[zxv]

A new native frame contact changes the paid profile from H2+H3 to H1+H4 while retaining every independent helper output. The complete conditional transfer gives κ = 0.00300120 and sufficient uniform rank 2^2299850000000, reducing the exponent of #4441's sufficient rank by 71.88×. At #4441's unchanged κ=0.00300105, the sufficient rank is 2^249900000000, a 661.53× exponent reduction. These are template bounds, not runtime speedups.

This builds on my 0.0023 construction, my higher-moment/logarithmic compiler work, Cinna Davis's query thinning and fresh-helper retiming (#4440/#4441), and Jacob Alan Sussman's mixed-target flow. The retained native, Clifford, BIT and outer sources keep their full contributor notices. Substantial OpenAI Codex assistance; no subagents. Apache-2.0.

Construction and complete consumer

At phase B scalar contact 480, replace frame 732 by the three-dimensional span [45,133,336], in both literal dual orientations. The four incident ranks change from [2,2,1,3] to [1,1,2,4]; strict concavity improves the paid moment for every 0<C<1. Scalar order/coefficient, warp and center contacts, main endpoints and all 408 productive helpers remain fixed.

• Complete p17 word: 19 full calls, 16 individually paid query shears, 3,584 whole idle jobs, 11,560 productive fields, 69,273 paid requests and rank surplus 800.
• Exact raw-root bracket: (0.0030012390170, 0.0030012390173); declared κ leaves explicit slack.
• Both completion and original-paid tails are charged at tested C=0.00300122, tensor power 675, cutoff 18^675, target floor 22^675 and higher-moment offset 3/25.
• Logarithmic compiler contraction 15/16, power 160, with exact finite-rank inequalities and previous-grid controls.
• Retains ordinary BIT admission 0.0034 with atom 0.004; all nine outer rows, 54 current predicates, four guards and 63 legacy predicates pass.

Start at the package README, proof, and literature assessment. The optional line/hyperplane min-cut discovery reproduces the explicit contact; exact replay needs no optimizer.

Concurrent work and source boundary

The submission refresh found #4447 at 322e0ec764aa7ef7801383feb1f656e460dd8bed, which reports the same B/480 contact and paid profile and declares the slightly higher κ=0.00300123. This contribution retains the reviewed κ=0.00300120 and supplies the smaller paid-tail and uniform-template bounds above, plus its separate discovery/replay path. No unique-discovery or strongest-κ claim is made.

Depends on unchanged pending #4440 (40e22a83ed660d3d6074c4f2dbf14bfb621eee51) and #4441 (5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39), included in branch ancestry. New work is confined to research/native-lattice-retiming/; the source/provenance manifest resolves against the public #4441 head. Canonical main and priority guidance were refreshed before submission.

This is an author-checked conditional construction awaiting independent scientific review. Native/all-column, owned-erasure, whole-job matching, finite precision, analytic, physical tape, prime and exact-recovery contracts remain premises. The enormous product/uniform words are algorithmically specified, not materialized. No unconditional/formal theorem or selected-frontier change is claimed.

Validation

CPython 3.12.8, macOS arm64:

python3.12 -B scripts/research_package.py --package research/native-lattice-retiming

• Registered replay passes: both native orientations, two interpreters, all 632 arbitrary persistent columns, owned-center erasure, and all four new edge types with absolute-phase decoding.
• Two exact moment engines, full invoice, both paid tails, compiler ranks and complete outer ledgers pass. Wrong-frame, phase-only, short-product and outer mutants reject.
• Git-free isolated optimized (-I -O -B) replay passes with exact receipt equality; changed-source and changed-receipt controls reject.
• Optional C++20 discovery reproduces the contact. Metadata/source pins and committed-byte checks pass on the submission branch.
• Full source-history preflight is unavailable in this shallow checkout; exact public source heads and consumed bytes are retained and pinned. No Lean, Docker, historical all-suite replay or hosted package pass is claimed here.