---

Subject

Date and paths. The reconstruction folder wiki/research/erdos_354 as it stood at 2026-09-28T05:03:27Z and its fourteen reconstruction pages:

• wiki/research/erdos_354/fan_remark_4_1_reconstruction.md
• wiki/research/erdos_354/fan_remark_4_2_reconstruction.md
• wiki/research/erdos_354/geneson_corollary_12_reconstruction.md
• wiki/research/erdos_354/geneson_theorem_9_reconstruction.md
• wiki/research/erdos_354/yu_chen_bg_reconstruction.md
• wiki/research/erdos_354/yu_chen_db_reconstruction.md
• wiki/research/erdos_354/yu_chen_fe_reconstruction.md
• wiki/research/erdos_354/yu_chen_lemma_2_1_reconstruction.md
• wiki/research/erdos_354/yu_chen_lemma_2_2_reconstruction.md
• wiki/research/erdos_354/yu_chen_lemma_2_3_reconstruction.md
• wiki/research/erdos_354/yu_chen_normalization_reconstruction.md
• wiki/research/erdos_354/yu_chen_theorem_5_1_reconstruction.md
• wiki/research/erdos_354/yu_chen_theorem_reconstruction.md
• wiki/research/erdos_354/yu_chen_windows_reconstruction.md

The reports graded are the fourteen independent focused reviews filed in this folder, wiki/research/erdos_354/evidence/verify/, one per page, each named after its page with the suffix _review (for example fan_remark_4_1_reconstruction_review). Each report names the same subject date and its page's path as its frozen subject, and each subject resolves: every path is present in the tree as of that time.

What the grader read, and at what depth. In docs/verification.md, the sections "Independence and the assignment", "Exact subjects and durable evidence", "Report contract", "Grading and claim standing", the shared "Audit checklist", and the Erdos-specific "Whole-claim report" and "Audit checklist"; in docs/evidence.md, "Source fidelity". Each of the fourteen reports in full. Each of the fourteen pages in full as of that time; the working-tree copies were byte-identical to that state at grading. The folder index and the evidence index as of that time, and the Statement and Status paragraphs of the problem page as of that time, read to check the theorem page's Standing sentence. The held sources, in the text layer (pdftotext -layout): the Fan v5 PDF at physical pp. 3--4 and 19--20 and the Fan v4 PDF at p. 19, with page images of v5 p. 19 and v4 p. 19 rendered at 100 dots per inch and read for the printed count and the version comparison; the Geneson PDF at physical pp. 2 and 11--13; the Yu--Chen PDF on all seventeen physical pages, closely at pp. 2--14 and 17. The source PDFs are the folder-name files under the three library cards (Fan (2026), Geneson (2026), Yu and Chen (2026)); the Fan card's provenance and label-map paragraphs were read to place the two versions. Every finding accepted below was adjudicated by the grader against the source text or page image and the page; the reviewers' re-derivations were checked step by step where a finding depends on them. The folder's evidence entry point was neither read nor run; no report relies on it, and the grade does not either. No web source was consulted.

Independence facts, by role. The grader is a fresh context given only the grading assignment, distinct from the author of the reconstruction pages and from each of the fourteen reviewers; the grader took no part in writing any page, any report or the folder's evidence, and had not seen the folder before. The grader is not blind, as a grader need not be: the assignment named the reports, and the grader read the folder index and the problem page's Status paragraph as part of the grade. Each report discloses its reviewer's incidental exposures (the library card's read status, overview, standing and bears-on text printed with its provenance paragraph; the opening lines of the problem page's Status paragraph printed while locating its Statement; the Standing paragraphs of input reconstruction pages; file names under evidence/). Materiality ruling, by the content test: immaterial for every report. None of the exposed text states a verdict on any reconstruction page or on any step of the reconstructed proofs; every finding in every report cites the page and the PDF, the direction of every attack follows the page's own steps, and nothing in any report could only have come from the exposed text. No reviewer read another review, any evidence file, or any web source.

Reports graded

A report passes when it has a subject block that resolves (subject date and path), stated independence facts and exposures, a restatement carrying the quantifiers, an explicit verdict on all ten items of the Erdos-specific audit checklist, weakest steps actually re-derived rather than paraphrased, a real strongest attack, the premises with their interfaces and reading depth, and a verdict; it is void otherwise. All fourteen reports pass. Each entry records what was checked.

1. fan_remark_4_1_reconstruction_review: pass. Subject block resolves; independence facts, allowed reading and the exposures are stated; the restatement carries the definition of $M_2^*$ with its "every sufficiently large $k$" quantifier; ten explicit checklist verdicts (source fidelity failed on F1 and F2); W1--W3 re-derived (the threshold deduction, condition (1.5), the incompleteness count with a check at $k=2$); a real attack, which found the false version claim and its v4 witness; premises with interfaces and depth; verdict faithful with corrections, sound.
2. fan_remark_4_2_reconstruction_review: pass. Subject resolves; artifact depth stated (v5 pp. 2--4, 19--20 in text and images, v4 p. 19); four exposures; restatement with the full quantifier structure and the antecedent $M_2^*=2$ marked as unproved; ten verdicts; three weakest steps re-derived (disjointness of the rescaled rays with an explicit threshold, divergence through fractional-part doubling, two elements per interval); a real attack that produced the $k_0=0$ witness; premises; verdict faithful, sound.
3. geneson_corollary_12_reconstruction_review: pass. Subject resolves; artifact depth (pp. 11--13 in text and images, pp. 1--2 for the convention, digest matched); three exposures; restatement with the existential and universal clauses separated; ten verdicts; three weakest steps re-derived (parity of the $\beta$ floors, the automorphism step with an independent irreducibility check, the tail exclusion in both directions); a real attack on the automorphism step; premises with depth (Dubickas not held); verdict faithful with corrections, sound.
4. geneson_theorem_9_reconstruction_review: pass. Subject resolves; artifact depth (pp. 11--12 in text and images, p. 1, the references); exposures; restatement with the $n\ge1$, $n\ge0$ and "arbitrarily large" quantifiers; ten verdicts ("Reproduction: outside remit" is explicit, with its reason); three weakest steps re-derived, including both exact evaluations term by term; a real attack on the sign adjustment, with a supplementary independent confirmation of the Salem identification; premises with depth; verdict faithful, sound.
5. yu_chen_bg_reconstruction_review: pass. Subject resolves; artifact depth (pp. 13--14 in text and images; pp. 2--3, 7, 11--12); four exposures; restatement with the order of the choices; ten verdicts; three weakest steps re-derived ((11.1), the return cost with the compactness argument, the geometric capacity with explicit thresholds); a real attack on the uniformity of the return-cost radius; premises; verdict faithful, sound.
6. yu_chen_db_reconstruction_review: pass. Subject resolves; artifact depth (pp. 10--11 in text and images); exposures; restatement with the explicit threshold behind "sufficiently large"; ten verdicts; three weakest steps re-derived (the phase mesh and its lift, the representation and width with the containment the page leaves implicit, the budget and the integrality step); a real attack at the boundaries of the coefficient square and at $n=0$; premises; verdict faithful, sound.
7. yu_chen_fe_reconstruction_review: pass. Subject resolves; artifact depth (pp. 7--9 in text and images, pp. 1--3); exposures; restatement with the constants; ten verdicts; weakest steps re-derived ((8.2), both cases of (8.5), the potential at its tightest parameters, the block partition); a real attack on the change of period at $w=2$; premises; verdict faithful, sound.
8. yu_chen_lemma_2_1_reconstruction_review: pass. Subject resolves; artifact depth (pp. 2--4 in text, p. 3 as an image); two exposures; restatement with conventions; ten verdicts; W1--W3 re-derived (unique maximal runs, no merging of shortened sets, reading off $h$); a real attack on the wrap-around with hand cases, and an exhaustive enumeration for $d\le12$ recorded as base-case coverage only; premises; verdict faithful, sound.
9. yu_chen_lemma_2_2_reconstruction_review: pass. Subject resolves; artifact depth (p. 3 as an image, pp. 2 and 4); two exposures; restatement separating the lemma from the page's and the source's consequence sentence; ten verdicts; W1--W3 re-derived (exhaustive cases, the in-hull bound, the induction); a real attack at the touching-hull case and the sharp boundary, with the non-monotone witness for F1; premises; verdict faithful (the reviewer wrote "with corrections" while requiring none), sound.
10. yu_chen_lemma_2_3_reconstruction_review: pass. Subject resolves; artifact depth (pp. 3--4 in text and images); exposures; restatement with the example showing the span hypothesis necessary; ten verdicts; three steps re-derived (the wraparound bound, the maximal runs of the truncated set, the reductions at both ends); a real attack seeking a wraparound block of length $k$; premises; verdict faithful, sound.
11. yu_chen_normalization_reconstruction_review: pass. Subject resolves; artifact depth (pp. 1--4 and 7 in text and images); two exposures; restatement of items 1--6 and the reduction with their ranges; ten verdicts; three weakest steps re-derived (the prefix gap bound with the telescoping identity, the normalization inequalities, the residue bound with its base case); a real attack on the reduction and on the gap bound; premises; verdict faithful, sound.
12. yu_chen_theorem_5_1_reconstruction_review: pass. Subject resolves; artifact depth (pp. 4--6 and 17 in text and images, pp. 2--3); four exposures; restatement with the hypotheses of Section 3 and the free-continuation clause; ten verdicts ("Reproduction: not performed by design", with its reason); W1--W3 re-derived (the endpoint bounds, the window cover, the chain to (5.1)); a real attack that re-derived the certificate table from Appendix A (125 nodes, 113 links, the cone test on 1404 forms) and probed the mesh bounds at concrete layers; premises; verdict faithful, sound.
13. yu_chen_theorem_reconstruction_review: pass. Subject resolves; artifact depth (the whole text layer, closely at pp. 1--2, 6, 7 and 13--14, with page images of pp. 1, 2, 6, 7 and 14); exposures; restatement with the quantifier order and the argument in the reviewer's words; ten verdicts; three weakest steps re-derived (finitely many qualifying pairs, every-integer spacing, the Theorem 5.1 interface with (5.2)); a real attack on the interface between Step 2 and (BG); premises; verdict faithful, sound.
14. yu_chen_windows_reconstruction_review: pass. Subject resolves; artifact depth (pp. 11--12 in text and images, the other pages at interface depth); three exposures; restatement with the quantifier order of $L$, $\varepsilon$ and $T_0$; ten verdicts; W1--W3 re-derived (the cubic advance with its threshold, the crossing and pre-crossing rationals, the simultaneous thresholds); a real attack (a badly approximable ratio refutes the cubic-advance claim read unconditionally, showing why incompleteness is essential); premises including a re-proof of the Dirichlet form used; verdict faithful, sound.

Corrections

Each correction was adjudicated against the held source and the page as of that time. Locations quote the page text as of that time.

C1. Page fan_remark_4_1_reconstruction, Source paragraph, the parenthetical "(this remark is new in v5; v4 has no counterpart)". Replace it with: "(the base-two example already opens Remark 4.1 of v4, p. 19, as the bound $M_2^*\ge2$, with the same set, the same displayed inequality and the same incompleteness count; v5 generalizes the remark to $M_\rho^*\ge u_\rho$ for $\rho\ge2$, adds the case $\rho>2$ and the random-set sentence, and moves the remark's second paragraph to Remark 4.2)". Basis: v4 physical and printed p. 19, Remark 4.1, first paragraph, read on the page image; the v5 text differs there only by "Theorem 1.1 shows that $M_\rho^*\le M_\rho$" for "Corollary 1.2 shows that $M_2^*\le5$", "gives" for "would give", and the slip of C2. From F1 of the review, required, accepted.

C2. Same page, Source paragraph; append after the sentence ending "Remark 4.2 page]]." the sentence: "The source prints the per-interval count as $|A\cap[2^k,2^{k+1}]|=u_\rho=1$ (v5 p. 19); since $u_2=\lceil2(2-1)\rceil=2$ by (1.6) on p. 3, the middle term is a slip, and the count is read as $u_\rho-1=1$, the count the bound $M_\rho^*\ge u_\rho$ needs (v4 prints $=1$)." Basis: v5 p. 19 page image prints "$=u_\rho=1$"; (1.6) on p. 3 gives $u_2=2$; the case $\rho>2$ on p. 19 uses $r=u_\rho-1$ elements per interval; the evidence guide's "Source fidelity" requires an incorrect formula in a source to be recorded explicitly. The mathematics of the page is unaffected. From F2 of the review, required, accepted.

C3. Page fan_remark_4_2_reconstruction, Step 1, the clause "so for $k_0\ge\max(s,t,0)$," before the displayed inclusion. Replace it with "so for $k_0\ge\max(s,t,1)$,". Basis: at $k_0=0$, allowed by the stated range whenever $s,t\le0$, the set $U_0(\alpha')$ contains $\lfloor\alpha'\rfloor=0$ whenever $\alpha'<1$, and $0\notin A_{\alpha,\beta}$ by (1.9); witness $\alpha=7/10$, $\beta=9/10$, where $s=t=0$. The page's own parenthetical justifies positivity for $k_0\ge1$ only and its next paragraph imposes $k_0\ge\max(s,t,1)$ before anything is deduced, so the argument is unaffected. From F1 of the review, filed as suggested; accepted by the grader because the displayed sentence is false at a value inside its stated range.

C4. Page geneson_theorem_9_reconstruction, Scope, "it gives no explicit $t$ and no numerical bound on one." Replace with "it gives no explicit $t$ and no numerical upper bound on one." Basis: the source, physical p. 12, last paragraph of Section 5, reads "it gives neither an explicit coefficient nor a numerical upper bound for one", and the page's own next sentence records the lower bound $5$ from van Doorn's Proposition 8, which the page's sentence contradicts. From F1 of the review, filed as suggested; accepted by the grader.

C5. Page geneson_corollary_12_reconstruction, Scope, "(the source, pp. 2 and 13, states it answers the "variable-base extension" of the two-sequence question)". Replace with "(the source, p. 2, states it answers the "variable-base extension" of the two-sequence question; p. 13 adds that the corollary does not resolve the original question with base $2$)". Basis: the quoted phrase occurs once in the artifact, on physical p. 2; physical p. 13 reads "This corollary does not resolve the original question with base 2" and carries neither "variable-base" nor "extension". From F1 of the review, required, accepted.

C6. Page yu_chen_theorem_5_1_reconstruction, Step 4, "The smallest weight not used in $P_r$ is $b_r=8dKq+8v_1+4v_2+2v_3+v_4\le8dKq+15$." Replace with "The smallest weight not used in $P_r$ is $b_r=2b_{n+\ell+2}+v_4=8dKq+8v_1+4v_2+2v_3+v_4\le8dKq+15$, where $v_4=v_{n+\ell+2}$ is the conversion at index $r-1$." Basis: the page defines only $(u_1,v_1)$, $(u_2,v_2)$, $(u_3,v_3)$; the recurrence $b_{i+1}=2b_i+v_i$ (source p. 2) gives the displayed value with $v_4=v_{n+\ell+2}\in\{0,1\}$, so the bound $\le8dKq+15$ stands. From F2 of the review, filed as suggested; accepted by the grader because a symbol in a displayed formula is undefined.

C7. Page yu_chen_db_reconstruction, Step 1, "Let $r_i=\{2^i\alpha\}$." Replace with "Let $r_i=\{2^i\alpha\}$ and $s_i=\{2^i\beta\}$." Basis: $s_n$, $s_{n+k}$ are used two sentences later without a definition. From F3 of the review, filed as a note; accepted by the grader for the same reason as C6.

C8. Same page, Step 3, "For $0\le j<q$, $|j\theta-jp/q|=j|\theta-p/q|<j/q^2<1/q$". Replace with "For $0\le j<q$, $|j\theta-jp/q|=j|\theta-p/q|\le(q-1)/q^2<1/q$". Basis: at $j=0$ the printed chain reads $0<0$; the corrected chain holds for every $j$ in the range, strictly in the first step for $j\ge1$ because $|\theta-p/q|<1/q^2$ and as $0\le(q-1)/q^2$ at $j=0$, and the conclusion (every point of the circle within $1/(2q)$ of a grid point and at distance less than $3/(2q)$ from a phase) is unchanged. From F1 of the review, filed as suggested; accepted by the grader because the displayed chain is false at $j=0$.

C9. Page yu_chen_bg_reconstruction, the three step headings. Replace "### Step 1: exact layers are dense (11.1)" with "### Step 1: exact layers are dense (Subsection 11.1)", "### Step 2: nontrivial returns cost many events (11.2)" with "### Step 2: nontrivial returns cost many events (Subsection 11.2)", and "### Step 3: geometric capacity (11.3)" with "### Step 3: geometric capacity (Subsection 11.3)"; the tag (11.1) on the display inside Step 1 stays. Basis: Section 11 of the source has one numbered display, (11.1) on physical p. 13; "11.2" and "11.3" are the subsection numbers printed on pp. 13--14, and the page's own Source paragraph separates "Subsections 11.1--11.3" from "display (11.1)", so the parenthesized numbers in the headings point a reader at displays the source does not have. From F1 of the review, filed as suggested; accepted by the grader as a source-label correction.

C10. Page yu_chen_theorem_reconstruction, Step 4, "pairwise distinct elements of $A_{\alpha,\beta}$ above $\max F$". Replace with "pairwise distinct elements of $A_{\alpha,\beta}$ above $\max(F\cup\{0\})$". Basis: $\max F$ is undefined for $F=\emptyset$, the case the next sentence uses; item 3 of the normalization page states the bound as $\max(F\cup\{0\})$, and the source (p. 7) chooses an upper bound for $F\cup\{0\}$. From F3 of the review, filed as a note; accepted by the grader because the expression is undefined at a case the page relies on.

None of C1--C10 changes a statement or a mathematical conclusion; C1, C2, C5 and C9 correct the pages' account of the artifacts, and C3, C4, C6, C7, C8 and C10 repair a false, undefined or self-contradictory clause in the pages' own text.

Rejected and downgraded findings

Every finding not listed under Corrections is recorded here with its disposition. "Downgraded" means the finding is right as an observation but does not require a change: it concerns labeling, an unmarked but correct reading, a locator that is incomplete without being wrong, or a precision that the page does not need. "Rejected as a correction" means the proposed text cannot be adopted by edit.

fan_remark_4_1_reconstruction_review. F3 (closed versus half-open interval): downgraded; both counts equal $1$ because no power of two lies in $A$, and the half-open interval is the one (1.8) uses, so the page's choice is the relevant one; the author may record the change. F4 (the case $\rho=2$ lies on p. 19 alone): downgraded; verified on the v5 page image, but the remark itself spans pp. 19--20 and the locator is not wrong. F5 (existence presupposed by "$M_2^*\ge2$"): downgraded; the page names Corollary 1.2 in the same sentence, as the source does.

fan_remark_4_2_reconstruction_review. F2 (the list of supplied steps omits the placement of the floors and the infinitely many carries): downgraded; verified against v5 p. 20, where both are stated without proof, but the page's proof supplies them correctly and the omission is a labeling matter. F3 ("Remark 4.1 of v4, p. 19, with the same content"): downgraded; v4's Remark 4.1 also contains the base-two example, so the parenthetical is loose rather than false, and C1 records the full relation on the sibling page. F4 (the readings of $\alpha'$ and of $H_1(A)=\{0\}$ as (1.5)): downgraded; both readings are right and the page's Step 3 proves (1.5) directly. F5 (the page read the canonical conversion and not the PDF): rejected as a correction; the sentence is an honest record of what was done, a replacement asserting a PDF reading cannot be adopted by edit, and the reviewer's own comparison found the conversion identical to the PDF at the cited pages, so no fidelity defect results; the author may record a PDF reading once made.

geneson_corollary_12_reconstruction_review. F2 (reading depth): rejected as a correction, for the reason given at F5 above; the reviewer found Section 6 of the conversion identical to the PDF clause by clause. F3 (the reading of "tail"): downgraded; the page's reading is the one the source's proof uses, and the reviewer showed the conclusion survives the wider reading. F4 (the order of the interleaving): downgraded; completeness is invariant under reordering occurrences.

geneson_theorem_9_reconstruction_review. F2 (reading depth): rejected as a correction, as above; the reviewer found Section 5 of the conversion identical to the PDF at every sentence and display. F3 (the proof of Proposition 11 spans pp. 11--12): downgraded; verified in the text layer, but the page's locator already names pp. 11 and 12 and nothing stated is wrong. F4 (unmarked one-line justifications; "$\subset(0,1)$" for the source's "$\subset(0,1/2)$"): downgraded; each supplied line is correct and the weaker containment is what the step needs. F5 (the van Doorn indexing caveat): downgraded; the page declares the comparison not reconstructed. F6 (the p. 334 locator): downgraded; the theorem number is carried and the page is not wrong.

yu_chen_bg_reconstruction_review. F2 (the Scope sentence locates the use of irrationality in (10.2) only): downgraded; the sentence correctly says the argument needs irrationality, and Step 2's direct use is on the page. F3 (integrality of the threshold and of $x$): downgraded; the hypothesis quantifies over integers, a real threshold can be replaced by its ceiling, and the page consuming (BG) supplies an integer $n_0$. F4 ($0\in\mathbb N$ so that $1\in\mathcal A$): downgraded; the convention is imported from the normalization page, whose Definitions the page cites. F5 (item 4 not named for the binary digits): downgraded; the page imports the conversions from the normalization page. F6 (standing of (10.2) at the point of use): downgraded; the page's Standing paragraph and the folder index say every page is author-recorded. F7 (the meaning of "the sequence is incomplete"): downgraded; the predicate is the single one the cluster uses, as the theorem-page review confirmed by reading every consumed Statement section.

yu_chen_db_reconstruction_review. F2 (real endpoints in the window lemma): downgraded; the page's hypothesis is weaker than the source's, its proof covers the wider form, and Step 5 uses integer intervals only. F4 ("window lemma" is the page's label; two further expansions unlabeled): downgraded; labeling only. F5 ("stated without proof" for a step the source gives a one-clause reason): downgraded; wording.

yu_chen_fe_reconstruction_review. F1 (the desc says "below the next weight" and that the count "decays"): downgraded; the desc is a summary and the Statement section states $Q_n\le C_02^ne^{-aK_n}$ exactly; the author may sharpen the desc, which the folder index repeats. F2 (the reading of "width" as $b-a$): downgraded; the source's display $R_n+2\ge(S_n+2)/(e_n+1)$ fixes that reading. F3 (item 6's gap bound is for $n\ge1$; the parenthetical "$B_n=1$" describes an impossible case): downgraded; at $n=0$ there is no internal run and (8.2) holds, and $B_n\ge M+N\ge5$ makes the parenthetical harmless. F4 (the interlacing inequalities used without citation): downgraded; imported from the normalization page, which the page's Definitions cite.

yu_chen_lemma_2_1_reconstruction_review. F1 (unique maximal runs asserted without argument): downgraded; the fact is elementary and the reviewer's derivation confirms it. F2 ("the first residue $s'+1$ of the next" when the next shortened set is empty): downgraded; the sentence reads correctly with "the next" as the next nonempty shortened set, and the separating residue $s+r\in X$ does the work. F3 (the desc presumes a missing run exists): downgraded; the $\max(0,\cdot)$ is in the statement. F4 ("Let $d\ge1$" not marked as a reading): downgraded; a modulus is positive.

yu_chen_lemma_2_2_reconstruction_review. F1 (the unused ordering hypothesis $c_1\le c_2\le\cdots$): downgraded; the page's Consequence is a true statement narrower than the source's informal sentence, every application in the folder feeds the weights in sorted order, and the reviewer's non-monotone witness confirms only that the ordering is not needed. F2 (the exact span and the preserved minimum are additions): downgraded; both follow from (2.2) iterated and from $c_i>0$. F3 ("the lemma gives $\min W_i=\min W_{i-1}$"): downgraded; the minimum is established in the first paragraph of the page's proof. F4 (where the source's sketch ends): downgraded; labeling.

yu_chen_lemma_2_3_reconstruction_review. F1 (the eight supplied sentences and the omitted aside are unmarked): downgraded; labeling. F2 (consecutive elements of $W\cap[0,m)$ are consecutive in $W$): downgraded; an element of $W$ between them would lie in $[0,m)$, an immediate observation the source also leaves unsaid. F3 (title "smaller" for the source's "any smaller"): downgraded. F4 (an empty "run" when $w_-=m-1$): downgraded; the inequality is unaffected. F5 (the letter $m$ clash with the mesh lemma page's index): downgraded; the index is never used.

yu_chen_normalization_reconstruction_review. F1 (the two lemmas invoked by link label only): downgraded; the links resolve to pages whose Source paragraphs carry the labels and pages. F2 (the convention $\mathbb N\ni0$ presented as the source's): downgraded; the source's index-$0$ weights force it. F3 (the indexed clause reached through the tail indices rather than by selecting an original index): downgraded; a valid variant. F4 (the range $n\ge1$ supplied for the gap bound): downgraded; harmless. F5 ("item 1--3" for "items 1--3"): downgraded; a typographical slip the author may fix.

yu_chen_theorem_5_1_reconstruction_review. F1 (the domain of "every choice of the later conversions"): downgraded; the reviewer's own derivation shows interlacing persists under arbitrary digits, so the statement is right under either reading. F3 ($S_n<L_n$ consumed without a citation and absent from the Scope inventory): downgraded; the Definitions section imports the prefix objects from the normalization page, whose item 6 states the bound, and the mathematics is unaffected; the author may name it. F4 (the reading of "$\ell$ exact doubling pairs"): downgraded; the page's reading is the one the displayed weights fix. F5 (supplied steps unmarked): downgraded; labeling.

yu_chen_theorem_reconstruction_review. F1 (the explicit threshold and the finite-pairs form are the page's expansions, unlabeled): downgraded; labeling. F2 (the normalized pair is not renamed; $n_1$ used twice): downgraded; the Definitions bind $M$, $N$, $P_n$, $h_n$, $K_n$ and $C_M$ to the normalized pair through the normalization page, and the second use of $n_1$ begins after the Claim's proof has closed. F4 (the Standing sentence about the problem page): resolved by the grader, who read the problem page's Status paragraph as of that time: the first question's recorded answer rests on a Lean proof accepted by a bounty site, which is a different proof, so the sentence is accurate.

yu_chen_windows_reconstruction_review. F1 (which deductions the page supplies is unstated): downgraded; labeling, and each supplied deduction was re-derived by the reviewer. F2 ("all four displayed properties of (10.2)"): downgraded; the phrase refers to the source's display, which has four clauses. F3 (where $1<p/q<2$ comes from): downgraded; the source's sentence after the pre-crossing display, correctly used. F4 (the symbol $q$ reused for the reduced denominator): downgraded; the inequality is right for either denominator, since $1/q^2\le1/q'^2$ when $q'\le q$.

Graded verdicts

Fidelity is "faithful" or "faithful with corrections" (naming them); the argument is "sound" or "sound with corrections" (naming them), a correction being counted against the argument when it repairs the page's own proof text.

• fan_remark_4_1_reconstruction: fidelity faithful with corrections (C1, C2); argument sound.
• fan_remark_4_2_reconstruction: fidelity faithful; argument sound with correction (C3, a false boundary value in a displayed range that the proof never uses).
• geneson_corollary_12_reconstruction: fidelity faithful with correction (C5); argument sound.
• geneson_theorem_9_reconstruction: fidelity faithful with correction (C4); argument sound.
• yu_chen_bg_reconstruction: fidelity faithful with correction (C9); argument sound.
• yu_chen_db_reconstruction: fidelity faithful; argument sound with corrections (C7, C8).
• yu_chen_fe_reconstruction: fidelity faithful; argument sound.
• yu_chen_lemma_2_1_reconstruction: fidelity faithful; argument sound.
• yu_chen_lemma_2_2_reconstruction: fidelity faithful; argument sound.
• yu_chen_lemma_2_3_reconstruction: fidelity faithful; argument sound.
• yu_chen_normalization_reconstruction: fidelity faithful; argument sound.
• yu_chen_theorem_5_1_reconstruction: fidelity faithful; argument sound with correction (C6, an undefined symbol).
• yu_chen_theorem_reconstruction: fidelity faithful; argument sound with correction (C10, an undefined expression at the empty-deletion case).
• yu_chen_windows_reconstruction: fidelity faithful; argument sound.

These verdicts are the graded readings of fourteen focused reviews, each of which took its input pages at their Statement sections and their imported theorems (Dubickas's fractional-part theorem and Salem identification on the Geneson pages, Dirichlet's approximation theorem on the windows page) as stated; the pages remain author-recorded reconstructions. No tier is assigned and no status changes.