[dillona]

Whole-idle transforms account for most of the current controller bill. This package deletes them and proves an explicit triangular endpoint for every pair count p: scalar conjugation gives a degree-(p-1) border whose constant term is the desired independent monomial map. It then prices recovery instead of treating the limit as an exact supplier.

The constructive result is partial: no new admitted supplier or κ. Removing idles also removes target rank. A determinant/Jensen certificate excludes C≥.006 complex and C≥.007 BIT for every p in the frozen #4470/BIT inventory and stated output model, even with free extraction and optimized main-degree allocation. The original >.01 objective therefore fails in this model.

Two concrete recovery routes are decisively priced. K≥2 whole-controller evaluations fail every concave moment even retaining fresh independent helpers; copied main inputs receive output credit only once. An exact copied-input X decoder has forced per-port query rank p−1 and also fails every concave moment before Y correction. These are scoped barriers; shared internal queries, cross-port methods, changed native words and different output contracts remain open.

A separate finite complex approximation lemma gives a global error/precision budget. Under explicit completed-oracle norm assumptions, the raw forward p16 controller has h=p−1 and H₀(f)=2^(97566f+S), with S the finite scalar norm allowance. This does not establish the amplified recursive caller, paid-oracle implementation or BIT scalar extension. Ordinary matrix tensor-degree reasoning is explicitly separated from chronological supplier substitution.

Only research/controller-border-interface/ is added (15 files). Start with README.md; DISCOVERY.md, BUDGET.md, DECODER.md and EXACTIFICATION.md contain the proofs, RESULT.json the exact receipt, and REVIEW.md the independent author-side AI review.

Validation: registered Python 3.12 replay; Python 3.12/3.14 isolated optimized runs; all Laurent coefficients p=1..8; independent rational p2/p3 implementation on 24 instances and all columns; exact all-p budget certificates; 48 wrong-weight controls, 4 polynomial-degree examples, 9 precision examples; 7 actual source/receipt/code mutation rejections. Committed-byte/source-history preflight and 18-file export integrity pass. Exported replay passes without Git under a network-denied process policy. Floating exploratory roots are excluded from the exact receipt. No selected cold replay, formal kernel or independent human review is claimed.

Scientific base and final refreshed main: f626db5; priority revision 7 unchanged. Scientific commit d5f8e3f; publication fd5d3be. The 10:33 UTC overlap refresh covered 397 open PRs and 3,560 Discussion records with complete reported pagination. Canonical investigation: #4611. This takes #4602's controller-level handoff with a changed endpoint contract; #4603 and #4610 address different fixed/exact interfaces. Selected frontier unchanged.

Credit Cinna Davis/1337isnot1337 (#4440/#4470), zxv, Jacob Alan Sussman and retained native/BIT/precision/outer contributors; Matarener/Mark (#4602/#4603) for the fresh diagnosis; DaysSky and Ryanson Jonathan for the quotient proposal/audit informing selection. Prepared by Dillon with substantial OpenAI Codex assistance and separate AI strategy, algebra, budget, exactification and review workers. Apache-2.0.

[dillona]

Hosted CI at publication head fd5d3be12b9d6ee92c8fa089d95bd529c3236563 failed in the shared planning job before package selection: run 39764590203. Package replay was skipped, not passed.

The onboarding suite reports 331 tests, four failures and 11 skips. All four are in test_research_current_status.py: the CI navigation still describes frontier1094, the selected decimal formatting differs, the historical-snapshot banner is absent, and a historical heading contains “selected.” The focused six-test module reproduces those same four failures locally on Python 3.12.15.

The test module and all three inputs it reads (docs/research/current-status.md, docs/ci-verification.md, certificates/selected-result.json) are byte-identical between canonical main f626db5c3 and this PR head. This is the existing shared navigation blocker also observed on #4532/#4586; no shared navigation or selected-frontier file is changed here.

Local scientific evidence remains separate: registered Python 3.12, isolated optimized 3.12/3.14, exact receipt, seven mutations, committed-byte/source-history preflight and final-publication Git-free/network-denied export replay all pass. An upstream navigation repair and hosted rerun remain necessary. No full native/selected replay or hosted package pass is claimed.