Conditional κ = 0.001661960547713947858091 by exact T37 grid refinement

[1337isnot1337]

The accepted T37 assembly rounds its outer witness to a 10^-18 objective grid. Replaying the same complete construction on a strict 10^-24 grid gives the exact conditional bound

κ = 1661960547713947858091 / 10^24 = 0.001661960547713947858091,

an increase of 858091/10^24 over the selected 0.001661960547713947. This is an extremely small numerical certification refinement, with no new circuit or practical runtime claim.

Status: conditional bound. Exact base: 8bddbee377e2f3ce1f1247196c4b290d55767d20; OS seed 24, complex-supplier track. Only research/t37-rational-refinement/ is added; the selected record and all original sources remain untouched.

The fresh full assembly reproduces the original output exactly, then replays the entire refined assembly. All 876 selected source files match, all 47 strict constraints pass, and both moment-engine tables, both seven-step bootstrap chains and every invoice input digest are unchanged. The 1024-bit complex charge, 2048-bit row extra, bit surcharge and all finite row/physical/tape/precision guards remain paid. The next fine-grid point is rejected. The exact source adaptation is three grid expressions; three derived kappa expectations and a hash-preserving portable pivot path are updated in the temporary specification.

Reproduce with standard-library Python 3.11+:

python3 -I -B research/t37-rational-refinement/verify.py
python3 -I -B research/t37-rational-refinement/test_package.py

Expected: PASS_T37_RATIONAL_REFINEMENT kappa=0.001661960547713947858091 sources=876 full_assembly=PASS strict_constraints=47 controls=7, then PASS_T37_REFINEMENT_PACKAGE relocated_full_assembly=PASS controls=8.

Seven controls reject finer/coarser adjacent points, zero eta/beta, insufficient complex/row charges and under-reported primitives. Eight package controls pass from a minimal standalone source closure with spaces in its path. The source-bound selected-record and whitespace checks pass. The full exact assembly, adaptation receipt, source pins and logs are reproducible; no receipt was edited into a pass.

Native geometry, ownership, emission and cold-ancestry evidence are inherited from the immutable maintainer-reviewed construction. This performs fresh complete pricing and assembly, rather than a new native emission. All-size/compiler, physical realization, precision/tape/recovery and analytic assumptions remain conditional; no full Lean or unconditional multiplication theorem is claimed.

Repeated full open-PR inventories and all-state searches found no matching finer-grid contribution. PR942's all-T 10^-18 grid result is preserved; no real-root or architecture-wide optimum is claimed. Larger pending PR987/1004/1005 use different local words and are not imported or treated as accepted. Jonathan Capalbo, Chafik Boukhalfa, Hao Yan, Jeremy Kothe and the full supplier/engine lineage retain credit. Substantial OpenAI Codex assistance and Apache-2.0 terms are disclosed in NOTICE.md. No pinned sprint coordination issue existed; the claim is local.