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Pass with named corrections. This is the distinct grade of the completed compilation review of six reconstructed results and two consumed external interfaces for integer thirteenth powers. It is a curated retention of that grade, not a new mathematical assessment or a grade of the later native rendition. The native transformation has since been accepted, and the same-checkpoint source-page standing reconciliation records only the bounded premise-relative compilation review below.

The recorded grader was a fresh-context grader acting in the corpus grader role on 10 September 2026. The primary reviewer and supplementary interface reviewer were distinct independent reviewers. These source-owned library records have no native L-tier to promote.

Exact assessed report and subject

The original report, coverage receipt and grade remain unchanged in working storage. Their full mathematics, coverage and findings are retained natively without a private-path or runtime dependency.

The grader verified both original reports, all ten native Markdown subjects, the four PDFs and the triage note against the assignment. The coverage record gives the exact paths and versions. The native subject is the repository as it stood on 2026-09-10T05:48:43Z. That state could not be resolved from the grader's review copy, so the grader relied on the fourteen subject-content hashes and required revision confirmation before ordinary-clone use. The native filing separately confirmed that state and its unchanged subject bytes.

The grader reported independently rederiving the mathematics against the frozen pages and four retained PDFs. That is the grader's historical inspection, not source reading by the native filing author. No mathematical program or certificate is part of the argument.

Full findings

The numbering below retains all 22 original findings. Private report-line references have been replaced by native section and source locators. Mathematical findings remain attributed to the grader.

Contract compliance

1. OK. All ten checklist items have explicit verdicts. The two inapplicable items state why no mathematical computation or executable reproduction belongs to the argument.

2. OK. All six results are restated with quantifiers and scope before their deductions; the composed conclusion is also explicit.

3. OK. Both interfaces name source, page, exact assumed statement and reading depth as claims checked. Bibliographic identities and versions are in the coverage record, which at the time also carried the PDF hashes; each PDF read is identified there by its edition.

4. OK. The grader corroborated the stated reading scope and exclusions: 17 primary renders covered manuscript pp. 1–6; Corvaja-Zannier PDF pp. 1–3 and 19; Heath-Brown journal PDF pp. 1–2 and 11; and v1 pp. 1–2 and 10–11. Seven supplementary subreview renders covered the stated Heath-Brown pages. The old images are disposable reading aids, not required native artifacts.

5. Required disclosure missing from the original. The report disclosed triage exposure but not that the assignment pre-named two of its three weakest steps. The triage had directed attention to coordinate normalization, the shell repair and the family convention. Those checks were independently derived, but the pre-directed attack selections were not independently identified. The native report now states this distinction in its subject and weakest-step sections.

   Exposure ruling. Besides the unretained triage note that assessed the reconstruction as complete and pre-named two of the three weakest steps, the commissioned read set as it stood on 2026-09-10T05:48:43Z carried the subject pages' own author-recorded standing (under library/diophantine_problems/pipeline_math_2026_tiling_complement/: _index.md lines 171–179, lemma_1_4.md 239–244, corollary_1_5.md 58–64, proposition_1_6.md 229–233, lemma_1_7.md 96–101, proposition_1_8.md 70–77, theorem_1_1.md 116–122) and public-acceptance text for the existence conclusion (_index.md lines 56–75; wiki/problems/diophantine_problems/E0477/_index.md line 7, lines 21–26 and 44–57); a separately commissioned materiality grader acting in the corpus grader role (model: Claude Fable 5.1) ruled on 18 September 2026 by the content test that all three exposures are immaterial, because none states or implies the premise-relative verdict asked of the reviewer and the review's reasoning rests on independent rederivation corroborated by the subreview and the grader, so the pass with named corrections stands unchanged.

6. Required obligation mapping missing from the original. The report deferred grading and listed exclusions without naming the specific recorded obligation a pass could discharge. The exact frozen, premise-relative obligation is now stated below and in the report. The later accepted transformation and standing reconciliation address only that obligation, without changing this historical finding.

Mathematics

7. OK: Lemma 1.4. The gcd/conjugate base-point argument, $h(p_1^{13}:\cdots:p_r^{13})=13e$, support from equal-degree ratios, normalized nonconstancy and $|\Sigma|\ge2$ all hold. All four active-coordinate counts, the two-vanishing-pair classification and $[F:R]$ surjectivity check out. Both $13e\le3(4e-2)$ and $13e\le3e-2$ are impossible for $e\ge1$.
8. OK: Corollary 1.5. Coprimality forces denominator $q=1$; oddness transfers non-power status to $-c$. Thus $N=-c$ is nonzero and not a rational thirteenth power. The affine-to-projective extension is exactly the one supplied in Lemma 1.4.
9. OK: Proposition 1.6 witness bound. $Q$ is strictly positive on the compact max-norm unit sphere; the origin, where $Q=0$, is excluded. Homogeneity and $|u-v|\ge1$ give $\kappa\max(|u|,|v|)^{12}\le(1+|c|)T^{13}$, and $C_c\ge1$ ensures the same $X$ also bounds $|t|$.
10. OK: fixed-shift shell repair. The shells $(R_{j+1},R_j]$ are disjoint and cover $(R_{J+1},X]$. The geometric sum contributes $K_F/(1-2^{-10/13})$ times $X^{10/13}$. The residual box has at most $(2\lceil R_c\rceil+1)^3$ points, absorbed because $X^{10/13}\ge1$. This proves the stated fixed-$c$ estimate.
11. OK: stronger restatement not endorsed. Journal PDF p. 2 defines the shell count on $B/2<\max|x_i|\le B$, whereas v1 PDF p. 1 defines a whole-box count. Manuscript PDF p. 2, Theorem 1.3, states the whole-box form with an $F$-only constant while citing the journal. The shell theorem does not supply that constant, because the residual box scales with $|N|$. The report says the journal does not supply it, not that the stronger assertion is false.
12. OK: exact external interfaces. Corvaja-Zannier p. 438 gives the recalled three-term bound $H(1:u:v)\le\chi$ when $z=0$ in (1.1) and $u,v$ are not both constant, and the four-term consequence under no vanishing subsum on the right, with no printed nonconstancy clause. Heath-Brown journal p. 1580 agrees with the native shell statement. Adding projective nonconstancy to the native four-term premise and specifying positive integer where the source says natural number both strengthen the assumed hypotheses and are safe for this application.
13. Additional context recommended. The nonconstant-family convention is used consistently and is inert because Corollary 1.5 excludes every nonconstant family. The original report cited journal p. 1589 and v1 pp. 10–11 but omitted stronger same-page context: journal p. 1580, Theorem 1, calls the $d=1$ case “essentially different linear parameterizations.” This observation is the grader's source finding. The native report attributes it accordingly; it is not new primary-reviewer or filing author source coverage.
14. OK: Lemma 1.7, Proposition 1.8 and Theorem 1.1. The empty-$C$ case, symmetry of $D$, exact $2T+1$ candidates for integral $T$, new-index distinctness, union-stage disjointness and odd-power injectivity all hold.
15. OK; two harmless additional divergences noted. No material defect was missed. The manuscript's Theorem 1.3 weakens natural-number $N$ to nonzero-integer $N$; the native application already handles the sign using $\varepsilon_c$ and $N_c=|c|$. Also, $F_c$ is one of two fixed forms, so $K_{F_c}$ can be absolute; the $c$-dependence enters through $R_c$, $\kappa$ and $C_c$. These observations do not weaken the conclusion and are not new numerical or uniform bounds asserted by this filing.

Standing

16. OK. No tier is claimed. The subjects are library reconstruction pages, not native L-claims. The grader reported finding no E477 L-claim in the inspected theory/research corpus; no tier exists to move on these pages.
17. OK. Both external proofs remain literature premises throughout; no local proof credit is taken for them.
18. OK, with an exact future acceptance scope. The original report implied no page edit and recognized that private working files were not a durable native warrant. After acceptance, the review can support discharge of the seven pages' fresh independent compilation obligation only for the frozen statements and deductions, relative to the recalled unit bounds and journal Theorem 2. It supports no change to catalog status, external-proof coverage, the unused general-$r$ Theorem 1.2 or stronger Theorem 1.3, other exponents, effectiveness or formal verification. That prospective scope is preserved here; the later accepted transformation and standing reconciliation record no broader coverage.

Presentation and durability

19. Conversion required for native filing. The original ASCII mathematics is converted to LaTeX in the native report, preserving the mathematical content and qualifiers.
20. Headline rider recommended. The original bold headline omitted an immediate premise rider, although the next paragraph supplied it. The native verdict now states the two literature premises inline.
21. Pair domain recommended. Lemma 1.7's abbreviated restatement omitted $(a,b)\in A\times B$. The native rendition makes the quantifier explicit without changing the frozen lemma.
22. Revision confirmation required. The frozen state did not resolve in the grader's review copy. Its fourteen content hashes were the substantive freeze. The filing confirmed that state in the author worktree; the frozen pages are named by path and date, their text then is not retained as copies, and the current pages differ from it in their verification wording and the source digest's description, updated: field and generated navigation (the standing reconciliation of 2026-09-10T07:43:28Z, rewrapped on 2026-09-17), in American spellings (2026-09-17: "canceling" in the Corollary 1.5 proof, "catalog" in the source digest and Theorem 1.1) and in the source digest's provenance wording (its sentence on the Heath-Brown entry's separate reading, reworded on 2026-09-17; its PDF digest lines replaced on 2026-09-18 by links to the Corvaja-Zannier and Heath-Brown source cards), not in any statement or proof step.

Grade and exact compilation obligation

The grader's mathematical conclusion was that every essential deduction of all six results and both interface applications holds. The external statements were compared with Corvaja-Zannier p. 438 and Heath-Brown journal p. 1580 / v1 p. 1. The fixed-$c$ shell repair is valid; refusing to endorse the manuscript's uniform whole-box restatement is correct; the family convention is consistently applied and immaterial after Corollary 1.5 excludes nonconstant families.

The required corrections were disclosure of pre-directed weakest-step selection and identification of the exact premise-relative obligation. Recommended changes were the same-page family context, headline premise rider, $A\times B$ quantifier, LaTeX presentation and durable retention. This rendition records those changes without treating them as a fresh mathematical verdict. Acceptance of the native transformation was a separate fidelity assessment, not additional mathematical review.

The exact obligation is the fresh independent compilation review recorded on these seven pages as they stood on 2026-09-10T05:48:43Z:

• The source digest's “Reading coverage and current verification”.
• Lemma 1.4's “Dependencies and current verification”.
• Corollary 1.5's “Dependencies and current verification”.
• Proposition 1.6's “Dependencies and current verification”.
• Lemma 1.7's “Dependencies and current verification”.
• Proposition 1.8's “Dependencies and current verification”.
• Theorem 1.1's “Current verification”.

The subject includes their exact statements, essential deductions and external interfaces, including the coordinate normalization and local journal-shell/small-scale deduction. The coverage record pins every page. The recorded compilation review is relative to the Corvaja-Zannier-recalled Mason-Stothers/Brownawell-Masser bounds and Heath-Brown's journal Theorem 2 under the qualified nonconstant-family convention. It does not prove the external premises or certify a stronger theorem.

The native transformation is accepted. At the same checkpoint, the seven source pages record independent compilation review of their exact frozen statements, essential deductions and consumed interfaces, with no material defect found relative to those premises. This discharges only the named premise-relative compilation obligation. Attack selection was partly pre-directed; the derivations were independently performed. The statements and proofs, consumer and both external interfaces remain untouched. No catalog-status change, native L-tier, external-proof coverage, new public-acceptance finding or formal verification follows from filing.

Transformation provenance

This native grade retains all substantive findings and the full scoped pass, but replaces private locations and original line numbers with native references and named sections. Historical reviewer and grader source coverage is attributed to the person who reported it. Disposable renders are not required artifacts. The original report, receipt and grade remain preserved byte-for-byte in working storage; they are exact assessed subjects, not silently rewritten verdicts.

The native record is source-owned living evidence, not an operational log. No new proof assessment, source fetch, PDF reading or mathematical execution was undertaken to produce this rendition. Later substantive changes to the mathematics would need their own assessment.