[chafreaky]

The retained compression layout has local halo fields of length L+2A; padding every one to 2L would multiply volume by 2^D. This uses dyadic side L and core stride C=L-2A, with a binary main coarse range t_i/L. The main tensor has exactly T records and supports the existing binary coordinate router.

An additive odometer emits all main halos in one fused source-tape walk. Its actual head travel, including the final rewind, is below 4T under the written overlap cutoff. Nonbinary tails and physical wraps are isolated in a sparse region: with the stated eventual parameters its tile volume is below T/p^5. Sorted requests, one input join, legacy local solves, and an ordered output repair are all charged. Sparse catalogue gaps are scanned explicitly. The main output uses inverse routing and fused padding removal, not a full-volume sort.

No new kappa or joint-axis Gaussian solver is claimed. This is the compression layout adapter. The main-box Gaussian arithmetic and expansion remain separate obligations. The analytic transfer retains the same global H, physical-period cuts, principal-window contraction, normalization and error allowance, with new core origins.

Run python -B research/fused-dyadic-halos/verify.py /absolute/new/output. Seven explicit streams cover 26,264 records and 28,112 odometer updates, including complete control restoration. Five operator shapes cover 291 probes and 67,685 exact output entries, with full basis columns for the two smallest shapes. Four mutations expose omitted wraps, omitted tails, wrong repair precedence and wrong core stride. Twelve large census cases are exact counts, explicitly not payload executions. The local fixture is a periodic three-point contraction with nearest-index selection, not a Gaussian inverse.

Fresh macOS Python 3.11.15/3.14.8 and Linux Python 3.12.3 wrappers passed with byte-identical complete CHECKS and RESULT artifacts. Nine source pins match parent Git bytes. Validation records the exploratory p^-6 cutoff failure at p=101 and the sufficient, consistently used p^-5 bound. GitHub CI is separate.

The all-size fixed-tape and analytic transfer is a written conditional argument. Finite controls do not prove it, and no Lean proof or unconditional multiplication theorem is claimed. Existing source files are unchanged.

Credits: the retained RaD/hipotures phase-cell, microbox, bulk-layout and arbitrary-source routing reports and their cited interfaces. New fused layout, sparse repair and controls by chafreaky with OpenAI Codex assistance. Apache-2.0.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Fused binary halo layout with sparse wrap and tail repair.

Review and limits: The finite local fixture is a three-point contraction, not a Gaussian inverse. Joint Gaussian arithmetic, expansion and all-size tape arguments remain separate obligations.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: f14e5881b7681641fade599b5389995843088e20. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.