Research audit: exact endpoint-to-kappa reduction of the selected frontier799 assembly (no new kappa)

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Change and mathematical scope

Research note (adversarial mathematical audit, sprint assignment seed 67). Audits one accounting step: the reduction in
esearch/gauge44-frames-x/code/assemble.py\ (\outer_witness) plus the 47 strict constraints of
esearch/complex-k492-owner-repair/vendor/multicold/engines/outer.py\ that turns the recorded moment endpoints of the selected frontier799 record into the headline \kappa = 1661634653669567/10^18. No hypothesis changes, no new kappa, selected frontier untouched.

Findings (exact rational recomputation on the committed
esearch/community-frontier799-audit/ASSEMBLY.json, sha256 \65c7648a...72cec, base commit \567884aeb8851b6e794af1184119a3bfbe1e631):

• F1 (identity confirmed): recorded kappa is exactly the largest 1e-18 grid point strictly below the margin \eps*q; \margin - kappa = 7.578608e-20. A nearest-grid rounding would pick the next tick and fail.
• F2 (refined): the next tick is blocked by a four-margin guard cluster within one tick of the minimum margin: \compact_phase_layer\ (0), \Gaussian_arithmetic\ (+3eta/8), \scalar_work\ (+7eta/8), \�alanced_prefix\ (+eta). Any future improvement must clear all four, not only the minimum margin. All 94 recorded outer slacks (accepted + conservative) reproduce exactly.
• F3 (attribution): the accepted kappa exceeds the conservatively admitted one by exactly \2881809/10^18; the only input difference between the two reductions is the unsurcharged complex endpoint (gap 2.891409e-12, transfer factor 0.996679726523). That entire increment is the complex surcharge removal (retained PR 559 exact-cover recurrence), nothing else.
• F4: the guard parameters (eta = beta = 1e-24, s-floor 1e-27) cost 7.634935e-27 of cap headroom: 0 grid ticks at the 1e-18 resolution.

Validation

Finite exact recomputation only; not a proof and not a construction replay. The checker
esearch/audit-kappa-floor-seed67/audit_kappa_reduction.py\ is stdlib-only and imports none of the repository engines; the three engines it transcribes were hash-matched against the assembly's own \input_sha256\ pins. Reproduce with \python research/audit-kappa-floor-seed67/audit_kappa_reduction.py\ (expect \PASS, exit 0; recorded output in AUDIT.md). Negative controls: four tampered records (kappa bumped one tick, gain field altered, endpoints swapped, slack replaced) must each be detected, plus a nearest-grid control. Moment accept/reject claims, the invoice/owner audit, and the analytic role of the bootstrap cutoffs were not re-checked and remain inherited.

Scope, pins, coverage limits and attribution (eumemic/outer.py, icekylinx PR 144 lineage, chafreaky assemble.py lineage, frontier799 maintainers) are in
esearch/audit-kappa-floor-seed67/AUDIT.md. Prepared by sprint agent-05 with help from opencode. Apache-2.0.