[Clear1nsight]

Change and mathematical scope

An exact typed complementary B/C consumer works, but its complete recursive bill loses. A stronger written bound excludes every positive saving for the declared serial fixed-owner model. This is a scoped construction and ceiling contribution; no new kappa or selected-frontier change is claimed.

On the 56 matched exceptional pairs, execute C1, then B2, then Y-=2X, with a shared central Q and disjoint seven-axis blocks D1,D2:

L(-2) B2 C1 = diag(D2 D1 Q, D2 D1 Q).

The other 56 ordinary pairs require L(-2 Q^-1), hence 56 paid rank-one query children. Replacing that correction with a scalar shear is false. All 1,040 independent persistent inputs are retained: 224 main fields and two disjoint banks of 408 helpers. Main targets are 112 rank-14 and 112 rank-15 jobs. Every inherited helper is credited once. Complete paid rank mass is 9,579 versus target mass 9,403: deficit 176.

This specifies exact typed endpoints and actual gatewise raw inverse transpose under the audited supplier/owned-temporary interfaces. It does not freshly emit or phase-check a complete 1,040-field native trace. Physical witness, positive caller moment and funded compiler/outer transfer remain separate milestones.

For n>=2 whole calls on the same 224 main owners, one shared Q and n disjoint seven-axis blocks, with only the source helpers as additional productive fields and main target ranks at most 7n+1, the optimistic target-minus-paid moment satisfies:

t=1-C, 0<C<1, n_B+n_C=n
M(C) <= 224*(7n+1)^t - n*(224*7^t+112) - 8*n_B*7^(-C) < 0.

Cleanup and finite work are granted free only for this rejection bound. At C=0 the upper bound is 224-112n-8n_B; two C calls only tie zero. The all-exponent proof normalizes the refreshed B/C direct-price gap and checks derivative bounds 1795/7 and 1857/7, then uses strict subadditivity. It is not an extrapolation from a tested point. Changed ownership, interleaved extra productive jobs, shared producer work or different geometry lie outside this ceiling.

Task and overlap

Task complex-new-helper-inventory, priority revision 7, explicitly changed to this donor-assigned complementary consumer study. Base/current main: 624de9dc66858af0945e5f8a0942488d62280d43. Scientific package head: 890fadd4683ac206fa0c39ad58ff80932bdba26b. Current additive head: d5772576a9f260768d39eea0adde36e08602e889, two commits / 17 changed files: 16 new scientific package files plus the shared test-fixture repair independently submitted in #4857. Scientific bytes are identical between those heads.

Exact predecessors: #4703 4cc96829fad977aecf0018b26beb067cfd2689a5; #4712 b75a27bf07f1584b20babfddf887493981cd5949; #4674 84cf25a580db9ed2b4b1371c40689a035711364e. Five unchanged source snapshots retain Git blob IDs and SHA256 pins. #4712's existing native endpoint/phase/cost audit is inherited, not repeated. #4674's direct-price proof method is credited; the explicit pair and the refreshed C-profile serial bound are the changed scope. #4660's older autonomous-B/A-path and #4712's dirty-helper/120-head query models are different covered rejections. #4839 is the separate actual centre-chain terminal policy.

Live targeted PR bodies, related heads and bounded Discussion windows were checked. The overlap helper could not refresh remote data because gh is unavailable; sparse local coverage and lack of exhaustive Discussion pagination remain explicit in OVERLAP.json. No exhaustive novelty or task-reservation claim is made.

Validation

Python 3.12.3, Linux, standard library only:

python3 -I -O -B research/complementary-consumer-feasibility/verify.py
python3 -B scripts/research_package.py --package research/complementary-consumer-feasibility
python3 -B scripts/check_research_commit.py --package research/complementary-consumer-feasibility --check-source-history

Registered replay, exact committed-byte/source-history preflight and a Git-free optimized export with PATH=/nonexistent pass. Actual source-byte and type-sensitive receipt corruptions reject. Mathematical controls reject the wrong exceptional coefficient, omitted ordinary Q^-1 correction and forward word substituted for raw dual.

A second agent independently rederived the derivative and universal-n proof, counted the paid/target profiles without importing this verifier, and checked a separate exact rational 2x2 fixture with non-involutive Q=-2/3. It confirmed the raw-dual order and rejected the ordinary scalar-only correction. Parent also read the proof/checker, recomputed the pair identity and reran optimized verification. These are automated/agent checks, not independent human or proof-kernel acceptance.

Not freshly run: the retained native phase suite, full physical caller, finite precision, fixed-tape compiler, Lean, outer admission or selected scientific cold replay. The initial hosted run failed before package replay because detached Git maintenance raced temporary sparse-fixture cleanup. Repair #4857 is included additively; run 39863812767 completed successfully at exact additive head: all 347 helper tests pass (11 expected skips), this scientific package replays successfully, and its committed-input mutation gate passes. Local exact-head registered replay and source-history checks pass. Scalar, movement, storage and precision bills remain separate finite obligations.

Credit

Chris R / Clear1nsight with substantial OpenAI Codex assistance, delegated construction and a separate agent proof/accounting check. Apache-2.0. Credit Dugongue #4703, Cao Yifan/intqwq #4610/#4712, Cinna Davis #4674 and controller lineage, zxv, Jacob Alan Sussman, DaysSky and all retained source notices. No independent human review is claimed.

Open next questions

See PROOF.md, README.md and TASK.json. Stop enlarging this serial consumer family. A useful successor must change ownership/incidence, share actual producer work, or improve the native paid profile enough to restore a discount. Begin with one actual cross-contact word and disjoint target census, then a favourable optimistic complete bill before implementation. Canonical result #4853 and the required handoff record the scope and next task.

Merge danger

Door: two-way. Blast radius: isolated research package plus a disposable-fixture test repair. No production helper, predecessor evidence or selected result changes.