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Subject

The folder wiki/research/erdos_501/ as it stood at 2026-09-28T05:03:27Z and its thirteen reconstruction pages, each read whole as of that time:

• wiki/research/erdos_501/ch_counterexample_reconstruction.md
• wiki/research/erdos_501/glazer_lemma_2_1_reconstruction.md
• wiki/research/erdos_501/glazer_lemma_2_2_reconstruction.md
• wiki/research/erdos_501/glazer_lemma_4_1_reconstruction.md
• wiki/research/erdos_501/glazer_lemma_4_3_reconstruction.md
• wiki/research/erdos_501/glazer_lemma_4_5_reconstruction.md
• wiki/research/erdos_501/glazer_proposition_4_4_reconstruction.md
• wiki/research/erdos_501/glazer_theorem_1_1_reconstruction.md
• wiki/research/erdos_501/glazer_theorem_3_2_reconstruction.md
• wiki/research/erdos_501/glazer_theorem_5_1_reconstruction.md
• wiki/research/erdos_501/lee_lemma_2_1_reconstruction.md
• wiki/research/erdos_501/lee_lemma_3_1_reconstruction.md
• wiki/research/erdos_501/lee_theorem_1_1_reconstruction.md

The folder index wiki/research/erdos_501/_index.md as of the same time was read for the author's description of the folder; it is not graded.

The thirteen reports graded, one per page, each read whole; they are the records filed beside this grade:

• ch_counterexample_reconstruction_review
• glazer_lemma_2_1_reconstruction_review
• glazer_lemma_2_2_reconstruction_review
• glazer_lemma_4_1_reconstruction_review
• glazer_lemma_4_3_reconstruction_review
• glazer_lemma_4_5_reconstruction_review
• glazer_proposition_4_4_reconstruction_review
• glazer_theorem_1_1_reconstruction_review
• glazer_theorem_3_2_reconstruction_review
• glazer_theorem_5_1_reconstruction_review
• lee_lemma_2_1_reconstruction_review
• lee_lemma_3_1_reconstruction_review
• lee_theorem_1_1_reconstruction_review

Sources read for adjudication. The eight-page draft rev10 held by Glazer (2026): the whole text layer, and physical p. 5 as a page image (the proofs of Lemma 4.1, Lemma 4.3 and Proposition 4.4, read for the findings on those pages). The six-page second version held by Lee (2026): the whole text layer; and the retained first version's text layer at the opening of its Section 3 and its reference list, for C7. Every finding was adjudicated against these texts and the frozen pages; where a report re-derived a step, the derivation was checked and, for the steps behind C1--C7, re-derived here. The cards for Erdős and Hajnal (1960) and for Newelski, Pawlikowski and Seredyński (1987) were located but not needed by any finding and were not read. Also read: docs/verification.md "Independence and the assignment", "Exact subjects and durable evidence", "Report contract", "Grading and claim standing", "Whole-claim report" and "Audit checklist"; the provenance paragraphs of the two library cards; and, of wiki/problems/set_theory/E0501/_index.md, the Statement, the References, the "Remaining gaps" paragraph and the "Progress" paragraph, to check the two pointers in the counterexample page's Boundary paragraph.

Independence facts by role. The grader is a distinct role from the author of the thirteen pages and from every reviewer: a fresh context given only the grading assignment, which took no part in writing any page or report, read the reports only after the assignment and the pages only as of that time, consulted no other review of these pages (none exists), and made no web search. The grader is not blind and read, as the wiki allows for the grading role, the folder index, the library cards' heads and the problem page's status paragraphs.

Ruling on the reviewers' disclosed exposures. Every report discloses that over-wide reads printed standing or acceptance text: the library cards' "Read status" and "Relation to E501" paragraphs, the problem page's Status paragraph, and in five reports the Standing or Proof sections of sibling reconstruction pages. By the content test of docs/verification.md "Independence and the assignment", nothing in any report could only have come from that text, and no attack or finding follows it: every finding rests on the frozen page and the held PDFs, and the one use of exposed text (the Theorem 1.1 report's confirmation of a Boundary sentence about the companion formalization from the card) concerns no mathematics. The exposures are ruled immaterial. No report read another review.

Reports graded

Each pass below was checked against the same list: a subject block whose subject date is the one above and whose path is in the tree as of that time; stated role, independence facts and exposures; a restatement carrying the quantifiers, hypotheses and conventions; an explicit verdict on each of the ten items of the Erdos-specific audit checklist; weakest steps re-derived rather than paraphrased; a strongest attack actually run; premises with their interfaces and reading depth; and a verdict. Every report also writes verdict words in full and names no person, seat, session, model or harness.

• ch_counterexample_reconstruction_review: pass. All parts present; the three weakest steps are re-derived (well-ordering, the one-sided inequality, the iteration with its boundary instance), the attack probes the symmetry of independence and the hypotheses used, and the ten checklist verdicts are explicit.
• glazer_lemma_2_1_reconstruction_review: pass. All parts present; the exhaustion, the choice of $n$ and the Tonelli count are re-derived, and the attack exhibits the counterexample without the uniform bound ($E=\{(t,s):t<s\}$ on $\mathbb N$), which was checked here.
• glazer_lemma_2_2_reconstruction_review: pass. All parts present; the measurability of $C'$, the finiteness of the removed part and the transfer of infinite measure are re-derived, and the attack targets the reading of "measurable".
• glazer_lemma_4_1_reconstruction_review: pass. All parts present; both cases of the proof and the import (R2) are re-derived, and the attack on the reinterpretation of the Borel isomorphism found the import gap accepted as C2.
• glazer_lemma_4_3_reconstruction_review: pass. All parts present; the root bound, the CH pigeonhole and the root identity are re-derived, and the attack on the Boundary paragraph carries a witness, accepted as C3.
• glazer_lemma_4_5_reconstruction_review: pass. All parts present; the transfer step, the Tonelli display and the reduction are re-derived, and the attack on the two appeals to (R2) succeeds, accepted as C4 with one repair to the reviewer's proposed text noted there.
• glazer_proposition_4_4_reconstruction_review: pass. All parts present; the three steps are re-derived, and the attack carries an explicit witness (two equal names read from $D_0\cup D_1$), accepted as C5.
• glazer_theorem_1_1_reconstruction_review: pass, with a form defect recorded. The checklist is filed against the shared canonical failure modes and named patterns rather than under the ten Erdos item names that govern the checklist part here. Each of the ten items is nonetheless explicitly decided in the report: Quantifiers and scope by the almost-all and exceptional-set entries and attack (b); Circularity by the circular-use and induction entries; Model and convention changes by the relaxed-system and model-class entries and attack (a); Finite and statistical overreach by the finite-verification, heuristic and uniformity-from-instances entries; Uniformity by the infinite-family entry; Extremal conclusions by the extremal entry; Consequences and composition by the three entries so named; Computation by the certified-bracket and harness entries; Reproduction by the reproducibility and gate entries; Source and verdict fidelity by the verifier-quotation and verdict-word entries with the clause-by-clause fidelity verdict in the Verdict section. Equivalent headings with unambiguous parts are acceptable under the report contract, so the report passes; a later report should use the ten item names.
• glazer_theorem_3_2_reconstruction_review: pass. All parts present; the graph's measurability, the column bound and the selection in $Z$ are re-derived, and the attack on the orientation of the graph is real.
• glazer_theorem_5_1_reconstruction_review: pass. All parts present; the transfer of (5.4), the truncation and the closing of the quantifiers are re-derived, and the attack on the coherence of the three identifications is real.
• lee_lemma_2_1_reconstruction_review: pass. All parts present; the lower bound (18), the choice (16) and the sections of $H$ are re-derived, and the attack aims at the one non-measurable set measured on the Lebesgue side.
• lee_lemma_3_1_reconstruction_review: pass. All parts present; the weight, the majorant and the limit are re-derived, and the attack transports the lemma to the Lebesgue $\sigma$-algebra under CH and exhibits the failure there, which was checked here.
• lee_theorem_1_1_reconstruction_review: pass. All parts present; the pool measure, the pool nonemptiness and the corollary are re-derived, and the attack on the corollary's route through $\mathrm{Con}(\mathrm{ZFC})$ is real.

Corrections

Each correction was verified against the held notes and the frozen page. "Current" quotes the page as of that time; "Replacement" is the exact text that replaces it.

C1. Page ch_counterexample_reconstruction.md, Proof, last paragraph. Current: "so $|x_n|<|x_0|-n$ for every $n$. For $n>|x_0|$ this gives $|x_n|<0$, which is impossible." Replacement: "so $|x_n|<|x_0|-n$ for every $n\ge1$. For an integer $n>|x_0|$ this gives $|x_n|<0$, which is impossible." Reason: at $n=0$ the universal sentence reads $|x_0|<|x_0|$ and is false; the chain proves the strict inequality for $n\ge1$ only, and the contradiction uses $n>|x_0|\ge0$, so the conclusion is unaffected. Lee p. 6 states the iteration without a universal quantifier and Glazer p. 8 does not spell it out; the quantifier is the page's own. Accepted from the report's F1.

C2. Page glazer_lemma_4_1_reconstruction.md, Conventions and imported facts, item (R4). Current: "(R4) Absoluteness. Standard Borel spaces, Borel sets and Borel maps coded in $M$ are reinterpreted in $M[G]$ from the same codes, and Borel statements about points are absolute between $M$ and $M[G]$. A name for an element of a standard Borel space $X$ is a name $\dot z$ with $\Vdash\dot z\in X$ for the reinterpreted $X$." Replacement: "(R4) Absoluteness. Standard Borel spaces, Borel sets and Borel maps coded in $M$ are reinterpreted in $M[G]$ from the same codes, a coded preimage, complement or countable union being reinterpreted as the preimage, complement or union of the reinterpretations; Borel statements about points of $M$ are absolute between $M$ and $M[G]$; and a $\Pi^1_1$ statement about the coded objects that holds in $M$ holds in $M[G]$ (Mostowski's absoluteness theorem, T. Jech, Set Theory, third millennium edition, Chapter 25), in particular that a coded Borel map is injective, carries a coded set into a coded set, or is inverse to another coded map. A name for an element of a standard Borel space $X$ is a name $\dot z$ with $\Vdash\dot z\in X$ for the reinterpreted $X$." Reason: the general case of the proof uses, for the point $\dot z$ of the extension, that the reinterpreted $\iota$ carries the reinterpreted $X$ into $X'$ and that $\iota^{-1}\circ\iota$ is the identity there; these are universal statements over all points of the extension with a Borel matrix in the codes, that is $\Pi^1_1$ statements, and "Borel statements about points" covers only points of $M$. The source (p. 5) says only "modify the reading on the null set", so the burden is the page's. The page's Standing paragraph promises to name the standard facts the proof rests on, and this one was missing. Promoted from the report's F1 (suggested) after verification; the proof's citations of (R4) need no change.

C3. Page glazer_lemma_4_3_reconstruction.md, Boundary paragraph. Current: "to the countable supports of $\omega_2$ names; there the sets $S_\alpha$ are pairwise distinct because each contains its own block $\{\alpha\}\times\omega$." Replacement: "to the countable supports of $\omega_2$ names. Those supports need not be pairwise distinct, since two names may share a support even though each support contains its own block $\{\alpha\}\times\omega$; this is why the precise statement above is given for an indexed sequence and returns an injection on indices rather than $\omega_2$ distinct sets. The sequence form is equivalent to the source's family form: a family of $\omega_2$ sets is the injective case, and a sequence with fewer than $\omega_2$ distinct values takes one value $\omega_2$ times, a $\Delta$-system with that value as root." Reason: containing one's own block does not prevent containing another's, so the deduction fails, and the source (p. 5, proof of Proposition 4.4) neither states nor arranges distinctness; two equal names read from one support $S\supseteq R_0\cup D_\alpha\cup D_\beta$ give $S_\alpha=S_\beta$. The equivalence sentence was checked: with fewer than $\omega_2$ values, the regularity of $\omega_2$ makes one value occur $\omega_2$ times. Accepted from the report's F1.

C4. Page glazer_lemma_4_5_reconstruction.md, six edits that make the closed-code route the main line, so that every set in the proof is Borel and the two appeals to (R2) fall within its hypotheses, and that state what the general Borel-code route needs.

(a) Reduction. Current: "Then some condition $q_0$ forces that such a $B$ exists for $\dot Z$; by the maximum principle (R3) there is a name $\dot B$ for a Borel subset of $2^P$, given by a name for a Borel code, with" followed by the display and "Since $q_0$ forces that some positive rational lies below $\nu(\dot B)$, strengthen $q_0$ to a condition $q$ deciding one: fix a rational $\varepsilon>0$ with $q\Vdash\nu(\dot B)>\varepsilon$ (the source's (4.4))." Replacement: "Then some condition $q_0$ forces that such a $B$ exists for $\dot Z$, and, by inner regularity of $\nu$ in the extension, that some closed such $B$ exists. Fix an enumeration $(U_n)_{n<\omega}$ of the basic clopen subsets of $2^P$ and, for $c\in2^\omega$, put $K_c=2^P\setminus\bigcup\{U_n:c(n)=1\}$: every $c\in2^\omega$ codes a closed set, every closed $K\subseteq2^P$ is $K_c$ for $c=\{n:U_n\cap K=\varnothing\}$, and the relation $v\in K_c$ is closed in $(c,v)$. By the maximum principle (R3) there is a name $\dot c$ for an element of $2^\omega$, mixed with a fixed default off $q_0$ so that $\Vdash\dot c\in2^\omega$; write $\dot B=K_{\dot c}$, so that" followed by the unchanged display and "Since $q_0$ forces that some positive rational lies below $\nu(\dot B)$, strengthen $q_0$ to a condition $q$ deciding one: fix a rational $\varepsilon>0$ with $q\Vdash\nu(\dot B)>\varepsilon$ (the source's (4.4); the source keeps $\dot B$ Borel, given by a Borel code, see the labeled point below)."

(b) A fresh petal. Current: "supports $q$ and reads the code of $\dot B$ through a Borel map $F$ from $2^T$ into the space of codes." Replacement: "supports $q$ and reads $\dot c$ through a Borel map $F\colon2^T\to2^\omega$."

(c) Factor over $T$ and $P_\alpha$. Current: "For $t\in2^T$ let $B_t\subseteq2^P$ be the Borel set decoded from $F(t)$, and consider". Replacement: "For $t\in2^T$ let $B_t=K_{F(t)}\subseteq2^P$, a closed set, and consider".

(d) Same paragraph, after "where $q$ is identified with a Borel subset of $2^T$ supporting it." append: "The set $W$ is Borel, being $\bigcap_n\{(t,v):F(t)(n)=0\text{ or }v\notin U_n\}$, and so is the base of the cylinder $W'$."

(e) Same paragraph. Current: "otherwise the measurable set $\{t\in q:\nu(B_t)\le\varepsilon\}$ has positive measure, and as a condition". Replacement: "otherwise the Borel set $\{t\in q:\nu(B_t)\le\varepsilon\}$, Borel because $t\mapsto\nu(K_{F(t)})=1-\sup_N\nu\bigl(\bigcup\{U_n:n<N,\ F(t)(n)=1\}\bigr)$ is a Borel function, has positive measure, and as a condition".

(f) Labeled point. Current: the whole text after "Labeled point (compilation remark).", from "The display for $\mu_{\Theta'}(W')$ needs $W$ to be measurable" to "With either reading the argument above goes through unchanged." Replacement: "The source takes $\dot B$ to be a Borel set given by a Borel code and folds both the measurability of $W$ and the transfer of the ground-model measure computation into the forcing relation into "by Fubini". The proof above shrinks $\dot B$ to a closed set first, a step the source does not take and not an author-issued correction: with closed codes every $c\in2^\omega$ is a code, $W$ is Borel, both appeals to (R2) are within its hypotheses, and (R1)--(R4), Lemma 4.2 and Tonelli's theorem for the completed product suffice. With general Borel codes the set of codes is coanalytic and not Borel, so $W$, $W'$ and $\{t\in q:\nu(B_t)\le\varepsilon\}$ are only coanalytic; they are still universally measurable (A. S. Kechris, Classical Descriptive Set Theory (1995), Chapters 29 and 35), so the display for $\mu_{\Theta'}(W')$ stands, but the two appeals to (R2) then need an import beyond (R1)--(R5): for a coanalytic $C\subseteq2^S$ coded in $M$, take in $M$ a Borel $C_0\subseteq C$ with $\mu_S(C\setminus C_0)=0$; the $\Pi^1_1$ inclusion $C_0\subseteq C$ holds in $M[G]$ by Mostowski's absoluteness theorem (T. Jech, Set Theory, third millennium edition, Chapter 25), so the condition $[C_0]=[C]$ forces $\dot G\restriction S\in C$ by (R2), which is what both steps use."

Reason: (R2) on the Lemma 4.1 page is stated for Borel $W$ coded in $M$. There is no standard Borel space of codes with a Borel decoding relation for all Borel sets (a Borel set universal for the Borel subsets of $2^P$ does not exist), so under the page's main line the set of codes is coanalytic, $W$ and $\{t\in q:\nu(B_t)\le\varepsilon\}$ are only coanalytic, and the two sentences "by (R2)" and the closing sentence "With either reading the argument above goes through unchanged" are not supported by the declared imports. The source (p. 6) says only "by Fubini", so the transfer is the page's supplied step. The closed-code route was re-derived here in full: inner regularity of $\nu$ inside the extension gives the closed set; with $S'=T\cup P_\alpha$ the Boolean value $\|\dot z_\alpha\in\dot B\|\wedge q$ equals $[W']$ by (R2) on the Borel base of $W'$; Lemma 4.2 and Tonelli give the display; the almost-every step uses (R2) on the Borel set $\{t\in q:\nu(B_t)\le\varepsilon\}$ and the same-formula reinterpretation of (R4). Accepted from the report's F1 (required), with one repair: the reviewer's proposed squeeze also transfers the inclusion $C\subseteq C_1$ into $M[G]$, which is a $\Pi^1_2$ statement (for all $t$, $t\notin C$ or $t\in C_1$, with $t\notin C$ analytic) and not covered by Mostowski's theorem; only the lower inclusion $C_0\subseteq C$ is needed, and the accepted text uses only that. The report's F2 (the name for the code must be a name for an element of a standard Borel space under the top condition) is discharged by the mixing sentence in (a).

C5. Page glazer_proposition_4_4_reconstruction.md, Proof, Supports paragraph. Current: "The sets $S_\alpha$ are countable and pairwise distinct, since $D_\alpha\subseteq S_\alpha$ and the blocks are disjoint." Replacement: "The sets $S_\alpha$ are countable. They need not be pairwise distinct, since two names may share a support: Lemma 4.3 as reconstructed applies to the sequence $\langle S_\alpha:\alpha<\kappa\rangle$ as it stands, and a member repeated inside the $\Delta$-subsystem below equals the root $R$, so its block lies in $R$ and its index is discarded under "Blocks inside petals"." Reason: the same non sequitur as C3, with the report's witness checked: for $X=2^\omega$, a bijection $e\colon\omega\to D_0\cup D_1$ and $\dot w_0=\dot w_1$ the name for $n\mapsto\dot G(e(n))$, the Lemma 4.1 reading of both names has support $D_0\cup D_1$, so $S_0=S_1$ after enlargement. The sentence is not used: if $S_\alpha=S_\beta$ for distinct $\alpha,\beta\in J_0$ then $S_\alpha=S_\alpha\cap S_\beta=R$, so $D_\alpha\subseteq R$ and $\alpha$ leaves at the next step. Accepted from the report's F1.

C6. Page glazer_theorem_3_2_reconstruction.md, Definitions, end of the paragraph "Outer measure one". Current: "This meeting property is the only use of (P1) below." Replacement: "This meeting property is the only largeness property of $Z$ used below; the other clauses of (P1), that $(\Omega,\nu)$ is a standard Borel probability space, are used for the Borel structure of $S^2$ and the $\sigma$-finiteness of $\mu$." Reason: the page's (P1) has two clauses, and its own proof uses the first twice ("$S$ is a standard Borel space", "each $\{m\}\times\Omega$ has measure one"); the source (p. 3) says "This is the only largeness property of $Z$ used below", a statement about $Z$ only. Accepted from the report's F1.

C7. Page lee_lemma_3_1_reconstruction.md, Source paragraph. Current: "The first version, also held, took the inequality from Kunen's theorem as stated in Fremlin's notes instead of proving it; the labels here are the second version's." Replacement: "The first version, also held, took the inequality from Kunen's theorem as stated in Fremlin's Measure Theory, Volume 5, Chapter 54, result 543C (its Theorem 3.1, citing its reference [3]) instead of proving it; the labels here are the second version's." Reason: verified in the held first version's text layer: its Section 3 opens "We use the following theorem of Kunen [3, 543C]", and its reference [3] is D. H. Fremlin, Measure Theory, Vol. 5, Chapter 54, "Real-valued-measurable cardinals" (the file chap54.pdf), while the separate survey notes "Real-valued-measurable cardinals" (rvmc.pdf, its reference [6] and the second version's [3]) are cited only for the equiconsistency and use the numbering 1D(e) and 2E. The folder's Theorem 1.1 page cites those survey notes, so "Fremlin's notes" pointed a reader to the wrong document. Promoted from the report's F1 (suggested) after verification against the held first version.

Rejected and downgraded findings

A downgraded finding is retained as an optional improvement that changes no mathematics; a rejected finding is one whose defect does not exist. Labels are the reports' own.

ch_counterexample_reconstruction_review:

• F2 (suggested), mark "without repetition" and the $\omega$-sequence as supplied: downgraded. Both supplements are correct and standard; the page does not present them as the sources' words.
• F3 (note), the desc attributes the construction rather than the result to Hechler: rejected. Both abstracts write "Hechler's counterexample" (Glazer p. 1, Lee p. 1), which is the desc's phrasing; the body's Source paragraph is exact, and the problem page records the open attribution question, as the page says.
• F4 (note), the Hechler citation omits the series name: downgraded. The volume, year and pages identify the note; adding "Sér. Sci. Math. Astronom. Phys." is optional.

The page's two Boundary pointers into the problem page, outside the reviewer's read set, were checked here: the "Progress" paragraph of E0501.md records the same construction along a well-ordering of order type $\mathfrak c$ under MA, and "Remaining gaps" (4) records the unresolved attribution. Both pointers are correct.

glazer_lemma_2_1_reconstruction_review:

• F1 (suggested), mark the product-$\sigma$-algebra reading of "measurable" as the page's: downgraded. The Definitions fix the convention the proof needs and the application satisfies; a parenthesis saying the source names no $\sigma$-algebra is optional.
• F2 (note), name the supplied routine justifications: downgraded; labeling only.
• F3 (note), the desc is compressed: downgraded; the phrase is readable as "removing the row of $t$ from $C$ leaves infinite measure" and is not wrong.

glazer_lemma_2_2_reconstruction_review:

• F1 (suggested), label the measurability step as supplied: downgraded; the step is correct and short.
• F2 (note), the source's cross-reference prints "theorem 2.1" and the page reads "measurable" as $\Sigma$-measurable: downgraded; both readings are right and the label artifact is the source's.
• F3 (note), Standing names no external input: downgraded; the two facts are section measurability and finite subadditivity, stated in the Definitions of the Lemma 2.1 page.
• F4 (note), "the inductive step" versus "the preservation half": downgraded; the sentence is loose, not false, and its second clause was re-derived by the reviewer and checked here.

glazer_lemma_4_1_reconstruction_review:

• F1 (suggested): promoted to C2.
• F2 (suggested), label the supplied "reads" terminology and enlargement remark inside the Statement: downgraded; the remark is correct and the Statement's first paragraph is the source's.
• F3 (note), "six-line proof": downgraded. The proof is five typeset lines on physical p. 5, checked on the page image; the count is a characterization that carries nothing.
• F4 (note), the source never defines $\mathbb B_{\omega_2}$: downgraded; the page's identification with $\mathbb B(\omega_2\times\omega)$ is the only reading consistent with the proof of Theorem 5.1 (p. 6), and saying that it is a reading is optional.
• F5 (note), Proposition 4.4 applies the lemma to names for elements of a general $X$: downgraded; the Boundary sentence names the instance the folder uses and is not wrong about it.
• F6 (note), the maximum principle for $\iota(\dot z)$ and $X\ne\emptyset$: downgraded; both steps are immediate and (R3) is listed.

glazer_lemma_4_3_reconstruction_review:

• F1 (required): accepted as C3.
• F2 (suggested), mark $[M]^{\aleph_0}$ as a reading including finite roots: downgraded; the Definitions state the convention, and the count $\aleph_1^{\aleph_0}$ bounds all countable subsets.
• F3 (note), "regular cardinal" and the two consequences unmarked: downgraded; both are correct expansions.
• F4 (note), locator for $\aleph_1^{\aleph_0}=2^{\aleph_0}$: downgraded; a one-line ZFC identity.

glazer_lemma_4_5_reconstruction_review:

• F1 (required): accepted as C4, with the $\Pi^1_2$ repair noted there.
• F2 (suggested), the code name must be a name for an element of a standard Borel space under the top condition: subsumed by C4(a), which mixes $\dot c$ with a default off $q_0$; no separate change.
• F3 (suggested), "imported below exactly as the source states it" overstates, since the import carries a measure-level gloss: downgraded. The gloss, that $\mu_{\Sigma\cup\Gamma}$ is the completion of $\mu_\Sigma\times\mu_\Gamma$, is a correct reading of "completed product"; saying so is optional.
• F4 (note), the normalized generic point and $\nu$ are the page's readings of (4.2) and (5.6): downgraded; the readings are correct.

glazer_proposition_4_4_reconstruction_review:

• F1 (required): accepted as C5.
• F2 (suggested), the isomorphism type needs injective enumerations: downgraded. "An enumeration $\langle d_n:n<\omega\rangle$" of a countably infinite set is read as injective, and every enumeration the page uses is.
• F3 (suggested), "Chapter 11" of Kechris names no unit of the book: downgraded. The book's numbered units are sections inside five chapters, so the locator's form is off; the correct unit was not checked against a copy here, and the fact (at most $2^{\aleph_0}$ Borel maps) is re-derived in the report and checked.
• F4 (note), the expansions are unmarked: downgraded; labeling only.
• F5 (note), $F_\alpha$ is renamed after enlargement: downgraded; harmless.

glazer_theorem_1_1_reconstruction_review:

• F1 (suggested), the informal sentence "Adding $\omega_2$ random reals over it ... yields a model of ZFC" presupposes a generic filter over $L^N$: downgraded. The sentence follows the source's own proof (p. 8), and the page's next sentence, "Formally, ...", carries the deduction syntactically with no generic filter; marking the first sentences as the source's informal shape is optional.
• F2 (note), the forcing theorem is used at the "Formally" step: downgraded; the import is named in Standing.
• F3 (note), "Boundedness is not assumed." sits inside the bold theorem: downgraded; the remark is the source's abstract (p. 1) and is true.
• F4 (note), the coordinate set $\kappa\times\omega$ comes from the proof: downgraded; the algebras are isomorphic and the source's proof fixes it.

glazer_theorem_3_2_reconstruction_review:

• F1 (required): accepted as C6.
• F2 (suggested), name the three supplied justifications in Standing: downgraded; labeling only, each justification checked.
• F3 (note), Lemma 2.2's null-fiber hypothesis is established one paragraph later: downgraded; the order is the source's and nothing is used before it is proved.
• F4 (note), "onto" is a reading: downgraded; the instance is onto and the Theorem 5.1 page relies on it, correctly, for the standard coding.
• F5 (note), the definition of $\nu^*$ is supplied: downgraded; it is the standard outer measure.
• F6 (note), the imported lemmas' standing is on their own pages: downgraded.

glazer_theorem_5_1_reconstruction_review:

• F1 (note), the truncation sentence paraphrases the source's reason with a different one: rejected. The page's sentence, that the truncation is what makes (P3) hold on all of $\Omega$ rather than only on $Z$, is true and does not purport to quote the source; adding the source's remark on conditional conullity is optional.
• F2 (note), $p\in G$ is not needed for the reading identity: downgraded; the premise is true and merely unused at that sentence.
• F3 (suggested), the direction of the forcing theorem used is not among (R1)--(R5): downgraded. It is named at the point of use, the heading of (R3) on the Lemma 4.1 page names the forcing theorem, and the Theorem 1.1 page imports it; an explicit statement is optional.
• F4 (note), "every open set has a code" inside $M[G]$: downgraded; true for the standard coding in every model, as the reviewer says.
• F5 (suggested), three expansions unmarked: downgraded; each checked.

lee_lemma_2_1_reconstruction_review:

• F1 (suggested), "countably many" open intervals: downgraded; the definition of $m^*$ ranges over countable covers, so the index runs over such a cover; the word is optional.
• F2 (suggested), the $\le$ half of the upper-integral identity omits the step $m^*(S)=\inf\{m(T):T\supseteq S\text{ measurable}\}$: downgraded. The omitted step is standard and follows from the cover definition, and the proof consumes only the $\ge$ half.
• F3 (suggested), supplied arguments unmarked: downgraded; labeling.
• F4 (note), "Two facts about $\nu$": downgraded; the second bullet concerns $m$ and $m^*$; wording.
• F5 (note), "Only the values ... enter": downgraded; the sentence's point, that no Lebesgue measurability of $A_y$ or $B_x$ is used, is right.
• F6 (note), $0\cdot\infty=0$: downgraded; the application has $a>0$.
• F7 (note), the label "(the source's (15))" covers more than the display: downgraded; the extra terms are the source's own justification.

lee_lemma_3_1_reconstruction_review:

• F1 (suggested): promoted to C7.
• F2 (note), the desc names the plane: downgraded; the desc describes the specialization (11) and the Statement is exact.
• F3 (note), the index range and the disjoint refinement: downgraded; with $n<\omega$ the bound is $1$ and the refinement is standard.

lee_theorem_1_1_reconstruction_review:

• F1 (suggested), label the corollary's derivation as supplied: downgraded; the page gives a derivation under a proof heading without attributing it to the source.
• F2 (note), "removes by forcing" can be read as an outright proof: rejected. Glazer p. 1 says "Our main theorem removes the measure-extension and large-cardinal hypotheses"; the page's sentence tracks the source, and the linked page states the theorem inside $M[G]$.
• F3 (note), locator for the comparison $\nu\le m^*$: downgraded.
• F4 (note), the notes are not held and only one direction is used: downgraded; correct and optional.
• F5 (note), the boundedness remark inside the bold theorem: downgraded; the source's remark follows the theorem and the page's sentence is true.

Graded verdicts

• ch_counterexample_reconstruction.md: fidelity faithful with corrections (C1, a quantifier the page added in its proof); argument sound.
• glazer_lemma_2_1_reconstruction.md: fidelity faithful; argument sound.
• glazer_lemma_2_2_reconstruction.md: fidelity faithful; argument sound.
• glazer_lemma_4_1_reconstruction.md: fidelity faithful with corrections (C2, an import used above its declared strength); argument sound, with C2 naming the absoluteness fact the general case rests on.
• glazer_lemma_4_3_reconstruction.md: fidelity faithful with corrections (C3, in the Boundary paragraph only); argument sound.
• glazer_lemma_4_5_reconstruction.md: fidelity faithful with corrections (C4); argument as filed defective at the two appeals to (R2), a supplied transfer step outside the declared imports under the page's Borel-code main line, and sound as corrected by C4. The lemma is not refuted; the source's own proof carries the same unstated transfer.
• glazer_proposition_4_4_reconstruction.md: fidelity faithful with corrections (C5); argument sound, the corrected sentence not being load-bearing.
• glazer_theorem_1_1_reconstruction.md: fidelity faithful; argument sound.
• glazer_theorem_3_2_reconstruction.md: fidelity faithful with corrections (C6, a remark on which clauses of (P1) are used); argument sound.
• glazer_theorem_5_1_reconstruction.md: fidelity faithful; argument sound.
• lee_lemma_2_1_reconstruction.md: fidelity faithful; argument sound.
• lee_lemma_3_1_reconstruction.md: fidelity faithful with corrections (C7, a citation in the Source paragraph); argument sound.
• lee_theorem_1_1_reconstruction.md: fidelity faithful; argument sound.

These are focused reviews and a distinct grade of author-recorded reconstructions; they do not certify the two notes, the companion Lean developments or the problem's status. No tier is assigned and no status changes.