Wiki
Wiki

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

Updated


Record, attribution and exact subject

PASS. A fresh reviewer checked the formulation-correction package for Problems 908 and 910: its source findings and six candidate pages. This half of the record retains the E908 part of that review. For this source it covers only the exact statement of Laczkovich's Theorem 3 and the opening definitions (printed pp. 217 and 224, measurable summand); it expressly excludes the Theorem 3 proof. Review completed 2026-09-06T04:57Z. Reviewer: a fresh review context distinct from the author of the reconstruction and from the compilation-supplied corrections; it did not build on the subject before reviewing it. No distinct grader is recorded, so no numerical claim tier is assigned.

Exposure disclosure. The frozen review packet's root contained, beside the mathematical subject, the author's report.md, the author's inputs/reconciliation/reconciliation.md, and two earlier independent reviews of the predecessor package, inputs/pass_02_quality_corrections_03_independent_review/review.json (lines 178-195 Q908-01 to Q908-03 PASS, line 246, lines 346-347 "no frontmatter status change") and inputs/pass_02_quality_corrections_03_title_independent_receipt/review.json (Keleti title delta only); whether the reviewer opened the three inputs/ files is not recorded, and the packet is not retained in this repository. On 2026-09-18 a distinct grader (model: Claude Fable 5.1) ruled the exposure immaterial by the content test: F908-01 rests on the reviewer's own source renders, and its overlap with the earlier Q908-01 answer is noted and does not change the ruling.

The reviewed subject was a frozen candidate package read from the review packet. The reviewed source page and problem candidates are not retained byte-for-byte here. The exact reviewed copies are not retained in this repository. On 2026-09-16 the current pages were compared with the report's description of the reviewed statements and agree with it; the retained version history since the earliest corpus snapshot shows only attribution and standing wording changes on these pages. A match of description is not a byte match, and any substantive change to the mathematics requires a new assessment. The pages the report names are identified as they stood on 2026-09-15, before this record's filing on 2026-09-16; the exact reviewed copies were review-packet candidates and are not retained, and the comparison recorded in this section says how the committed pages relate to them.

This record was filed on 2026-09-16 from a retained report, the review text and its machine-readable companion, and was afterwards divided by source home. This half retains the report's E908 parts together with the joint verdict, completion time and subject list; its E910 parts are retained with the Rudin source as the [[analysis/rudin_1958_connected_subset_plane/evidence/verify/formulation_review|other half of the same review]]. The filing changed only the wrapper, participant identifiers, private paths and operating-history material, and the division changed only which parts each half retains; neither records a new verdict, and the first-person readings and judgments below belong to the historical reviewer, not to the filing author.

The frozen review package also carried text outside the mathematical subject: the author's packet report.md (lines 5–6 and 29–33: review pending, all credits zero, imported statuses preserved) and, under the packet's inputs/ directory, the earlier compilation's reconciliation/reconciliation.md (lines 179–193 and 197–227, "Verdict: preserve the hold" and the correction paths) and the earlier independent review pass_02_quality_corrections_03_independent_review/review.json (lines 254–255 and 348, "PASS_AT_DECLARED_SCOPE; HOLD_REMAINS" and the E910 no-status-change hold); none of these packet files is retained in the repository, and whether the reviewer opened the two inputs/ files is not evidenced, since the review cites only render images under that directory. On 2026-09-18 a distinct materiality grader (model: Claude Fable 5.1) ruled the exposure immaterial by the content test: none of the exposed text states or implies the PASS verdict the reviewer was asked for, and the reviewer's reasoning shows no reliance on any of it.

Retained report

Verdict: PASS. All findings and six page candidates pass. No candidate delta is required.

Reviewed manifest: 90/90 entries independently checked. Review completed: 2026-09-06T04:57:17.094057+00:00.

Finding decisions

FindingVerdictResult
F908-01PASSThe formulation split is exact. De Bruijn printed p.195 states measurable g in the weak three-summand conjecture; the Sierpiński/CH discussion on that page refutes only the two-summand difference property. Its local-L2 sentence concerns replacement of the difference class and corresponding summand class, not an assumption that f itself is locally L2; the exact Section 5 theorem remains queued. Laczkovich printed pp.217 and 224 and Mátrai printed pp.1–2 use measurable g, whereas Erdős 1982 printed p.76 says continuous g and attributes the claim to Laczkovich.
F908-04PASSThe Keleti PDF has 18 physical pages, with printed p.15 first and p.32 last. The correction from 15–38 to 15–32 is exact, and all four metadata value guards apply and reverse exactly.

Candidate subjects

The candidate targets were read from the review packet's copies of these paths; the exact copies are not retained in this repository:

  • wiki/problems/analysis/E0908/_index.md
  • wiki/problems/analysis/E0910/_index.md
  • library/analysis/debruijn_1951_functions_whose_differences_belong_given_class/_index.md
  • library/analysis/rudin_1958_connected_subset_plane/_index.md
  • library/analysis/keleti_1998_difference_functions_periodic_measurable_functions/_index.md
  • library/analysis/laczkovich_1980_functions_measurable_differences/_index.md

All four original existing-page snapshots matched the assigned versions. The six forward guards and six inverse guards replay exactly. All four Keleti metadata replacements apply and reverse exactly. The imported statement bytes and the primary candidate frontmatter statuses remain unchanged.

Source conclusions

  • De Bruijn printed p.195 separates the two-summand Sierpiński obstruction from the weak three-summand conjecture and places local L2L_2 in the difference-class replacement; the exact Section 5 theorem remains queued.
  • Laczkovich printed pp.217 and 224 and Mátrai pp.1–2 use a measurable summand. Erdős 1982 p.76 says continuous and is retained as a conflicting retrospective attribution.
  • Keleti Corollary 2.18 p.23 gives exactly the finite subgroup and square-wave witness. Notation 2.1, Theorems 2.9 and 2.13 retain the measurable/C∗C^* hypotheses and pointwise-versus-a.e. quantifiers. The PDF has 18 physical pages and printed range 15–32.

Independent source renders

The 21 assigned pages were rendered directly from all seven pinned PDFs at 180 dpi and visually read.

SourcePhysical / printed page
debruijn_19513 / 195
keleti_19981 / 15
keleti_19982 / 16
keleti_19983 / 17
keleti_19984 / 18
keleti_19985 / 19
keleti_19987 / 21
keleti_19988 / 22
keleti_19989 / 23
keleti_199818 / 32
laczkovich_1980223 / 217
laczkovich_1980230 / 224
matrai_20031 / 1
matrai_20032 / 2

Limits

  • The general de Bruijn, Laczkovich, and Keleti source proofs were not recursively reconstructed.
  • De Bruijn Section 5 remains uncompiled or held.
  • No formal, retrospective acceptance, intended-variant status, or canonical-integration credit is assigned.

No candidate, canonical page, Git state, Lean artifact, or certificate was modified or executed.