[CubeJerry]

Change and mathematical scope

Execute every coordinate carry on every complete low-type fiber, then physically permute the low blocks and retire the old cache after its last consumer. The source is #4989's actual frame506, in both directions. For fixed N=8s and odd prime q, arbitrary runtime odd Q and positive Z, the literal program has complete O_(N,q)(V) transitions and an explicit visited-cell bound, V=|GL_N(F_q)| Q^(N²) Z.

This joins the unchanged #5332 decoder, #5849 complete-owner rotation and #5487 low commit. It extends #6241's one-leaf connection to the full supplied domain and resolves that component's #6296 cache-lifetime gate. All extents, staging, owner installation, rewinds and cleanup are executed and priced.

The map is B_M:(G0,H)->(G0 M mod q,H+C_M(G0)); the opposite source direction computes B_(M^-1), generally not B_M^-1. The separate homogeneous high action is required for the full matrix route.

Sources and verification

Base: 7c49fe3. SOURCES.json pins all 16 live inputs by Git blob and SHA256; no predecessor files change.

python3 -B scripts/research_package.py --package research/bit-whole-low-carry-commit

Expected: PASS_REGISTERED_RESEARCH_PACKAGE. Author and lead normal/-O runs passed: 18 complete cases, all 48 GL2(F3) low types, Q=1/3, Z=1/2, both source directions, two independently implemented literal interpreters and two regenerated tables. Actual source binding covers 1,920 carry occurrences. A separate rational/modular review checks all actual source column envelopes and 5,280 reduced cases, including composite Q and shared q,Q factors.

Ten controls cover wrong cache/order, premature commit/erasure, wrong carry direction, omitted coordinate zero, owner aliasing, missing installation, wrong low permutation and endpoint-preserving extra work. Complete remote tree matches the tested twelve additions.

Limitations and credit

No new κ. N,q and s are fixed before runtime; the full GL8 payload is not executed. The supplied complete-stream ABI, blank private-tape precondition and successful-return contract are explicit. Homogeneous routing, literal selected-layout production, full dispatcher/stock/tariff and outer admission remain open. No human or proof-kernel acceptance is claimed.

By @CubeJerry with substantial OpenAI Codex assistance and separate AI review. Credit the cited predecessors, David Arias's literal-machine lineage, and #5985's unit-modulus observation; #6467/#6474 are comparison-only open work. Apache-2.0.

Proof, exact pins, executed evidence and open questions.