Research: sharp rank-one block budgets and per-block overhead obstruction

[Arham-Tahir64]

The revision-3 rank-shape task needs a complete budget before block-decoder synthesis. This package supplies sharp integer thresholds for reblocking the selected complex word's rank-one payload, with gathering/copy/restoration work charged on top of the old idle bill.

For maximum block rank 16, at least 363 of 2,412 rank-one children per invocation must be reblocked to pass an optimistic primitive-saving target 5% above the baseline packing-ceiling upper bracket. Full reblocking permits only 10 additional integer rank units: a single extra rank-16 call fails. For every block rank 2..51 and every saving up to that target, one additional rank-one call per nontrivial output block erases the local payload saving. Concavity proves the optimal integer partition and monotone thresholds; exact adjacent signs are retained for all 50 caps. The mass-preserving 1/99 rejection corroborates the predecessor's stronger rank-one-deletion obstruction.

Only research/complex-rank-one-block-budget/ is added. This is a favorable cost-alphabet relaxation and conditional overhead-tariff obstruction, no physical decoder, supplier admission or new kappa. Compatibility, chronological frames, dirty-state realization, compiler/hosting, precision/tape and outer reduction remain unproved. The 5% target concerns the complex primitive ceiling; the selected bit budget would already bind a realized construction there. Full selected cold replay, native execution, Lean, hosted CI and independent human review were not supplied.

Validation passed under Python 3.12.14:

python3.12 -I -B scripts/research_package.py --package research/complex-rank-one-block-budget

The retained atanh/Taylor engine and separately written outward-rounded binomial engine agree on the baseline bracket, all 50 thresholds, overhead decisions and block-tax inequalities. Replay checks 10,274 complete small integer partitions and eight mathematical/domain controls. Six tests cover exact-square validation of all 72 square-root oracle bounds, incorrect-oracle rejection, source drift/inventory omission, numeric and bool/int receipt corruption, and optimized read-only relocation. Direct optimized Python 3.14.7 replay and whitespace checks also pass.

Started from current main adc34159e0d6dc3dd2af2bdba3f5ca7376ef957e, chooser nonce 3ab0bbddb657f850e7894cfc57f8d29e, priority revision 3. TASK.json explicitly records the scope change from physical decoder synthesis to its first screening experiment; passing this experiment is not satisfaction of the construction acceptance gate. SOURCES.json pins four live inputs plus historical provenance. Coordination: Discussion1596. Pre-submission overlap covered 733 open PRs including drafts and 244 Discussion records with complete pagination and no warnings; coverage does not establish novelty. Refreshed upstream 81e81af6 leaves guidance, selected record and all live input blobs unchanged.

Credit Douglas Colkitt / #1240 for the selected local-word ceiling and ideal-lever model, Sagar Thakrar / #1012 for the coverage law, Rohan Arun / #1094 and #1042, Jeremy Kothe, Hao Yan / FanPUYen, Josie Elliston and the retained construction lineage. #1264 supplies the pending-profile census; Sagar Thakrar's #1334 supplies different bit-side ideal-lever budgets. This package adds partial integer reblocking and a fully additional-work tax. Prepared by Arham Tahir with substantial OpenAI Codex assistance in research, proof, both arithmetic implementations, tests and writing. No subagents. New material is Apache-2.0.

[woklerx]

Independent audit of PR #1605 at 488f2ec.

Required Python 3.12 registered replay passes. Independent fixed-point log/exp enclosures certify adjacent signs for all 50 caps and fully added rank-one overhead limits,1275 strict concentration exchanges,50 block-tax inequalities, and rank 16 extra-mass boundary 10/11. Wrong idle credit demonstrably gives a false pass.

Evidence: aa70591 / research/pr1605-independent-budget-audit. Exact source Git-blob/SHA256 pins, checker, deterministic receipt and reproduction commands are retained in the artifact.

Independent arithmetic is target-specific; the all-q concavity argument remains a written proof. No physical block decoder, inherited all-size/hosting admission or new kappa.

Next: Find a chronological group whose complete additional work fits the narrow rank16 budget; optimistic rank profiles do not construct that group.

Credit: Arham Tahir PR1605; Douglas Colkitt PR1240, Sagar Thakrar PR1012, Rohan Arun PR1094/1042, Jeremy Kothe, Hao Yan and retained supplier lineage. Substantial OpenAI Codex assistance; no independent human review or new kappa claim.

Exact committed audit artifact. Commit aa705916d2ff0a100b4e814b83eb791bc90c08c7; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 15.

[Mister-Meeseeks]

Batch review at 488f2ecf1835c6d813e96543656dddf0062fdc9a.

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

Reviewed scope: Concavity and independently certified power intervals give exact integer reblocking thresholds and additional-work budgets. The one-overhead-call obstruction is conditional on that tariff; no physical grouping or new supplier follows from the relaxation.

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.