[1337isnot1337]

Coordinating 49 scalar-contact frames with 13 arbitrary helper entrances improves the round-two word in Cao Yifan's #4610 while preserving its actual full eight-axis main interface. The p16 raw crossing moves from about .00302155515 to the rigorously enclosed (.0030216758, .0030216759). Fresh native, absolute-phase, finite/compiler and outer arithmetic checks support conditional κ = .00302166, under the retained assumptions. This is not a frontier advance: #4610 also contains a stronger round-three word, priced at conditional κ=.0030217754 in #4635. The pinned input here is research/warp-interface-20261022/ACTUAL-WORD.json.gz, not research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz. The construction is a small positive result for the former. The completed rebound found no profitable candidate among 511 rank-one, 2,937 rank-two and 512 rank-three common-kernel cuts, allowing coherent center changes and shared native-map changes. SEARCH.md states the exact restricted family and floating discovery boundary; SEARCH.json and the optional search code bind the newer input and case counts. These are bounded observations, not exact ceilings.

The new local invoice is:

paid   {1:2183,2:416,3:507,4:135,5:40,8:8}
helper {4:28,7:5,8:38,9:337}

Both local rank masses increase by 13; the entire p16 rank surplus remains 752. All 408 helper inputs remain arbitrary, independent and productive. Scalar opcodes/order/coefficients, native G maps, main endpoints/adapters, eight paid rank-eight centers and owned lifetimes stay fixed.

The constructive search mechanism is a fixed common-subspace deletion/extension at chronological contact nodes. Nested frame constraints turn its exact rank-power energy into a minimum-weight closure/minimum-cut problem. The successful patch is replayed independently of the floating discovery solver. Formerly zero paid edges require explicit representation if they may become paid; the proof separates the smaller first search from that extension.

Validation on Linux CPython 3.12:

• Registered package replay passes both retained all-column interpreters on all 632 persistent inputs, both orientations.
• All 11 changed paid frame pairs and 13 changed helper normalizers pass exact Clifford/tableau and absolute-phase lowering, both orientations.
• Exact rational local-gain and complete p16 raw-crossing signs pass; rank and global-phase mutations reject.
• Two rational moment engines, funded paid/productive completion tails, finite uniform-rank bounds, ordinary BIT stock, and all 54 strict plus four functional outer predicates pass. Four unsupported parameter patches reject.
• Metadata/pins and committed source-history integrity pass. Huge finite uniform word bounded, not materialized.

Only research/hyperplane-retiming/ is added. The vendored source closure is unchanged and pinned. Base main: b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, refreshed before submission. Selected κ remains .00302015. Physical/native, compiler, precision/tape, analytic and recovery assumptions remain; no unconditional theorem or independent human review is claimed.

Credit Cao Yifan, Cinna Davis's #4470 lineage, Dugongue's #4654 chart grammar, zxv, Jacob Alan Sussman and all retained scalar/native/Clifford/compiler sources. Prepared by Cinna Davis with substantial OpenAI Codex assistance, Apache-2.0.

Open next steps: compound cuts that create new paid transitions; change native maps jointly with the common subspace; seek a center/controller change that increases rank surplus materially.