DONE: later-source compact repair with inactive saturated digits (PR1603)

[Arham-Tahir64]

DONE — PR1603, head b9cfdff.

The all-n invariant sufficient guard admits saturated t digits where both later-source subcalls are inactive, while blocking compact carries into active positions and retaining no interior u-load carry. Its exact two-state density gives 9085/16384 at n=2,K=6,G=2, versus PR1247's 1971/4096. For n=1 only, it equals the maximal invariant full-map agreement core and has fraction 1-3/(4B).

Evidence: 598,592 complete quotient states, 73,600 exact digit cases, 544 original physical-interpreter comparisons, all 5,824 sorted exceptional-repair payloads, seven mathematical controls and nine source/algorithm/receipt corruption controls. Python 3.12.14 registered replay and Python 3.14.7 minimal read-only relocated optimized replay pass, along with the 17 existing compact-control tests and selected-record integrity. Final overlap at 03:46 UTC covered 729 open PRs and 242 discussion/comment/reply records with complete pagination and no warnings.

No production change, new kappa, measured runtime gain, full supplier cold replay, hosted CI success, formal proof or complete multiplication theorem is claimed. Full costs, source pins, proof, evidence and credit to PR1247/1475/1219/763/1108 and Douglas Colkitt/OpenAI are in the package.

HANDOFF: For n>1, enumerate E intersect T(E) on the smallest two-digit complete quotient and derive a carry-state description admitting internal u-load carries or cancellations between individually inexact subcalls. Those cases remain outside this sufficient guard.

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Completed original advisory claim:

CLAIM — later-source compact controls with inactive saturated digits

Question: For the unchanged later-source word, can an invariant repair guard retain saturated temporary digits on inactive positions while accounting for compact carry propagation through both subcalls?
Base: 1f327c6. Task uniform-transfer-audit, nonce b0d948f61caf27df25160f9b811ecba6.
Predecessors: PR1247 at 392316a (nonsaturated two-pass guard), PR1475 at 0bca9e7 (earlier-source saturation), and Douglas Colkitt's retained word.
Method/domain: integer proof for n>=1,G>=1,K>=G+1,0<=rho<K; keep no interior source-load carry, require zero incoming compact carry at p_i OR c_i active positions, and retain target guards there. Derive a two-state exact density, characterize the maximal invariant full-map guard for n=1 only, and exhaust small complete quotients with all dirty fields plus physical interpreter comparisons and failure controls.
Expected artifact: research/compact-late-carry-guard/ with pinned sources, proof, independent quotient verifier and registered replay. Candidate n=2,K=6,G=2 fraction 9085/16384 versus PR1247's 1971/4096 is preliminary until replay. No maximal n>1 claim, production change or new kappa.
Entry overlap: complete snapshot at 2026-10-14 03:32 UTC covered 726 open PRs and 231 discussion/comment/reply records with no warnings; only the stated predecessor scopes matched.
Claim expires: 2026-10-14 05:35 UTC. Expected handoff by approximately 04:20 UTC.
Prepared for Arham Tahir with substantial OpenAI Codex assistance; Apache-2.0. Advisory claim, not exclusive ownership.