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Conditional κ = 0.00167975495612554452133567099392070257699831143850258029546032752016286454826032563882630565613284: tighter free epsilon over PR2044 - #2161
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…58029546032752016286454826032563882630565613284: recertified 1e-30000 supplier endpoint and 1e-30010 slacks (kappa +2.00336e-500 over PR1897): fine source-prime padding (PR1786) at the free epsilon -> 1 point, with gauge-free interiors and the radix-distributed union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier
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This was referenced Oct 15, 2026
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This builds directly on pinned PR2044 (
322949a53488d64023fedb89a6774927707e57ba) and tightens only the free outer epsilon point. Delta changes from2*r0to(1025/1024)*r0, withr0=10^-30010, epsilon1-delta, and beta1-3*delta.The exact conditional kappa gain is approximately 1.67811457042620316926405412772e-30013. It first changes the 30,013th decimal place. The supplier endpoint, precision, native words, owners, paid invoice and inherited hypotheses remain unchanged. This is an extremely small arithmetic refinement, not a structural supplier improvement. The exact kappa and gain are in
research/frontier2044-epsilon-refinement/CLAIM.json.This PR depends on #2044. The new contribution is confined to
research/frontier2044-epsilon-refinement/; the inherited parent package is unchanged byte for byte. Its proof bounds the gain around(1023/1024)*q*r0to within one floor-grid step and shows the tight gamma margin remainsr0/1024 > 0.Validation:
PASS_SOURCE_BOUND_COMPLETE_FINITE_OUTER_REFINEMENT: unchanged supplier full finite admission, fresh changed-word native replays, both exact moment engines, adjacent-grid rejection, both sets of 47 outer inequalities, and 114 admission / 12 bit / 15 controller / 8 owner / 6 geometry controls.make verifystops at a confirmed pre-existingsplit-skip-checkpin mismatch forscripts/audit_fused_block.py(both source and frozen pin unchanged from Conditional κ = 0.00167975495612554452133567099392070257699831143850258029546032752016286454826032563882630565613284: recertified 1e-30000 supplier endpoint and 1e-30010 slacks (kappa +2.00336e-500 over PR1897): fine source-prime padding (… #2044). The extra unit suite was interrupted after an inherited Git environment affected isolated fixture setup; settings restored. No whole-repository green or hosted-CI pass is claimed.The parent has a reproducibility limitation: its committed outer artifacts use CRLF, while Linux regeneration uses LF. The unchanged outer checker passes byte-for-byte on Windows. The unchanged native supplier checker runs on Linux. This contribution binds the two completed components without changing any parent assertion or certificate; it does not claim Linux
PASS_RELEASEfor the aggregate parent wrapper. Reproduction and the full gate are documented in the package README.All inherited all-size/compiler, realization, hosting, precision/tape, recovery, analytic, prime-theorem and bit-supplier obligations remain conditional. No unconditional theorem or independent human review is claimed.
Credit PR2044 and Jeremy Kothe's package; PR1786 (Chafik Boukhalfa / Tim Trudgian), PR1673 (Vlado Vojdanovski), PR1758 and the retained outer lineage; PR1625, PR1672, PR1319, PR1297 and retained supplier/native contributors; PR1956 (Josie Elliston), PR1964 (Sagar Thakrar), and PR2029. Existing notices retain the detailed lineage. Prepared under dataisfire with substantial OpenAI Codex assistance. Apache-2.0.