[Clear1nsight]

Change and mathematical scope

Retaining #4694's eight arbitrary center inputs changes an actual search premise: #4841/#4690 froze every owned-center scalar contact. This package exposes all 184 such contacts while fixing all 640 endpoint charts, every other chart, the native maps and scalar chronology. It retains all 408 independent helper jobs and charges every incident old-field and center transition. The baseline paid profile remains {1:2201,2:412,3:510,4:127,5:40,8:8}. Independent center productive reward remains zero.

The coherent-block ceiling is strict: for each of 1,022 one-transvection alternatives to the empty chart, every nonempty subset of its 176 contacts increases the optimistic complete paid moment by at least 2-2^theta>0 for every 0<theta<1. This includes long and noncontiguous blocks across different centers. The proof uses 9,198 exact integer maxflow/mincut certificates for nine concave-prefix tariffs, with uniquely empty first-prefix minima.

The complete 188,048 single-contact neighbors and 1,834,488 same-transvection adjacent-pair neighbors have exact minimum paid loss 1+7^theta-8^theta>0. Every actual incident binary rank is recounted. No higher κ, new native supplier, independent center jobs, completed caller admission or selected-frontier change is claimed. The coupled ABI is not substituted into #4610's owned-center caller.

Task and overlap

Task complex-rank-shape-decoder, priority revision 7; scope changed to the retained-centre contact invoice. This is a changed-contract continuation of Cinna Davis's #4694/#4698, Cao Yifan's #4610 and Dugongue's #4841. Permitting nonmonotone general-Lagrangian contacts changes #4696's fixed-subspace phase restriction and #4700's monotone canonical-chart restriction. The old frozen 632-role contact search is not repeated.

Canonical main was refreshed and remains 624de9dc66858af0945e5f8a0942488d62280d43. The #4841 compiler/neighborhood source is pinned at 6debdcdac8fe1c87958f8cd42ccb7db73c0a0eef. Fresh open-PR and Discussion overlap was inspected; #4694/#4698 remain the relevant coupled-interface sources. The separately assigned shared-producer work owns changed-demand exploration. Live #4859 (45352b400f986482a5f9cc16ce76292da5f6bcc3) counts shortest binary chart words, while #4860 (e36ff5b6431d3014b9ca0a1a49a5274d82788252) concerns cyclic canonical-checkpoint costs. Nick Petalas's live coordinated-chart claim targets general cycle-constrained tuple enumeration and expressly leaves source-specific application open. This package certifies the actual retained-640 cost instance; it makes no novelty claim for the general neighborhood theorem. Only research/sol1337-contact-frontier/ changes. A tree-preserving provenance merge retains the exact #4841 history without importing its files into the publication tree.

Contribution head: 5e4cce12a9851fbb46cd7c32cc8177e983771539.

Validation

On CPython 3.12.3 and GCC 13.3 C++20: metadata/source pins, registered replay, normal and optimized scientific replay, committed-byte/source-history preflight, and official 22-file export integrity and extracted Git-free optimized replay pass. The verifier regenerates the 640-role graph, every candidate class and all 9,198 integer cuts. Flow capacities/conservation, feasible flow values, equal attaining cut capacities and residual strictness are checked. Three controls reject a false paid gain, a negative cut and false uniqueness.

A separate read-only AI audit reports no correctness finding. It reran the full verifier, independently recomputed all 34,830 baseline edge ranks, checked all 145 maps are symplectic, confirmed the 176-contact group and 256 internal rank-zero edges, and directly priced 35 nonempty subsets across seven axes. This is independent AI review, not human or proof-kernel review.

python3 -I -B research/sol1337-contact-frontier/verify.py
python3 -I -O -B research/sol1337-contact-frontier/verify.py
python3 -B scripts/research_package.py --package research/sol1337-contact-frontier
python3 -B scripts/check_research_commit.py --package research/sol1337-contact-frontier --check-source-history

Expected marker: PASS_RETAINED_CENTER_COHERENT_CHART_CEILING. Requires c++; compiled binaries and graphs stay in temporary directories. Hosted run 39864815675 passed at exact head 5e4cce12a9851fbb46cd7c32cc8177e983771539: all 346 shared helper tests pass with 11 expected skips, only this package is selected, scientific replay passes and the committed-input mutation gate passes. No native amplitude/all-width phase compilation, replacement 640-column native word, selected cold replay, Lean or outer theorem was run. This is a source-bound optimistic cost model.

Credit

Cinna Davis #4694/#4698 and #4690/#4696/#4700; Cao Yifan #4610; Dugongue #4841; #4470 and its cumulative native/helper/controller lineage; zxv; Jacob Alan Sussman; and all retained scalar, E8, Clifford, precision, compiler and outer authors retain credit. Exact source paths, Git blobs and byte-preserved copies are pinned in SOURCES.json.

Prepared for Chris R with substantial OpenAI Codex assistance by a dedicated gpt-6.1-sol HIGH agent in user-authorized parallel research. Apache-2.0.

Open next questions

The ceiling permits one identical-chart group to move toward one common one-transvection alternative. Mixed alternatives, simultaneous different original groups, independent paired axes and changed scalar/controller/native operations remain outside its scope. Before another expansion, supply one literal changed operation or actual changed request, its arbitrary-input endpoint and complete producer/consumer bill. A role-dependent monomial router must retain each role's address action and dirty restoration; more chart seeds or root digits do not change this ceiling.

Merge danger

Door: two-way. Blast radius: isolated research package, with a tree-preserving provenance merge. No selected record, shared helper or predecessor file changes.

Canonical investigation #4840 and the required handoff record the stopping decision and exact changed-mechanism follow-up.

[Clear1nsight]

DONE / RELEASED — the prospectively declared independent adjacent-pair experiment is complete. PR #4888, exact head b33e3d8670dc604d430e9cbeb86682f258acd52e, archives the result as an additive extension to the existing common-axis package.

All 261,632 opposite-neighbour assignments lose. Their 1,831,424 exact incident-rank checks yield44 histograms, reproduced independently in Python; every complete invoice dominates 3H1+H7-H8, hence costs at least two extra units for0<=theta<=1. Geometry plus the authenticated #4867 single/coherent-pair certificates also closes every different-hyperplane rank-zero pair. All8 rank-eight edges have the exact external inventory giving Delta>=2+6^theta-8^theta>=2-2^theta>0 for0<=theta<1. Their nominal8,355,872-case scan was not run. Together these cover arbitrary independent distance-one neighbours on any one of264 actual internal edges, with all640 endpoints/408helpers fixed and zero centre credit. Larger independently changed blocks and changed words/targets remain unexcluded.

Registered verification, committed-byte/source-history preflight, official33-file export and Git-free normal/optimized science replays pass. A separate read-only agent confirmed allsourcepins and both analytic extensions at the exact head. Hosted run39871223220 passed at exact final head b33e3d8670dc604d430e9cbeb86682f258acd52e:346 helper tests with11 expected skips, original normal/optimized common-axis checks, independent pair replay and committed-input mutation gate. This is registered automated replay, not independent mathematical acceptance. There is no new kappa. The changed-operation successor is Discussion #4902; this graph-screen claim is released.

Original prospective record (retained for provenance):

CLAIM — independent adjacent centre-chart choices sharing one original hyperplane.

Base 624de9dc66858af0945e5f8a0942488d62280d43, priority revision 7. This fixed-invoice experiment changes the common-transvection restriction: for each of the 256 rank-zero internal edges between empty-chart centre contacts, its two endpoints may take the two DISTINCT one-neighbour charts sharing the same original eight-dimensional hyperplane. There are 511 such hyperplanes and two endpoint assignments, giving a declared domain of 261,632 candidates once the source grouping is authenticated. Other contact charts, scalar operations, native maps, all 640 endpoints and all 408 independent helper jobs stay fixed. Centre productive reward is zero.

The motivation is an interaction absent from a common-axis move: opposite neighbour choices can leave their shared edge at rank one, while their distinct external interactions might each lower an eight-rank transition. The illustrative bill 2H8 -> 2H7+H1 is only a question to test against every actual incident edge; it is not a found construction or an available budget. Begin by authenticating neighbour grouping and actual changed ranks, then perform one deterministic complete-domain screen at the stronger developed #4610 saving. Every candidate gain needs an exact rational moment and a literal paid-profile recount before native/phase/raw-dual/caller/compiler work.

#4867 supplies the actual graph and single-group ceiling; the completed common-axis mixed-group extension is being archived separately. Nick Petalas #4864 at eac6ce76eeabdd027b6cb5cbedd0e006e784bfce and Dugongue #4841 supply credited general chart geometry. Picking the two endpoint charts independently changes the construction domain; general geometry is not claimed anew. This task is separate from #4840's retained-centre/prefix-reader experiment. Fresh neighbouring PR reading was bounded and cannot certify unpublished work.

Expected artifact: one source-bound favourable complete paid assignment for physical verification, or a scoped stopping result for exactly this independent adjacent-pair family. Stop if the complete optimistic invoice cannot improve; no random seeds, larger block search or new kappa claim is authorized by this screen. Clear1nsight / Chris R with substantial OpenAI Codex assistance from a dedicated gpt-6.1-sol/high agent. Expiry: 2026-10-23T00:58:01+00:00.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"complex-rank-shape-decoder","scope":"Declared261632 opposite-neighbour invoices completed negative, plus analytic all-adjacent-independent-neighbour closure; supporting source-bound ceiling in existingPR4888, no kappa","base":"624de9dc66858af0945e5f8a0942488d62280d43","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/4888"}