research: all-endpoint nonlinear recovery obstruction for PR2918

[RossRichardson]

Change and mathematical scope

PR #2918 excludes scalar paired extraction of helper408 at one rank-seven endpoint. This package strengthens that fixed-word obstruction: for both pinned PR2894 providers, every endpoint of rank at most seven prevents exact recovery of any nonconstant eligible-input function, including arbitrary nonlinear decoding, eligible-only entrance recoding, and finite appended processing with fixed, monotone frame dependencies.

The exact census covers all 43,435 rank-seven subspaces, grouped into 239 complete terminal supports. Every support has a purely scalar forbidden-input minor with a dyadic-unit determinant. Independent protected inputs can therefore mask every eligible-input change. The known PR2908 rank-eight pre/post pair still passes, giving sharpness for every nonzero dyadic module within this frozen interface.

This is finite exhaustive evidence plus a written all-parameter proof. It is not a word-independent rank-eight bound, a new supplier, a paid-cost improvement, or a new κ. The entrance cut, independent dirty inputs, inherited center-cut frame convention, fixed output identities, and complete data/control dependencies are explicit. Changed words, extra observations, new warp resets and free pooling across incomparable endpoints are outside the result. Native/physical realization, complete recursive costs and outer admission remain unproved here.

Task and overlap

• Base: 997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6; canonical guidance refreshed at 2026-10-17 14:22 UTC.
• Task: complex-new-helper-inventory; scope key pr2918-all-rank7-unit-nuisance-nonlinear-monotone-barrier. Changed scope: the user assigned a generalisation of the fixed-word obstruction. This does not satisfy the card's positive changed-interface construction gate; it rules out endpoint-only repairs under a larger decoding/causal contract.
• Scientific source: Exclude rank-seven helper408 extraction at the fixed terminal cut #2918 at 9360ba7312cf8961e672e9eb26c612719028d39d; Conditional κ ≈ 0.001720398337: two-sided helper extraction and charged T74 packing #2908 at 51309592971e3b5be935599eed2a95404dc7781e; Conditional κ = 0.001720184528377469: two more staged quartets on #2863's shared-kernel words #2894 at 18d03c447886895ef9abf888398178e0428533ca.
• Nearest comparison: Conditional κ ≈ 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969) #2979 at be191346391661f4d35fc0d1508d0a6029572576 already contains all-endpoint pairing screens on later words and a changed-word rank-seven positive. The addition here is the unit-minor census and nonlinear causal consequence for the two old pinned words. The underlying indistinguishability/quotient principles are standard.
• Canonical investigation in Discussion #2612. Live overlap refresh completed at 14:23 UTC with complete pagination over 290 open PRs and 1,943 discussion records, plus local package/ledger coverage of closed work. It does not search all diffs or establish literature novelty.

Validation

CPython 3.12.12, standard library only:

python3.12 scripts/research_package.py --package research/rank7-terminal-information-barrier
python3 scripts/check_research_commit.py --package research/rank7-terminal-information-barrier

Both pass at reviewed head 0a632b00ef59a9f43b1f6c7965ff1ca7a3f188f3. The first runs two exact implementations under -I -O -B: the authenticated predecessor forward engine with a new census, and a separately written reverse-adjoint/RREF/Bareiss verifier. Both consume the fixed certificate and check the rank-eight positive. The primary has eight rejecting controls per provider; the independent path has seven with exact expected diagnostics. Source pins and all 13 package/input files match the commit.

Fresh pre-submission mathematical, verifier and packaging reviews led to explicit cut/control/ancilla premises, nonzero-module sharpness, and corrected changed-scope metadata. No unresolved issue was found in that declared domain. See VALIDATION.md for the evidence boundary. Hosted CI is separate. No full historical supplier suite, selected cold replay, formal-kernel proof or independent human review is claimed. Only the new package changes; predecessor sources and selected records are unchanged.

Credit

Ross Richardson's #2918 supplies the original obstruction; Jeremy Diviney's #2908 supplies the rank-eight extraction; Jeremy Kothe's #2894 supplies the parent words; Marius-Paul Dumitrean's #2979 supplies the prior all-endpoint comparison. Earlier input/preload/exact/native credits remain in the predecessor notices. No predecessor sources are re-vendored. Apache-2.0, with substantial OpenAI Codex assistance and separately assigned mathematical/verifier reviewers.

Open next questions

TASK.json and the README identify the bounded follow-up: choose one existing changed-word rank-seven positive example, determine exactly how it destroys the certified nuisance block, and bind the entire entrance, source, restoration and recursive bill. This could identify a useful paid escape; a rank defect alone neither constructs nor prices it. No further synthesis or stronger bound is claimed in this PR.