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 E910 part of that review. For this source it covers only the exact scope of Rudin's theorem on printed p. 15 (the continuum hypothesis assumed, countable complement concluded), read across all six physical spreads; it does not reconstruct the construction proof. It also covers the separation of the Erdős 1944 and 1982 questions from the current clauses. 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 E910 parts together with the joint verdict, completion time and subject list; its E908 parts are retained with the Laczkovich source as the [[analysis/laczkovich_1980_functions_measurable_differences/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
| Finding | Verdict | Result |
|---|---|---|
F910-03 | PASS | The four historical statements are accurately separated: Erdős 1944 p.443 asks for continuum-sized complement, p.445 asks for a nonhomeomorphic nondegenerate connected subset, p.446 assumes intrinsic dimension greater than one and asks for 2^c subsets, and Erdős 1982 p.77 assumes intrinsic dimension greater than one and asks for more than c. No theorem match or current-open claim is inferred for the intended variants. |
F910-04 | PASS | Rudin p.15 explicitly assumes CH and proves only that every nondegenerate connected N subset M has countable complement in M. This yields at most c connected subsets under the theorem hypothesis but supplies neither common homeomorphism type nor a checked intrinsic-dimension property. The complete six-spread paper was visually read; p.24 closes the construction proof and does not strengthen those conclusions. |
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.mdwiki/problems/analysis/E0910/_index.mdlibrary/analysis/debruijn_1951_functions_whose_differences_belong_given_class/_index.mdlibrary/analysis/rudin_1958_connected_subset_plane/_index.mdlibrary/analysis/keleti_1998_difference_functions_periodic_measurable_functions/_index.mdlibrary/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
- Erdős 1944 pp.443, 445, and 446 pose three different questions. Erdős 1982 p.77 changes the cardinal target but retains intrinsic dimension greater than one.
- Rudin p.15 explicitly assumes CH and concludes countable complement. All six physical spreads were read; no common-homeomorphism or intrinsic-dimension theorem was found.
Independent source renders
The 21 assigned pages were rendered directly from all seven pinned PDFs at 180 dpi and visually read. Four additional Rudin spreads were also rendered and read, completing the six-spread article scan.
| Source | Physical / printed page |
|---|---|
erdos_1944 | 2 / 443 |
erdos_1944 | 4 / 445 |
erdos_1944 | 5 / 446 |
erdos_1982 | 18 / 76 |
erdos_1982 | 19 / 77 |
rudin_1958 | 1 / 15 |
rudin_1958 | 2 / 16–17 |
rudin_1958 | 3 / 18–19 |
rudin_1958 | 4 / 20–21 |
rudin_1958 | 5 / 22–23 |
rudin_1958 | 6 / 24 |
Limits
- The general Rudin source proof was not recursively reconstructed.
- The historical intended E910 theorem matches/currentness remain 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.