Research: rank-eight coded-helper endpoint and complete mixed-cost obstruction (no new kappa)

[nightangelflowerwin-ops]

PR781/PR855 follow-up: shorten the coded helper from rank nine to rank eight in both provider placements and both supplier families. Two early restoration reads plus fully billed internal dirty-response compensation give four new native words. All 714/717 arbitrary columns pass in both orientations. The fixed end-B inverse row proves that rank eight is the minimum endpoint for the remaining monotone cleanup.

The paid local change is 4 H1 - H2 - H3; the freed hosting rank must still be filled. An independent positive-binomial power engine, Cartesian packing census and four-variant residue DP exclude all 1,282,974 nonempty mixtures of the original and new variants under the fixed PR626 geometry. Every favorable complete invoice exceeds the threshold by more than 0.018922942318, even granting extra preparation, phase, access and scalar work free. Consequently no phase/global supplier admission or new kappa is claimed. This is a reproducible limitation after native integration, not a claim of improved selected exponent.

The pinned selected PR799 target requires a larger complex saving; normalized moments are monotone, so the same fixed-geometry obstruction excludes matching that target. This does not refute PR799's different construction or alternatives outside the explicit geometry/programs.

Reproduce (Python 3.11+, stdlib, fresh external output):

python -I -B research/coded-helper-early-end8/verify.py --out /fresh/external/directory
python -I -B research/coded-helper-early-end8/test_controls.py /fresh/external/directory

The parent also supports -O; native children explicitly retain assertions. EXPECTED.json freezes full constructions, receipts, recounted invoices and the minimum witness. PROOF.md explains the algebra, lifetime lower bound, packing relaxation, complete mixture DP and outward rounding. SOURCES.json pins all five repository inputs and the unchanged vendored PR855 package.

Validation: normal and isolated optimized eight-word replays; five new native failure controls, five retained original controls, original recompression control, three potential controls; all 1163 patterns/43,031 potential inequalities and nine exact square-root checks; offline minimal-root relocation with spaces; source-drift rejection and selected-record integrity. VALIDATION.md records the signed-rounding correction, initial relocated receipt mismatch and successful final checks. The companion PR865 aggregate repository run stopped on eleven ten-second timeouts in an unchanged historical test. No repository-wide or hosted-CI pass is claimed.

Credit NeoKazuya's #781 and #855 for the coded core, provider embeddings, whole-helper relaxation and residue potentials; retained notice credits Douglas Colkitt, Chafik Boukhalfa, DreamingOfClouds and predecessors. This package extends the helper lifetime and independently reimplements the enclosure/census/mixed-variant check; no priority for predecessor methods is claimed. Upstream refresh through #888 found no new consumed predecessor; main is still f567884aeb8851b6e794af1184119a3bfbe1e631.

Prepared for nightangelflowerwin-ops with substantial OpenAI Codex assistance, Apache-2.0. No selected/frontier/upstream edits. Inherited all-size/compiler, physical realization/hosting, precision/tape and analytic assumptions remain; no full multiplication theorem or practical speedup claim.

[Mister-Meeseeks]

100-PR batch review at 9778ba2d891468996b81eb50c389bb4169df0025.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Early rank-eight coded-helper endpoint and exact fixed-model mixture rejection with idle completion charged.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.

[nightangelflowerwin-ops]

Milady