Conditional κ = 0.0017148565406944334: pre-life hosting and a frame-refit alias on the #2588 T74 words

[philippeVV]

Summary

Conditional κ = 0.0017148565406944333620724957866041817002… (exact kappa in research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json; κ = C − 10⁻³⁰⁴⁶ − 10⁻³⁰²², with C the certified 10⁻³⁰⁰⁰ complex endpoint). This exceeds #2588 (jeremykothe2, 0.001714252039260245…) by +6.045e-7 (≈0.035%), and #2673 (0.001714600409398252) by +2.56e-7. Built on #2588's head 8cd9dc8. The exact gates are in verify_release.py.

New mechanism: pre-life hosting. After a cold width-4 helper h has restored itself and retired, it hosts the entire life of a later width-9 helper L that starts at dimension 0.

• One B warp carries h's cold-end frame onto a dim-4 frame E at L's first gate.
• L's dirt-compensation reads become anticipatory corrections t += c·K_op(h), pulled back through the target-only precondition.
• h stops being cold, so its zero buffer is freed.
• Six hostings are used: 482←273, 483←275, 494←289, 495←291, 507←305, 519←321. This is the only admissible form of "gap borrowing" we found. Live-lender gaps fail, because B-phase warp records cannot be undone before cleanup.

Frame-refit alias. Gate B894 (add 515 += 563) is lowered from dimension 6 to dimension 5. That is its exact propagated floor. The lowering makes the retired-lender alias 653←563 legal.

• A refit census finds 48 refit-OK pairs and no fixed-frame ones.
• Only 653←563 pays. The width-5 followers lose money, because their freed width becomes isolated rank-5 idle.

Fill. We used an LNS/evacuation fill on the stacked words. Their certified packing ceiling is C ≤ 0.00171514043461; the bound is an interval-arithmetic LP dual plus a lattice-index tightening, shipped as search-side evidence. Per call this gives 415 helpers (#2588: 422), local profile {1:2374, 2:646, 3:297, 4:120, 5:26, 7:8} and widths {4:26, 5:9, 7:62, 8:78, 9:240}. Idle is {1:17428, 3:6614, 5:5163, 7:170, 39:1, 48:26535}.

Verification

From a fresh git archive of 2e2cf56 on Linux (Python 3.12; numpy, gmpy2, sympy, mpmath, psutil):

python verify_release.py --main <archive root> --work <dir> --native-cache <dir> --jobs 2

• Run 1 (12 min): PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION 0.0017119208420413077…, then PASS_RELEASE 0.00171485654069443336207249578660418.
• Run 2 (8 min): same PASS_RELEASE.
• diff -r against a fresh archive is empty, so verification does not mutate the package.
• Stages checked by new/rebuild_borrow.py: prelife, refit563, alias1.
• Controls:
  • pre-life: 78 per word, cleanup re-derived, all rejected for the expected reason;
  • refit: the un-refitted frame is rejected with "warp frame mismatch";
  • alias: rejected for real reasons.
• Also passing: both words pass audit_local forward and dual. The native chain (5 steps), Lemma G, and Conditional κ = 0.001714252039260245: swapped helper labels for lenders 80 and 88 on #2530's source-partner words, with an evacuated owner fill #2588's PR2478/PR2508 guards and ENTRANCE-WIDTH-BINDING also pass.
• Two inherited checks changed (documented in the README):
  • the lemmag_stage borrow-mutant control now picks a warp with from-frame strictly between ZERO and FULL;
  • width_spot_helpers was updated, because 482 and 494 are now pre-life borrowers.

Independent checks (separate code, not the package's):

• A randomized non-commutative matrix replay of both shipped words passes forward and dual. The derived cleanup equals the shipped one, and the paid profile and inventory match.
• The fill keeps every role inside its window with no overlaps. Its idle profile matches, the deficit identity holds (23680), and the rank mass is 4,816,512.
• A 40-digit root of Σ n_r (r/73)^(1−a) = 66304 over the total profile gives C = 0.0017148565406944334….

Scope. All of #2588's and #2530's conditional assumptions are inherited unchanged. The bit side is not binding, with headroom ≈2.9e-5.

Credits

• zxv: Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530 source-partner words, order and dispatch.
• jeremykothe2: Conditional κ = 0.001714252039260245: swapped helper labels for lenders 80 and 88 on #2530's source-partner words, with an evacuated owner fill #2588 label swap, plus Conditional κ = 0.001713879320009017: owner evacuation on #2530's source-partner words #2575/Conditional κ = 0.001703713039257905: a sixth #2436-type alias (helper 656 borrows lender 88) on the entrance-raised T74 words #2526/Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474/Conditional κ = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words #2462/Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447/Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435 and the package this builds on.
• rohanarun: Conditional κ = 0.0017137844912361143: repacked owner fill on #2530's source-partner words #2571.
• tekuuu: Conditional bound: four aliases + 24 entrance raises give κ = 0.001699160892139825 #2436.
• Vlado Vojdanovski: Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322/Conditional kappa = 0.001677160151714381 via capped phase-cell fusion #1673.
• mdumitrean: Verifier: audit_local.py accepts non-centre cut gates; additive guard and regression fixture (no new κ) #2478/Conditional κ = 0.001676896669021299: pivot-566 helper-donor kernel on PR1319's T74 exact fill (+4.14e-8) #1625.
• ywz65: Reject helper endpoint aliases before independent frame checks #2508.
• Cinna Davis: Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226.
• All other inherited credits are retained in the README.

New here, by Philippe Van Velzen with substantial Claude Code assistance: pre-life hosting, the refit alias and census, the fill search with its certified ceiling, and the controls.

🤖 Generated with Claude Code