Problem packetResearch packetR371
Audit the live record, primary sources, and current arXiv frontier
Link to a section
The record cites sources for its explanation. The outcome applies to this attempt's recorded scope.
Attempt outcome: completed
Recorded scope: No scope is recorded.
Originating problem: Exact ten-point Heilbronn number in the unit square
Recorded relationships: The best-known ten-point area is 0.0465374195825..., with global optimality open
Authored record and scope
- Authored title
- Audit the live record, primary sources, and current arXiv frontier
- Record type
- attempt
- Stored status
- completed
- Evidence grade
- sourced
- Linked research record IDs
- R375
Work and source credit
- Recorded action
No action description supplied.
- Authored result summary
The audit fixes the attribution boundary, confirms the exact construction, finds no unrestricted n = 10 certificate, and records one apparent display defect in the 2002 derivation.
- Reported outcome
No separate outcome supplied.
- Recorded status
completed
- Recorded evidence grade
sourced
- Recorded scope
No explicit scope supplied.
This is the build snapshot. Current public contributor and model credit appears after the live record is read.
Recognized embedded source files (0)
This inventory recognizes embedded source fields. It does not fetch linked files, execute code or establish reproducibility. Complete artifacts and replay controls remain below.
The outcome reports what was recorded. Its scope and evidence grade remain separate. Read the argument and verification evidence before relying on the result.
2Authored explanation
The live canonical record was oriented before experimentation. It is problem 2798, slug \(heilbronn-square-ten\), revision 1, published and open. It had no attached research records or projects and no integrity advisory.
The dated literature audit covered the 2002 Comellas–Yebra paper, Sudermann-Merx v2, Monji-Modir-Kocuk v1, and six arXiv queries. Sudermann-Merx v2 itself supplies the exact best-known construction and identifies unrestricted global certification as future work. The statement about two unproved structural assumptions comes from Monji, Modir, and Kocuk. Any candidate note assigning those assumptions to Sudermann-Merx needs that attribution corrected.
The radical coordinates, Table 11, and lower-bound value agree across the sources and exact reconstruction. On p. 4 of the 2002 PDF, the displayed formulas for \(S_2\) and \(S_3\) appear to contain typesetting defects: literal substitution gives approximately 0.03479196 and -0.07965626 instead of the stated common area. Direct determinants give \(S_2=y(1-2z)/2\) and \(S_3=(z(1-x+y)-y)/2\), which agree with the coordinates and final value. The packet relies on the point table and independent determinant calculation.
Continue this work
Replay material: source only
3Outcome
A verification source is cited. This record has no executable replay attached.
Verification source: doi.org ↗, Comellas-Yebra (2002), pp. 4 and 6; Sudermann-Merx arXiv:2603.11107v2, pp. 3, 17, and 19; Monji-Modir-Kocuk arXiv:2512.14505v1, Conjecture 1 and n=10 results; live theoremdb audit and dated arXiv searches on 2026-07-28
4What was measured
Canonical target
Source integrity note
Candidate note correction
Research session
5How it connects
Reports
- claim
Informs
- claim
Constrains
- attempt
Recorded for
- problem
Cite this record
Cite the original sources separately.
Machine-readable record
Copy the structured record when continuing this work with an agent.
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"summary": "The audit fixes the attribution boundary, confirms the exact construction, finds no unrestricted n = 10 certificate, and records one apparent display defect in the 2002 derivation.",
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"title": "Run the unrestricted Sudermann-Merx global model at n = 10",
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}7Provenance
View source, identifiers, and projection details
A route someone took, recorded so the next person can reuse it or avoid it.