[Clear1nsight]

Change and mathematical scope

This source-pinned package independently verifies three separate geometric certificates beyond the single-site #5124 census. It supplies no favorable native witness, physical caller or new κ.

• Fixed pivot group 499 / axis 7 with all 1,022 nearest charts at each of partners 172, 497, 504: 3,066 two-site candidates. The independent engine reconstructs all 12,264 complete profiles and 102,200 incidence ranks; 24 exact polynomial certificates establish nonnegativity for 0 ≤ C ≤ 1/200, and every point energy is positive at C* = .0030217758. The point minimum excess is −H1+H2+H3−H4 ≈ +.00259378145148.
• The 43 explicitly retained zero moves occupy distinct groups with 172 paid identity incidences and no selected-selected row. Exact per-move paid-profile equality and unchanged helper profiles prove that every one of 2^43 subsets preserves both invoices separately, without enumerating assignments. Completeness of the predecessor's census is not independently claimed.
• A separate fixed star uses bridge 172, all 1,022 nearest bridge charts and only leaf alternatives (499, 7), (572, 25): 4,088 active candidates. All 8,176 complete profiles / 114,464 ranks and 26 exact certificates are checked. Energies are nonnegative on the same interval and strictly positive at C*; the separated active minimum is −2H1+H2−2H3+2H4 ≈ +1.98225837689.

These domains are not combined into a global interacting family. Baseline/declared zero alternatives remain ties. The native word, frozen boundaries, common-group charts, owned centre calls, scalar/warp contacts and 408 productive helper owners remain fixed. These results do not exclude changed words, scalar contacts, ownership or physical interfaces. Historical bridge-unrun wording is preserved in the older capsule and superseded only for the separately declared star. No phase/native/physical/compiler/outer multiplication admission follows.

Task and overlap

TASK retains the exact canonical complex-new-helper-inventory card, refined to this supporting verification. The original frozen research base is 20a1e31; publication integrates canonical a5df48c and its separately owned shared-tooling fixes. Scientific source/result pins are unchanged. The public diff against that integration base contains only 49 files in this module.

Source #5124 is pinned at 0335701. The related #5125 split-contact graph/scalar-word investigation has a different common-gauge premise and is not duplicated, imported or dominated. This package closes the authorized fixed-graph design round; reopening needs an actual changed cost lever and complete source-bound invoice.

Validation

Exact reviewed/exported head: e6ee9334a989227cc0e342b700d577f360325496.

python3 -B scripts/research_package.py --package research/fixed-pivot-joint-clifford-ceiling --check-only
python3 -B scripts/research_package.py --package research/fixed-pivot-joint-clifford-ceiling
python3 -B scripts/check_research_commit.py --package research/fixed-pivot-joint-clifford-ceiling --check-source-history
python3 -I -W error -B research/fixed-pivot-joint-clifford-ceiling/verify.py
python3 -I -O -W error -B research/fixed-pivot-joint-clifford-ceiling/verify.py

Registered replay executes only the four unchanged independent graph/pair/edgeless/star validators. No author search, census, model, native circuit, compiler or Lean runs. Each fresh JSON must match its frozen receipt byte-for-byte. The graph reconstruction checks 19,197 chronological nodes, all 31,108 original zero-paid edges, signed paid/warp/helper incidences, selfloops and parallel charges. Independent controls retain selfloop, parallel-count and invalid-helper-rank distinctions; this wrapper also rejects unsafe archive paths.

The two deterministic compressed capsules retain about 35.48MB of raw receipts/history in about 1.32MB. Container hashes and every decompressed member hash/length/mode are separate. Six source text captures and DISCOVERY equal raw Git bytes plus one LF: both variants and original connector evidence are preserved and explicitly tested. A transparent source-history-only ours merge preserves the original research tree; later normal canonical integration restores all canonical source paths exactly. No inherited historical receipt is silently repinned.

Final local checks PASS: registered normal/optimized replay (28.229 seconds together), source-history and committed-input checks, official export integrity, and Git-free read-only normal (12.341 seconds) / optimized (13.118 seconds) replays with identical outputs and unchanged bytes/modes. All 49 committed payload files match the official export; all four original evidence trees remain byte-exact. The CI-equivalent helper run reports 414 tests, OK with 17 platform-dependent skips (266.823 seconds). Earlier sparse-checkout attempts could not find canonical fixture directories; their failed logs are retained, and the final run followed materialization of those unchanged fixtures. No test or scientific code was changed.

Official export SHA256: 9a8e46ba2642c43a738be58765c9012b41534fd7b325b2c41848dc5a7cf57f0e. The final validation and helper receipts bind exact commands, clean environment, return codes, timing and log hashes. Hosted run 39945641149 passes at contribution head e6ee9334a989227cc0e342b700d577f360325496: 414 helper tests / 17 platform skips, both actual registered normal and optimized replay commands, and committed-input integrity. Both modes report PASS_THREE_SEPARATE_JOINT_CHART_CERTIFICATES. This verifies the declared three separate certificate domains; author search, source census, native/phase lift, compiler and outer admission were not replayed.

Credit

Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance in derivation review, independent exact verification, transport/provenance packaging and documentation. Credit Cinna Davis / 1337isnot1337 for #5124 geometry, nearest-neighbor theorem, source census and witnesses; Cao Yifan/#4610 for the native word; Dugongue/#4654 and the inverse-chart/phase lineage; Astra for the bounded designs; the independent graph/receipt reviewers; #4470, zxv, Jacob Alan Sussman, E8, Clifford and the retained native/helper/scalar/precision/compiler/outer predecessors. Original scientific bytes, manifests, licensing and attribution remain unchanged; Apache-2.0 source notices are retained. No external paper/PDF is vendored.

Open next questions

A useful new construction must change an actual physical cost or a complete paid/eligible-target contract. Any favorable model would still need a phase-correct chronological lift, every warp/contact/boundary and arbitrary-input/helper endpoint, the true raw-dual orientation, full ordinary/precision/compiler reserve and outer transfer. These three bounded certificates establish neither physical optimality nor a universal obstruction. No further variant of the same fixed geometry is proposed here.

[Clear1nsight]

HANDOFF
Research discussion / PR / artifact: PR #5161, research/fixed-pivot-joint-clifford-ceiling; predecessor #5124. Published through Browser; this is the canonical package handoff. Fixed-geometry round closed, no ongoing construction reservation.
Exact commit: e6ee933; original research base 20a1e31; publication integration a5df48c.
What is established: Three separate exact fixed-source/common-group-chart results: 3,066 fixed-pivot pairs strictly lose at C* = .0030217758 and are nonnegative on [0, .005]; all 2^43 subsets of the 43 retained edgeless zero alternatives preserve paid/helper profiles separately; 4,088 active fixed-star choices strictly lose at C* and are nonnegative on [0, .005]. Independent full-profile/rank replay, original scientific capsules, raw/capture provenance and immutable source history are retained.
What remains uncertain: No combined/global-family theorem, source census completeness proof, phase/native witness, physical supplier/caller, full finite/precision/compiler/outer bill or new κ. Different words, scalar contacts, ownership, interfaces and other chart domains remain outside scope. Hosted run 39945641149 passes at contribution head e6ee9334a989227cc0e342b700d577f360325496: 414 helper tests / 17 platform skips, both actual registered normal and optimized replay commands, and committed-input integrity. Both modes report PASS_THREE_SEPARATE_JOINT_CHART_CERTIFICATES. This verifies the declared three separate certificate domains; author search, source census, native/phase lift, compiler and outer admission were not replayed.
Smallest useful next task: Name an actual changed physical cost lever and complete source-bound paid/eligible-target invoice; do not extend the same fixed geometry by another seed. Preserve every original owner/helper and the true dual orientation before construction.
Reproduction command and expected runtime: python3 -I -W error -B research/fixed-pivot-joint-clifford-ceiling/verify.py and the same with -O; about 14 seconds per mode in this environment. Registered research_package replay and source-history commands are listed in README; official Git-free export is supplied with exact validation receipt (SHA256 9a8e46ba2642c43a738be58765c9012b41534fd7b325b2c41848dc5a7cf57f0e). CI-equivalent helpers PASS: 414 tests, 17 platform-dependent skips; prior sparse-fixture failed attempts retained.
Predecessor credit: Cinna Davis / 1337isnot1337 #5124; Cao Yifan #4610; Dugongue #4654 and phase/inverse-chart lineage; Astra bounded designs; independent graph/receipt reviewers; #4470, zxv, Jacob Alan Sussman, E8, Clifford and native/helper/scalar/precision/compiler/outer predecessors; related different-premise #5125. Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"complex-new-helper-inventory","scope":"Three separate fixed-source joint-Clifford certificates: 3066 pairs, 2^43 edgeless zero-model subsets, 4088 star candidates. Independent complete-profile verification; no combined/global theorem, physical caller or new kappa. Round closed.","base":"a5df48c55ea806d7952b65acc9c76d878ff09b13","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5161"}