Conditional κ = 0.001676855229071321886...03439: 200-digit outer refinement over PR1536

[midhatn]

Summary

Conditional κ = 0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439, an exact rational increase of 9.000000e-200 (+9/10^200) over PR #1536 (527d7623009f295b7311e98ae36f5e2fbdbbc3e5).

Complete local finite admission passed. Certificate refinement on PR #1536; physical construction, native words, owners and paid profile are unchanged.

What changed relative to PR #1536

1. 200-digit grid resolution: PR Conditional κ = 0.001676855229071321: finer certified endpoints (1e-200) and deeper outer witness on PR1424 (82 bootstrap steps, eta=beta=1e-210, kappa grid 1e-199); construction unchanged #1536 established 1e-200 certified endpoints but evaluated on a 199-digit grid (grid_digits = 199, stopping at ...0343). This witness deepens the grid to grid_digits = 200, resolving the exact 200th digit (extracting 9 at 10^-200).
2. Deepened outer witness settings: bootstrap_steps = 90 (up from 82), margin_digits = 250 (eta = beta = 10^-250, target backoff 10^-253), endpoint_digits = 200.
3. Soundness repair preserved: Retains PR1519/PR1536'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 0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439

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 / 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. Prepared by Midhat / Antigravity with AI assistance. Apache-2.0; all predecessor notices retained.

[Mister-Meeseeks]

Batch review at f98c217351ff1a5e5d831d75070c3adb4422c1bf.

This remains open after scoped triage. Next review step: Refines only the outer witness of the pending PR1319 family. Review the arithmetic separately, but whole-head admission requires resolving the parent regenerated-container binding and completing its controller/invoice/geometry replay; do not promote an unadmitted parent through a finer numerical grid.

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.