[RossRichardson]

Change and mathematical scope

The T740 owner0/port0 transfer child10 -> child12, axis16 lowers the concave recursive child bill (48,48 -> 47,49) but changes the operator. This source-bound proof tests one-site absorption through reciprocal linear charts that may mix every address, stream and arbitrary dirty spectator restored at exit.

All twenty cuts fail similarity to one pure native tensor phase on active volume N=2^73, even granting any rank 0–73, either direction, any nonzero scalar and free new implementation costs. The required squared trace is 5N at six sites and 6N at fourteen; every positive-rank native tensor requires 7N. The first trace also excludes rank-zero scalar phases. Complete symbolic address sums establish those finite invariants; the written conjugacy argument covers arbitrary charts and restored spectator dimension.

Original separate translations stay fixed. Added address-dependent phases such as iZ_v, nonreciprocal adapters, joint rewrites and increased active volume remain outside scope. No supplier, selected-frontier change or new kappa is claimed.

Task and overlap

Task complex-new-helper-inventory, changed scope: Discussion1167 assigns a changed recursive-cost interface; this closes the pure-native-child/global-chart obligation rather than searching a new helper inventory. Canonical claim.

Base 463113d675af7410ac91d53a4fed51ec6494eb9a, priority 6, unchanged at the 21:19:58 UTC refresh. SOURCES.json pins every runtime source to canonical ancestry, PR3148's allocation lineage, and PR3275's exact cited head 74d54090585e4b2c6d648be30f4ac0e8e4466c67.

PR3254 permits fixed scalar stream charts; PR3275 permits character-dependent charts and arbitrary middle eigenvalue functions while keeping characters separate. This result permits global mixing but requires a pure native middle tensor, so the PR3275 domains are incomparable. Arham Tahir's related uniform tensor-lane trace classification is credited; the new calculation concerns the nonuniform required T740 cut operators.

Submission overlap fully paginates 348 open PRs including drafts, 2630 closed/merged PRs and 2147 Discussion records at 21:20:05–21:21:28 UTC, without warnings. Text/metadata and local-ledger coverage omit arbitrary diffs and unpublished work.

Validation

At 45f5aec228cacc6d31a31e3bbc23fc32fd2584c8:

• Registered CPython 3.12 replay passes with both optimized exact checkers. They authenticate all 2,717,280 fill rows, establish the complete symbolic baseline and twenty full cut operators; the primary also checks 200 finite literal cuts at ten characters.
• Both optimized CPython 3.14 checkers pass from the committed read-only Git-free export. All 30 publication/input files and 31 export files including its manifest verify. Three final source-bound local checkpoint stages executed fresh. The export includes the inherited loader's actual selected-record/catalogue reads.
• Separate phase representations, quadratic elimination and direct connected-component enumeration agree. Each quadratic oracle checks all 549 forms through three bits and 15 four-bit parity forms. Successful cross-character conjugacy, rank-zero active-i phase, expanded iZ_v spectral boundary, omitted translation, bridge sign and inverse-order controls distinguish the scope.

python3.12 -I -B scripts/research_package.py --package research/idle-global-chart-similarity

Hosted CI and maintainer review are separate from local validation. The eight-stream completed-child projection remains inherited; full native/supplier cold replay, physical adapter tariffs, all-size implications and formal-kernel verification are unrun.

Credit

Ross Richardson/PR3275/3254/3220/3229, Gonzalo-Mier/PR3199, Nick Petalas/PR3187, Jeremy Diviney/PR3148, Gareth Davidson/PR1387, Arham Tahir's reciprocal Clifford trace work, Rohan Arun, dcharb78, Marius-Paul Dumitrean, Jeremy Kothe and the retained native/geometry/selected-source lineage. Ross Richardson with substantial OpenAI Codex assistance (GPT-6.1 Sol Max), including a separately tasked automated mathematical checker. No independent human review. Apache-2.0; frozen predecessors unchanged.

Open next questions

PROOF.md and TASK.json state the reopening contracts. Before testing a joint rewrite, paid nonreciprocal adapter or changed middle address-phase alphabet, specify its actual arbitrary-dirt endpoint and complete recursive/source/frame/routing/volume/stock/precision/restoration bill. iZ_v only passes a spectral boundary control here; no chart or affordable implementation is supplied. No further search is reserved.