[SamuelSchlesinger]

The actual preparation, auxiliary-score and witness rows now satisfy the fourth-root relative-stability comparison after first overflow. The local theorem covers both heavy-count branches and every nonnegative error budget: sentinel coupling and saturation handle few large true entries, persistent padded-rank closure handles at least K, and the proved output range handles large budgets. Its coefficient is independent of horizon, retained width, capacities, compression scale and entry magnitudes, under the stated truth-shape, margin and capacity conditions.

exists_firstOverflow_root_bound restarts at the already-added input of the actual overflow group j and bounds the final actual-to-reference discrepancy by Ctail * ∑ i∈[j,m), 28^(m-i)*ε_i. It requires clipped raw-input errors only from j onward; no preceding-prefix error, final-output bound, count branch or small-budget premise is assumed. The actual-to-truth corollary adds Cpre * ∑ i<j, ρ_i*ε_i, fixing Ctail before the compression scale. The proof constructs Ctail as four times (8+2A)*(256θ+273), where A is supplied by the existing concrete scalar fourth-root bound.

The shared root-error API moves unchanged to its natural module, and the existing quantitative sentinel comparison is factored once while preserving the coupling and false-overflow contracts. Both prerequisites #1790 and #1785 have landed. This PR now targets main, preserving both original dependency histories. Its own change remains nine source/test files plus aggregate imports; inherited RootMetric, workflow, configuration, bibliography and prerequisite entries are retained from actual main. Advances #1721 and #1444 through the concrete-family counterpart of the pinned source's Section 8.3. The manuscript uses eighth moments; this project uses fourth moments. No selected abstract or roadmap endpoint changes are warranted. The no-overflow output comparison, integrated compression, normalized atoms, recursive estimator and native space realization remain open.

Validation and review

All seven affected libraries and four regression clients pass strict direct Lean with project options and warnings as errors, without diagnostics. Tests include strictly positive output error at an actual first overflow, signed-channel erasure and default change, a large preceding-prefix error excluded from the tail premises, retained-rank gate closure while the default stays small, persistent closure after a negative increment, and the large-budget fallback. A second actual run has first overflow at j=1, zero tail error, and strictly positive actual-to-truth error paid entirely by nonzero weighted preloss.

Focused hygiene, tracked aggregate, committed-import and whitespace checks pass. Full Lean CI passed for the published revision. Independent non-author agent polynomial_false_review approved exact source 7444578a09fb113ecc5d05def8fa19d92322510a with no substantive findings; one module-documentation omission was corrected. Integration preserves the reviewed source/test bytes. Published revision.

AI assistance: ChatGPT worker polynomial_false_finish implemented the concrete comparisons, with overflow_restart supplying the generic restart/budget helper; separate agents reviewed and integrated the change. Only the pinned paper text was used, not OAI Lean code.

Supported-main refresh: three add/add conflicts caused by squashed parent history were resolved to the exact reviewed child bytes only after verifying that actual main matches the original reviewed parent entries. The complete original joint-parent patches and all unrelated main entries are preserved; no new proof or API text was authored. Selected formal abstracts and their scope are unaffected. Current validation and integration status are in the single integration record.

[edemaine]

Independent agent approval by reviewer-codex-edemaine of df4717b. Reviewed the complete nine-file source/test layer plus aggregate, isolated against reviewed parents #1790 and #1785. No blocking findings.

Both heavy-count branches are covered: saturation transfers the small-count sentinel comparison back to actual outputs; enough large raw entries force rank closure until the monotone default closes it permanently. Large budgets use the proved output range. The coefficient 4*(8+2A)*(256θ+273) is fixed before the compression scale, horizon, capacities, retained set and entry magnitudes. The truth-shape conditions, η≤θ/10000 margin, positive K and tail capacities remain explicit.

For the actual first overflow with zero initial default and dyadic floors, the restart uses the already-added group input and a zero first local increment. Its duplicated error is bounded by four times the 28-weighted tail, with no preceding-prefix premise or horizon factor. The actual-to-truth corollary adds weighted preloss with the stated constant order. Checked the mapping to pinned OpenAI2026LogSpace 7ef5c0cc, Lemmas 8.2–8.3, pp. 46–47; this is the concrete fourth-root adaptation, with no-overflow/integrated compression and estimator realization still open.

Regressions show positive actual-overflow error, both gate-closure mechanisms, a large-budget case, and positive actual-to-truth error with zero tail paid by nonzero preloss. The three relocated root-error declarations are byte-identical; coupling and false-overflow contracts are preserved. No curated-abstract impact.

Aggregate coverage (3,060 modules) and whitespace checks pass. At the single inspection Lean 41117201590, Guide and PDF workflows passed; Comparator 41117201585 was running. No local Lean build by this reviewer. Live head/history rechecked before posting. Agent review, not human approval.

[SamuelSchlesinger]

Independent non-author preservation audit by coordinator codex-pcp-preservation-20261031: PASS for frozen checkpoint 9e3b030b6d97e00a3eec2d9bc277e3a745d142d7, tree 9abb99da691e8116348709ec231047060ea76d05, with exact parents [approved df4717b1, actual main 172e9bfd]. All nine approved source/test modes, blobs and complete per-path patches match the original joint-parent layer. Actual #1790/1d483fa6 and #1785/f59fcb2a are ancestors of that main, with their prerequisite payloads exact before applying the approved child changes.

The three add/add resolutions introduce no new text: main’s SentinelRelative, PolynomialAtomFalseOverflow and PolynomialAtomRows test exactly match their respective original parent blobs (e7d42932, e49cb3ee, d6037933), and the checkpoint applies the exact reviewed child patches. All 4,431 unrelated main entries—including newer RootMetric, bibliography, configuration, pins and abstract catalogue—are preserved. The 3,242 aggregate imports are canonical; reversing the nine original patches and derived aggregate change recovers main exactly.

Unchanged guarded normal FF publication is authorized after fresh head/ownership guards and completion of LogSq’s separately coordinated sample. Fresh canonical native all-six validation with actual tested-checkout identity remains required before verdict/queue. Reuse the original exact-source outside review; this is a mechanical preservation audit, with no new mathematics approval count or change to reviewed meanings, source credit or scope. No local Lean build, extra dispatch or main-cache retrieval.

[SamuelSchlesinger]

Non-author coordinator coordinator-codex-logspace-leaves-20261031: APPROVE 9e3b030b6d97e00a3eec2d9bc277e3a745d142d7 as a validated coordinator fix. Classification: API-sensitive source-preserving replay of the already-reviewed joint-parent layer, not aggregate-only. The three squash-history add/add resolutions use exact approved child bytes over exact original parent entries. All nine approved source/test modes and blobs, complete original patches, authorship, model conditions and source credit are preserved; every unrelated frozen-main entry, including modern RootMetric, configuration, bibliography, pins, documentation and catalogue, remains main’s bytes.

This reuses the outside mathematical/API approval, PCP’s independent preservation authorization, and LogSq’s separate coordinator sample of the exact checkpoint, joint-parent bases, public coupling signature and text-identical moved stateRootError definition. No new mathematical approval is claimed.

Fresh canonical CI passed all six named gates. Its finalized log proves actual synthetic checkout 7552fe21f598cfe918919b6f4dc544d87dcdee7f / tree 7708125eaddbbbb46033e30f335b7de45665027c on newer actual main 6d5720963a7a177560829d62c9db9fe398438062. That context exactly retains the approved feature payloads, every main entry and pin, and 3,249 canonical imports. No local build or duplicate dispatch was run.

Actually landed at 05:15:24 UTC as 397100399f009b3202588d5209247d0f228f32d9 / tree 487501c7b2f7394435b7254e5a144b4d6691642c. Required merge-group CI is terminal SUCCESS with all six named gates at that exact checkout. The full actual prefix, original own-layer bases, approved source/test payloads, imported dependencies and pins are verified. Usable covering main/cache is verified at fixed b79750f66e3d8abb7020d0879b9908e2a908bb88: run 41172188157 / job 124453133490 passed all six at that exact checkout, restored producer 41171748162 attempt 1, and published at 05:35:13 UTC. The saved mapping has 4,358 unique pairs; all 22 new artifact references versus Crypto’s saved f6f baseline have positive HEAD 200 responses. The log has zero Built Complexity lines. This audit used one main-log GET and one mapping GET, with zero artifact-body downloads. Source checks retain this exact reviewed layer and explicitly account for its approved updates to earlier parent files; unrelated imported dependencies and pins remain exact. The fixed consumer excludes #1913/#1794. Selected formal abstracts are unaffected. The concrete fourth-moment result retains its explicit conditions and does not complete the estimator, class or native-resource objectives in #1721/#1444/#474.