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 at the exact frozen nine-artifact candidate tree. The same fresh reviewer replayed operations I1--I8, confirmed the byte-identical placement of the independently approved Remark 1 companion and the six authorized prose replacements, and checked links, statement scope and status. Recorded 2026-09-06T06:51:16Z. This review adds no mathematical proof credit; the Theorem 1 credit rests on the Theorem 1 review, and the Remark 1 companion's own review report is not retained in this repository. 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.
The delivered subject included standing and prior-review prose of the pages
under review —
library/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/theorem_1.md
lines 91–94, .../_index.md lines 104–109 and
wiki/problems/discrete_geometry/E0505/_index.md lines 7, 92–98 and 102–107 as they
stood at 2026-09-10T05:35:49Z — because those spans were the six authorized
replacements
and the status scalar the reviewer was commissioned to check; a separately
spawned grader (model: Claude Fable 5.1) ruled the exposure immaterial by the
content test on 2026-09-18: the text does not state or imply whether the
replacements and byte comparisons were exact, and the review grants no proof,
status or acceptance credit that it could have anchored.
The bodies of all seven result pages of this source as they stood at
2026-09-10T05:35:49Z, named below, are byte-identical to the approved
candidates (checked at filing on 2026-09-16); _index.md and theorem_1.md
have since been edited, and the other five are unchanged.
This record was filed on 2026-09-16 from a retained report, the review text and its machine-readable companion. The report text is retained below in full. The filing changed only the wrapper, participant identifiers, private paths and operating-history material; it records no new verdict, and the first-person readings and judgments below belong to the historical reviewer, not to the filing author.
Retained report
Recorded UTC: 2026-09-06T06:51:16Z
Verdict
PASS at the exact frozen nine-artifact candidate tree. The composition implements reviewed operations I1--I8 exactly. It installs the independently approved Remark 1 companion byte-for-byte, applies each of the six authorized single-occurrence prose replacements to the exact reviewed prior version, and preserves I8 as a deferred generated-navigation instruction without changing a candidate byte.
The final author manifest, the candidate tree digest and the complete 44-file package digest are working-storage receipts, not retained here. Every package, candidate, authority, source-prior version, Remark-prior version, and canonical-before check passed.
Operation replay
Reviewed with this repository as it stood at 2026-09-10T05:35:49Z.
- I1 replaces the conservative source-package
remark_1.mdwith the independently approved companion file, whose body is the body of the committedremark_1.mdat the date above. The archived authority, install source, and final candidate are byte-identical. - I2--I7 each find exactly one authorized old span. Independent replay gives the same old-span, new-span, before-file, intermediate-file, and final-file hashes as every operation receipt.
- I8 changes no candidate byte and preserves the exact instruction to regenerate tool-owned source navigation and managed metadata only after the complete tree is placed for integration.
I independently reconstructed composition.diff; it is byte-identical to the
frozen diff (working storage; not retained). Exactly four artifacts changed from
the reviewed source package: _index.md, remark_1.md, theorem_1.md, and
E0505.md. The other four Markdown components and the PDF remain
byte-identical.
Candidate files
The candidates are the following files at the revision above.
asymptotic_dimension_transfer.md, equal_cut_construction.md,
external_inputs.md, theorem_1.md, theorem_2.md, E0505.md and the PDF
carry the reviewed bytes there; _index.md and remark_1.md carry the
reviewed bodies below ***, their generated frontmatter differing.
library/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/_index.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/asymptotic_dimension_transfer.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/equal_cut_construction.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/external_inputs.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/remark_1.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/theorem_1.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/theorem_2.mdwiki/problems/discrete_geometry/E0505/_index.mdlibrary/discrete_geometry/kahn_kalai_1993_borsuk_counterexample/kahn_kalai_1993_borsuk_counterexample.pdf
Statement, links, and scope
The imported E0505 prefix beginning at **Statement.** and ending before ## Progress is byte-identical to the reviewed prior version. The frontmatter
scalar remains exactly status: disproved. All links appearing in the
replacement spans resolve, and no introduced folder-home link omits /_index.
The source index and E0505 page now distinguish the compiler-supplied Remark 1 repairs from the printed derivation, preserve all three external theorem boundaries, retain the dimension-63 and Lean qualifications, and contain no stale private review-queue assertion. The problem statement and mathematical status are unchanged.
This exact composition review adds no mathematical proof credit. The one Theorem 1 proof-chain credit and one Remark 1 companion credit remain anchored to their prior independent reviews. This review grants one composition credit and zero external-proof, formal, new-solution, status, acceptance, canonical integration, or Git credit. Canonical integration still requires applying I8 with the repository wiki tool and pinning the resulting tool-managed bytes.