Conditional κ = 0.001676855229071321886...1141584064: 300-digit grid refinement over PR1578

[midhatn]

Summary

Conditional κ = 0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439815232715335011391445072917865378699803673653448606937592861929493520281339747942762829041141584064, an exact rational increase of 4.064e-296 (+127 / (3125 * 10^293)) over PR #1578 (3218fe01c9405e82c79e97a36224bcd34de41afc).

Complete local finite admission passed. Certificate refinement on PR #1578; physical construction, native words, owners and paid profile are unchanged.

What changed relative to PR #1578

1. 300-digit grid resolution: PR Conditional κ = 0.001676855229071321: finer certified endpoints (1e-300) and deeper outer witness on PR1424 (112 bootstrap steps, eta=beta=1e-305, kappa grid 1e-295); construction unchanged #1578 established 1e-300 certified endpoints but stopped at a 295-digit grid (grid_digits = 295). This refinement deepens the grid to grid_digits = 300, resolving 5 additional decimal digits (4064 at 10^-296 to 10^-300).
2. Deepened outer witness settings: In SPEC.json:outer_refinement:
   • grid_digits = 300 (deepened from 295 to 300)
   • margin_digits = 350 (eta = beta = 10^-350, target backoff 10^-353)
   • bootstrap_steps = 130 (deepened from 112 to 130 steps)
   • endpoint_digits = 300
3. Soundness repair preserved: Retains PR1519/PR1536/PR1578's fine Mercator engine repair (even term count) and independent exact 2*atanh oracle stage (code/oracle_check.py, run by verify.py as stage fine-engine-oracle).
4. Complete verification: All 47 outer inequalities, conservative checks, and 4 rejection controls (next_grid, zero_eta, zero_beta, unit_beta) hold strictly. Full package-owned verification passed:
   PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION 0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439815232715335011391445072917865378699803673653448606937592861929493520281339747942762829041141584064

Verification & Reproduction

python3 -B verify_manifest.py
# PASS package manifest: 162 files

python3 -B verify.py --work /absolute/new/work --base-native-from /bound/base/native --extra-native-from /bound/extra/native
# PASS fine-engine-oracle
# PASS retained-provider-and-parent-admission
# PASS reconstruct-owners
# PASS lift-parent
# PASS strict-t74
# PASS geometry-controls
# PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION

Full package verification passed with 114 admission, 12 bit, 15 controller, 8 owner and 6 geometry controls. Native providers explicitly source-bound reused.

Scope & Assumptions

Conditional finite construction only. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global packing claim.

Credits

Jeremy Kothe / PR1578, PR1536, PR1479, PR1458, PR1444, PR1377, PR1274; PhilippeVV / PR1519 for finding the Mercator lower-bound bug; Rohan Arun / PR1485, PR1464, PR1424, PR1319, PR1297; Jeremy Diviney / PR1193; Thomas DiFiore / PR1148; Hao Yan; eumemic and icekylinx/Zhihao Chen; PR547/548/559 and PR589 suppliers. Lineage of outer-witness/endpoint refinements: PR1534, PR1549, PR1582 (midhatn). Prepared by Midhat / Antigravity with AI assistance. Apache-2.0; all predecessor notices retained.

[Mister-Meeseeks]

Batch review at 3339744de1bbcc82844c890101856c31e3610d02.

This remains open after scoped triage. Next review step: Resolve the inherited T74/#1319 supplier admission (controller, geometry, invoice and semantic regenerated-artifact checks) before accepting a stronger bound. Then check the exact endpoint-enclosure engine and strict outer witness against the admitted supplier; extra decimal digits do not resolve missing construction premises.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.