Distinct grade of the Problem 1221 reconstruction reviews

Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Sep 28

Subject

Rules read. docs/verification.md, the sections "Independence and the assignment", "Exact subjects and durable evidence", "Report contract", "Grading and claim standing", "Whole-claim report" and "Audit checklist" (the shared list of canonical failure modes and the ten Erdos items); docs/evidence.md, the section "Source fidelity".

Source artifacts read for adjudication. The PDF held by de Bruijn and Erdős 1949, image-only: its four printed pages (PDF pp. 2--5, printed pp. 14--17) rendered at 200 dots per inch and read on the images for Section 1, the displays (3.1), (3.2) and the two general- $r$ displays of Section 3, the sentence "It follows that its length is less than", (4.1), (4.2), the multiplicity display, the general- $r$ display and (4.3) of Section 4, (5.1)--(5.7) with footnote 3 and the p. 17 chain of Section 5, and Section 6. The PDF held by Clément and Steinerberger 2025: text layer, read for the abstract and Section 1 (the piece count), Theorems 2 and 3 with the remark after Theorem 3, the two-length remark of p. 4, and the derivation paragraph of p. 9. The PDF held by Korsky 2026, improved lower bound: text layer, all eight pages, read whole. The PDF held by Korsky 2026, resolution: text layer, all sixteen pages, read whole, with Sections 2--8 read display by display where a finding needed adjudication. The page-number position of each display was taken from the text layer's page breaks. The papers of Larcher (2015), Halász (1981) and Schmidt (1972) were not read; the corpus holds a card for Schmidt 1972 under library/discrepancy/ and none for the other two, and nothing below relies on them.

Independence. The grader is a role distinct from the author of the pages and from every reviewer: a fresh context given only the grading assignment, taking no part in writing any page or report, with no contact with their authors and with no other review of these pages read. The working-tree diff of the folder index was seen while resolving the subject; an untracked research page was not read. No web search was made.

Ruling on disclosed exposures. Every report discloses over-wide prints: the problem page's Status paragraph, the library cards' read-status and relation paragraphs, sibling pages' Standing paragraphs and source-card proof pointers, and, for the (5.7) review, the shared audit-checklist section. Ruling by the content test: immaterial. Nothing in any report could only have come from that text, no attack direction or verdict followed it, and the exposed text concerns the problem's status and the cards' own read status, not the pages under review; no reviewer received a verdict on its subject. The reviews stand as independent.

Reports graded

Each report is graded as a focused review record; none carries a tier. A pass means the contract parts are present and real, not that every finding is right; findings are adjudicated separately below.

clst25_theorem_2_reconstruction_review: pass. Subject block with path and date; independence facts and three exposures; restatement with every quantifier; ten explicit checklist verdicts; three weakest steps re-derived; a strongest attack that succeeded with a witness and a demonstration that the imported input cannot close the gap; premises with interfaces and depth; verdict. F1 is accepted as C1 and F2 as C2.
dber49_inequality_3_3_reconstruction_review: pass. Complete contract; the general- $r$ completion is re-derived with coincident points included; the artifact was read on the images at the displays cited. F1 is accepted as C3.
dber49_inequality_4_3_reconstruction_review: pass. Complete contract; the coincident-point witness against the span step is correct and the restriction argument it proposes is right. F1 is accepted as C4 and F3 as C5.
dber49_inequality_5_7_reconstruction_review: pass. Complete contract; the printed-denominator finding is re-derived and the case split closed at both edge values of $j$ . No required correction.
ko26a_lemma_3_1_reconstruction_review: pass. Complete contract; the time-convention attack is a real attack with an explicit witness under the alternative reading. No required correction.
ko26a_proposition_4_1_reconstruction_review: pass. Complete contract; the active-gap count is re-derived as an explicit potential and the arc argument closed. No required correction.
ko26a_theorem_1_1_reconstruction_review: pass. Complete contract; the epoch recursion and the two decay rates are re-derived with the uniformity of the epoch constant checked. No required correction.
ko26b_lemma_2_1_reconstruction_review: pass. Complete contract; the displacement bookkeeping, both interval inclusions with their endpoint conventions and the exchange of integrals are re-derived. No required correction.
ko26b_proposition_3_1_reconstruction_review: pass. Complete contract, with explicit constants behind every $O(\cdot)$ term. F1 is accepted as C9.
ko26b_lemma_4_2_reconstruction_review: void. The checklist part gives its verdicts against the shared list of canonical failure modes and named patterns, not against the ten Erdos items that govern the checklist here (docs/verification.md "Audit checklist" under Erdos-specific: "this list governs the checklist part here"). The item "Source and verdict fidelity" has no checklist verdict at all (fidelity is discussed only under Strongest attack and Verdict), and "Quantifiers and scope" beyond almost-all and exceptional sets, "Model and convention changes" and "Computation" have none by name; silence is not a verdict. Every other contract part is complete, and the report's findings were adjudicated below; its F1 is accepted as C6 on the grader's own verification of the artifact. A repaired report that adds the ten verdicts would be small.
ko26b_lemma_6_1_reconstruction_review: pass. Complete contract; the zero-sum step, the floor cost and the $kr$ -span decomposition are re-derived under the cyclic-order convention. F3 is accepted as C7.
ko26b_lemma_6_2_reconstruction_review: pass. Complete contract; the transport identity, the one-atom bound without a smallness assumption and the averaging are re-derived. F2 is accepted as C8.
ko26b_lemma_6_3_reconstruction_review: pass. Complete contract; the exact cancellation between the $L^1$ slack and the mean is re-derived. No required correction.
ko26b_proposition_6_4_reconstruction_review: pass. Complete contract; the uniformity of the descent threshold over $D$ is re-derived from the Lemma 6.2 interface. F1 is accepted as C10.
ko26b_lemma_7_2_reconstruction_review: pass. Complete contract, with explicit values of $c_4$ and $S_0$ . No required correction.
ko26b_theorem_1_1_reconstruction_review: pass. Complete contract; the quantifier-order attack on Section 8 is real. Its one required finding, F1, is rejected below; F2 and F3 are accepted as C11 and C12.

Corrections

Each correction is confined to the page named, outside any statement: field (the pages carry none); the location is quoted from the frozen text.

C1. clst25_theorem_2_reconstruction, the derived range. The page restricts its reading of Theorem 3 to $R\ge2$ because the instance $R=1$ is false for both sequences, then defines $R^-=\max\{R\in\mathbb N:\ R+c\log R\le r\}$ and applies Theorem 3 at $R^-$ ; for every $r<2+c\log2$ , always including $r=2$ , $R^-=1$ and the lower-bound step and the small- $r$ branch of the constant use the excluded instance. Verified: $R+c\log R\le2$ fails at $R=2$ for every $c>0$ , and Theorem 3 at $R\ge2$ alone cannot bound the smallest $r$ -span when $r+1\le c\log2$ (the review's grid-plus-cluster configuration, re-derived). Exact change, five edits:

Statement: replace "such that for every integer $r\ge2$ and every $n\ge n_1(r)$ " by "such that for every integer $r\ge2+c\log2$ , with $c$ the constant of Theorem 3, and every $n\ge n_1(r)$ "; replace "the restriction to $r\ge2$ is explained below." by "the restriction to $r\ge2$ is explained below, and the further restriction to $r\ge2+c\log2$ is the range on which the derivation from Theorem 3 goes through (see the proof and the Source notes)."
Proof, first paragraph: replace "fix $r\ge2$ " by "fix an integer $r\ge2+c\log2$ "; replace the display defining $R^-$ by " $R^-=\max\{R\in\mathbb N:\ R\ge2,\ R+c\log R\le r\}$ "; replace " $R^-$ exists because $R=1$ qualifies" by " $R^-$ exists because $R=2$ qualifies when $r\ge2+c\log2$ , and $R^-\ge2$ keeps Theorem 3 at $R^-$ inside the range $R\ge2$ of the import".
Asymptotics of $R^\pm$ : replace "For $2\le r<r_1(c)$ the ratio is at most $R^+(r)/1\le R^+(r_1)$ " by "For $2+c\log2\le r<r_1(c)$ the ratio is at most $R^+(r)/2\le R^+(r_1)$ ", and "gives the statement for every $r\ge2$ " by "gives the statement for every $r\ge2+c\log2$ ".
Source notes: in "Boundary at $r=1$ ", replace "the derivation above is for $r\ge2$ " by "the derivation above is for $r\ge2+c\log2$ "; add the bullet "The range $2\le r<2+c\log2$ is not derived. For such $r$ no integer $R\ge2$ has $R+c\log R\le r$ , and Theorem 3 at $R\ge2$ alone gives no lower bound on the smallest $r$ -span: when $r+1\le c\log2$ , $n-r$ equally spaced points with $r$ further points clustered next to one of them satisfy every Theorem 3 inequality at $R\ge2$ (a closed arc of length $R/n$ holds between $R-1$ and $R+1$ grid points once $n\ge Rr$ , plus at most $r$ cluster points) while one $r$ -span is arbitrarily short; the source gives no value of $c$ . The source asserts Theorem 2 for all $r\in\mathbb N$ ; on this finite range its bound needs an input not imported here, such as a minimum-gap bound for each sequence."
Reading addressed: replace " $(r\ge2)$ " in the display by " $(r\ge2+c\log2)$ ".

An alternative that keeps the range $r\ge2$ is acceptable only if it imports, with a label, a minimum-gap bound for each sequence (for the van der Corput sequence the two gap lengths $2^{-k}$ and $2^{-k-1}$ for $2^k\le n<2^{k+1}$ stated on p. 4 of the source; for the Kronecker sequence a three-gap bound not held).

C2. clst25_theorem_2_reconstruction, Definitions, the parenthesis "(the source's introduction counts $n+1$ pieces of a broken stick $[0,1]$ , but Theorem 2 is stated on $S^1$ , and the circle convention, the one of Problem 1221, is used here)". Verified on the text layer: the abstract says the circular stick $S^1$ is broken into $n+1$ pieces, Section 1.1 says "we have $n+1$ intervals", and Section 2 sets $x_0=0$ . Replace by "(the source's abstract and introduction count $n+1$ pieces of the circular stick $S^1$ after $n$ breaks, and its Section 2 sets $x_0=0$ , so the source treats $0$ as an extra break point; here $0$ is not a break point, the convention of Problem 1221)".

C3. dber49_inequality_3_3_reconstruction, The contradiction, "the note's (3.1) for $r=1$ ". Verified on the page image (printed p. 15): the printed (3.1) reads $kM_n^1(a)<\varrho$ $(n\le k<2n)$ , with the subscript $n$ on $M$ , a misprint for $k$ that the page corrects without saying so; docs/evidence.md "Source fidelity" requires an incorrect formula in a source to be recorded. After "the note's (3.1) for $r=1$ " insert "(the printed (3.1) carries the subscript $n$ on $M$ , a misprint for $k$ : its range $n\le k<2n$ , the chain drawn from it and the conclusion 'for at least one $k$ ' all read $M_k^1$ )".

C4. dber49_inequality_4_3_reconstruction, the paragraph "Each arc is a span of an intermediate stage." through its display. Its sentence "Conversely, a point of stage $k_i^*$ lying on $A_i$ is a point of stage $N$ lying on $A_i$ , hence, by the definition of the cyclic order, one of $a_{k_i},\ldots,a_{k_{i+r}}$ " is false when a point outside the window coincides with an endpoint of $A_i$ , a case the page admits. Verified witness: $r=1$ , $n=2$ , $a=(0,1/4,0,1/2)$ , order $(1,3,2,4)$ , $i=2$ , $k_2^*=3$ : the stage- $3$ points on $A_2=[0,1/4]$ are $a_1,a_2,a_3$ . The conclusion holds by restriction of the cyclic order. Replace the paragraph by: "Each arc is a span of an intermediate stage. Define $A_i$ as the union of the $r$ stage- $N$ intervals between the consecutive listed points $a_{k_i},a_{k_{i+1}},\ldots,a_{k_{i+r}}$ . The list $(k_1,\ldots,k_N)$ restricted to its entries at most $k_i^*$ is a cyclic order of the stage- $k_i^*$ points in which coincident points stay adjacent, so the arcs between its consecutive entries are the intervals of stage $k_i^*$ (the cyclic sequence of interval lengths does not depend on the order inside a block of coincident points). The entries $k_i,\ldots,k_{i+r}$ are consecutive in the full list and all at most $k_i^*$ , so they remain consecutive in the restricted list, and the $r$ intervals between them are $r$ consecutive intervals of stage $k_i^*$ : $A_i$ is an $r$ -span of that stage. Hence" followed by the existing display $|A_i|\ge m_{k_i^*}^r(a)$ $(1\le i\le N)$ .

C5. dber49_inequality_4_3_reconstruction, The counting inequality, "the note's (4.2), whose right side is $1$ when $r=1$ ". Verified: the page's display is $r>\varrho\sum_i1/k_i^*$ and the printed (4.2) is $1>\varrho\sum1/k_i^*$ (p. 16), so the $1$ stands on the left. Replace "right side" by "left side".

C6. ko26b_lemma_4_2_reconstruction, Source paragraph, "Section 4: Theorem 4.1 (p. 7, with its derivation from Larcher's proof) and Lemma 4.2 (p. 8)". Verified on the text layer: p. 7 ends with the display of Theorem 4.1 and p. 8 opens with "Derivation from Larcher's proof". Replace by "Section 4: Theorem 4.1 (p. 7), its derivation from Larcher's proof (p. 8) and Lemma 4.2 (p. 8)", and give the subheading "The source's derivation, as stated" the locator "(p. 8)".

C7. ko26b_lemma_6_1_reconstruction, "From $r/n$ to $r/t$ ", the sentence ending "so $\sum_i|S_i-r/t|\le2A+r/t$ ." The page's Role paragraph and the Lemma 6.3 page cite the sharper bound $2A+r(t-n)/t$ "from the proof of Lemma 6.1", which is what the displayed cost gives and what the exact constant of Lemma 6.3 needs, but the proof never writes it. Replace by "so $\sum_i|S_i-r/t|\le2A+r(t-n)/t\le2A+r/t$ ."

C8. ko26b_lemma_6_2_reconstruction, Definitions, "Notation as on the Lemma 2.1 and Lemma 6.1 pages". Verified: the page consumes the range of $s(u)$ , the injection $T_u$ and the exchange of integrations from the Lemma 2.1 page and carries no wikilink to it. Replace by "Notation as on the Lemma 2.1 page and the Lemma 6.1 page".

C9. ko26b_proposition_3_1_reconstruction, frontmatter desc, "when every r-span is within A/t of its mean". Verified against (2.1) on p. 4 of the source: the hypothesis is $a_t+b_t\le A$ for the two one-sided errors, and the source says that controlling the sum is what gives the coefficient $3A$ ; "within $A/t$ " gives only $a_t+b_t\le2A$ , under which the proposition yields $6A$ , not the $3A$ the summary promises. Replace by "when the r-spans lie between (r - a_t)/t and (r + b_t)/t with a_t + b_t at most A".

C10. ko26b_proposition_6_4_reconstruction, "Integer times", the sentence "The threshold on $n$ comes from (6.9) at the time $(1+\theta)n$ , from $4r/n\le A$ and from the largeness needed by the finitely many comparisons, none of which depends on $D$ ; so one late time serves every $0\le D\le S$ ." The descent step is one Lemma 6.2 instance for each $D\in(0,S]$ , whose threshold does depend on $D$ through the requirement that the arc of length $D/t$ be shorter than $1$ , and identity (6.4) needs $D\le n$ ; both are uniform once $n>S$ , which the page does not say. Replace by "The threshold on $n$ comes from (6.9) at the time $(1+\theta)n$ , from $4r/n\le A$ , from the finitely many chain comparisons behind (6.9), and from the descent comparison, whose transport error $8A+4r/t$ is free of $D$ and whose only $D$ -dependent largeness requirement (Lemma 6.2 page, end of proof) is that the arc of length $D/n$ be shorter than $1$ ; identity (6.4) needs the same. Since $D\le S$ , any $n>S$ meets both at once, so one late time serves every $0\le D\le S$ ."

C11. ko26b_theorem_1_1_reconstruction, "Imported inputs and gaps", "Nothing else is imported: Lemmas 2.1, 4.2, 6.1--6.3 and Propositions 3.1, 6.4 are reconstructed in full on their pages." Verified: the page's Source paragraph names the Lemma 7.2 page as an input and that page carries a full proof. Replace by "Nothing else is imported: Lemmas 2.1, 4.2, 6.1--6.3, 7.2 and Propositions 3.1, 6.4 are reconstructed in full on their pages."

C12. ko26b_theorem_1_1_reconstruction, "Readings addressed", first bullet, "The 1949 bounds place these at $\frac12+o(1)$ ". Verified against the (3.3) and (4.3) pages: the note proves $\Lambda_r-r\ge\frac12+o(1)$ and $r-\lambda_r\ge\frac12+o(1)$ , one-sided bounds and not values. Replace by "The 1949 bounds give at least $\frac12+o(1)$ for each".

Rejected and downgraded findings

Findings not listed under Corrections are recorded here with the reason. "Optional" means a wording or labeling improvement the page may take without any change to what it proves or attributes.

clst25 F3 (note): downgraded to optional. The Kronecker witness as written refutes Theorem 2 at $r=1$ ; the one-line inference to Theorem 3 at $r=1$ (a gap shorter than $1/n$ gives a closed arc of length $1/n$ with two terms) is immediate.
clst25 F4, F5 (notes): optional labeling ("the corpus's completion" also covers the asymptotics and the constant) and an omitted "for all sufficiently large $r$ "; neither changes an attribution.
(3.3) F2, F3 (suggested): optional. The precise display is identified by its wording, and the passage to the limit is a routine justification of what the note asserts; the labeling rule is met in substance.
(3.3) F4, F5, F6 (notes): rejected. The identification of the final display as (3.3) is what Section 6's grouping with (4.3) and (5.7) gives; the proviso $k\ge r$ is never violated on the page; the strict bound holds for every $n\ge1$ and the " $(n\ge2)$ " qualifier is harmless.
(4.3) F2 (suggested): optional. The finite form's extra term relative to the printed general- $r$ sum is already recorded in the Source notes.
(4.3) F4 (note): optional. The transfer of the bound from all sequences to distinct sequences goes the right way (a supremum over a smaller family is no larger); the page's sentence is descriptive.
(5.7) F1 (suggested): downgraded to optional. Verified on p. 17: the note runs its argument for every natural number $n$ ; the page's $n\ge2$ is its own restriction, stated with its reason, and loses nothing since only $n\to\infty$ matters. An attribution would help a reader comparing with the note but no result changes.
(5.7) F2--F5 (notes): rejected as wording. The supplied reasons are correct and routine; "allows" versus "does not exclude" is a nuance; the fixed- $r$ range $r\ge2$ is on the linked page; "exceeds $1+1/r-o(1)$ " is true with a slightly larger $o(1)$ .
ko26a L3.1 F1, F2 (suggested): optional. $\rho>1$ and $n\ge r$ are harmless narrowings that every use satisfies; a label would be tidy.
ko26a L3.1 F3 (suggested): downgraded to optional. The witness shows the other reading of "split at time $T$ " is false, but the page's Definitions fix that a split is the insertion of a point and its proof places the two pieces at time $T$ , which is the source's reading; the Statement may add the clause but is not wrong as written.
ko26a L3.1 F4 (note): rejected. A label slip in the canonical conversion is not a defect of the page, which cites no equation labels.
ko26a P4.1 F1 (suggested): downgraded to optional. At $N^+=N+1$ the line "by the minimality of $N^+$ " should read "by $\beta<1$ "; the page assumes $\beta\in(0,1)$ in its Definitions, so the fact is available and the proposition holds.
ko26a P4.1 F2, F3, F4 (suggested, suggested, note): optional precision. The page's "protected block" is introduced only for epoch steps, so the active-gap count is epoch-restricted as written; an unsplit gap is its own piece; the two usages of "split at time $T$ " are each correct in place.
ko26a P4.1 F5 (note): rejected as immaterial. The source's accounting is one paragraph of five sentences, not two; the quoted formula is accurate and nothing depends on the count.
ko26a T1.1 F1 (suggested), F3, F4, F5 (notes): optional labeling and wording; the supplied constants are correct, $\rho>1$ follows from $R_n\ge1$ , and the comparison with the 1949 note is a remark.
ko26a T1.1 F2 (note): downgraded to optional. The proof itself writes $C_0=C(r,\eta,\rho)$ ; the Source note groups the constants loosely.
ko26b L2.1 F1 (suggested), F2, F3, F4 (notes): optional. Hypothesis (2.1) is stated in the page's Definitions as the section's standing assumption, as in the source; the supplied condition $kr<|P_s|$ is harmless; the arc list under Uniformity omits arcs whose shortness needs only $t_->E$ ; the gloss on $D$ is approximate.
ko26b P3.1 F2 (suggested): downgraded to optional. The two descent displays follow from (2.2) and (2.3) multiplied by $D$ ; the page's route through the Lemma 2.1 proof is correct but longer.
ko26b P3.1 F3 (note): optional. "If it contained $r+1$ " should read "at least $r+1$ " with the first $r+1$ of them; the source has the same compression.
ko26b L4.2 F2 (suggested): downgraded to optional. The remark on Schmidt's theorem states the theorem it uses and marks the deduction as what is checked; the corpus holds a card for Schmidt 1972, which the remark may link.
ko26b L4.2 F3 (suggested), F4, F5 (notes): optional. The supplied justifications are correct; "intervals holding at most $S$ points" is a gloss used consistently across the folder's summaries for arcs of expected count at most $S$ ; the box convention changes no supremum.
ko26b L6.1 F1 (suggested): downgraded to optional. The cyclic-order indexing is fixed by the page's own gloss "the sum of $k$ consecutive $r$ -spans starting at $p$ " and by the source's convention on p. 1.
ko26b L6.1 F2 (suggested), F4, F5 (notes): optional wording: the nominal mean $kr/t$ , the inherited time quantifier and the placement of the multiplicative-interval remark.
ko26b L6.2 F1 (suggested): optional. The time quantifier is the section's standing convention, as the review itself records.
ko26b L6.2 F3, F4 (notes): rejected. The range "pp. 10--12" is over-inclusive, not wrong; the justification of (6.4) is correct and routine.
ko26b L6.3 F1 (suggested), F2 (note): optional. The import carries its own threshold, which includes (6.1) at $n$ ; the span notation reaches the page through the Lemma 6.1 page.
ko26b L6.3 F3 (note): resolved by C7, which displays the sharper bound on the Lemma 6.1 page; the reindexing $i\mapsto i-r$ is a bijection mod $n$ and needs no sentence.
ko26b P6.4 F2 (suggested): downgraded to optional. The source's reuse of $C'$ in the descent display is a loose constant; the page's $C''$ is correct and labeled absolute, and the page does not attribute that line to the source.
ko26b P6.4 F3, F4 (notes): optional. "Small" covers $2\theta<1$ and $\Lambda>1$ ; the desc gloss is as for L4.2 F4.
ko26b L7.2 F1, F2 (suggested), F3, F4, F5 (notes): optional. The single-threshold reading is the source's and is what Proposition 6.4 supplies; the supplied details are correct; $P_0=\varnothing$ is the only reading; the integration order is immaterial by Tonelli; $B\ge1$ is carried from the source unused.
ko26b T1.1 F1 (required): rejected as wrong. The sentence "the 1949 bound is $r(\mu_r-1)\ge1$ , the fixed- $r$ improvement is $1+1/(r^2-1)$ ..., and the theorem claims $\log r/100$ " is written in the units of the third expression $r(\mu_r-1)$ , in which the note's $\mu_r\ge1+r/(r^2-1)$ is exactly $r(\mu_r-1)\ge r^2/(r^2-1)=1+1/(r^2-1)$ and the 1949 bound is $1$ , as the linked Korsky-note page states in its own Reading addressed section; the review's comparison with $1+1/r$ mixes the two units. The page is correct; an optional clarification is "the fixed- $r$ improvement is $r(\mu_r-1)\ge1+1/(r^2-1)$ ".
ko26b T1.1 F4, F5, F6, F7 (notes): optional. The distinct-points bullet may say "at most one point inserted before the threshold time"; the natural logarithm is fixed on p. 1 of the source and may be stated; the witness sequences of the upper bound have distinct terms; the routine justifications are correct.

Graded verdicts

No tier is assigned and no status changes. The pages remain author-recorded reconstructions; the verdicts below are those of the graded focused reviews, read with the corrections above.

clst25_theorem_2_reconstruction. Fidelity: faithful with corrections (C1, C2); the statements of Theorems 2 and 3, the circle-form remark, the derivation paragraph with its two label slips and every locator match the artifact. Argument: defective as written on the range $2\le r<2+c\log2$ , where the lower-bound step applies the imported Theorem 3 at the excluded instance $R=1$ ; sound for every $r\ge2+c\log2$ ; the reconstructed statement is not refuted, and C1 restricts the derived range to what the import supports.
dber49_inequality_3_3_reconstruction. Fidelity: faithful with corrections (C3). Argument: sound; the general- $r$ completion is correct with coincident points included.
dber49_inequality_4_3_reconstruction. Fidelity: faithful with corrections (C5). Argument: sound, with the justification of the span step replaced by C4; no conclusion changes.
dber49_inequality_5_7_reconstruction. Fidelity: faithful, the printed denominator $rn+n-1$ correctly recorded as a slip. Argument: sound.
ko26a_lemma_3_1_reconstruction. Fidelity: faithful. Argument: sound.
ko26a_proposition_4_1_reconstruction. Fidelity: faithful. Argument: sound; the corpus's active-gap expansion is correct.
ko26a_theorem_1_1_reconstruction. Fidelity: faithful. Argument: sound.
ko26b_lemma_2_1_reconstruction. Fidelity: faithful. Argument: sound.
ko26b_proposition_3_1_reconstruction. Fidelity: faithful with corrections (C9, the summary line only). Argument: sound.
ko26b_lemma_4_2_reconstruction. Report void; no graded review verdict stands for this page. The grader's own reading of the page against Section 4 of the source found the statement, the imported Theorem 4.1 and the proof faithful apart from C6, and the argument sound relative to the imported Theorem 4.1; this reading is not a focused review, and the page needs a repaired report before it carries a graded verdict.
ko26b_lemma_6_1_reconstruction. Fidelity: faithful. Argument: sound; C7 writes the bound its consumers cite.
ko26b_lemma_6_2_reconstruction. Fidelity: faithful. Argument: sound; C8 links the consumed page.
ko26b_lemma_6_3_reconstruction. Fidelity: faithful. Argument: sound.
ko26b_proposition_6_4_reconstruction. Fidelity: faithful with corrections (C10). Argument: sound; the clause that the threshold does not depend on $D$ is true, and C10 supplies its reason.
ko26b_lemma_7_2_reconstruction. Fidelity: faithful. Argument: sound relative to the imported Theorem 7.1.
ko26b_theorem_1_1_reconstruction. Fidelity: faithful with corrections (C11, C12). Argument: sound relative to the two imported theorems (Theorem 4.1 as derived from Larcher's proof, Theorem 7.1) and to the input pages; the composition inherits those unchecked premises, as the page says, and the source's claim remains unrefereed and unreviewed.

No tier is assigned and no status changes.

Linked from (3)

Consecutive-gap constants on the circle Reviews of the Problem 1221 reconstructions Distinct grade of the second Korsky Lemma 4.2 review

Graph