine intervals intersect these enclosures. They are read as data only.

5. κ. The reduction gives exactly κ = 1661960547713947/10¹⁸ and the conservative κ = 83098027241579/(5·10¹⁶). Each is the largest grid point strictly below its margin, and the complex side binds.

Negative controls

1. The next endpoint claimed as accepted.
2. One extra rank-one child.
3. m = 72.
4. The bit model without the surcharge: the next grid point is no longer rejected.
5. κ + 10⁻¹⁸.
6. A truncated exponential, which fails closed.
7. A corrupted pin.

Each is rejected for its stated reason.

Reproduce

make t37-endpoints-independent-verify

Expected: PASS_T37_ENDPOINTS_INDEPENDENT_REPLAY, then 5 tests OK. It takes about 2 s on standard-library Python 3.10+ with no network.

Scope

This verifies one chain: profile, endpoint certification, κ.

It does not check:

• the 47 outer inequalities beyond the binding margin (PR813 covered those for an earlier assembly);
• the bootstrap cutoffs, the owner map, the local word or the hosting;
• the inherited all-size, realization, precision/tape, analytic or bit H1–H5 assumptions.

The surcharge model and the reduction formula are re-implemented, not re-derived. This is not a formal proof.

Related

• Conditional κ = 0.001661960547713947858091 by exact T37 grid refinement #1019 (open) refines the κ grid with the pinned engines. That is a different object, and this package does not use or check it.
• Earlier independent endpoint checks covered older checkpoints: PR960 (binomial enclosures), PR706 (integer root bounds), PR678.

Credit

• Jonathan Capalbo: the selected record (PR942).
• Chafik Boukhalfa, Jeremy Kothe, NewBArch and Hao Yan: its lineage.
• DreamingOfClouds and eumemic: the bit supplier (PR589, PR555).
• The retained engines' authors: the recorded intervals.
• tekuuu: PR991's scoping.

Prepared by Sagar Thakrar with substantial AI assistance from Claude (Anthropic) via Claude Code. New material is Apache-2.0.