Claim

The September 2026 Erdős–Chvátal simplex conjecture preprint states that if 2≤d<k and (d+1)k≤dv, every d-simplex-free family of k-subsets of [v] has at most binom(v−1,k−1) members, with equality only for a full star.

Type TEXTUAL · truth-evaluable: yes · status at snapshot: ACTIVE · created seq 17805 · qualifiers {"translation":"Notation and theorem wording follow the arXiv abstract.","source_edition":"e59de2b5-85db-8734-aec3-bf336b31e6e2"}

32 words; atomic claims are usually under 25a conjunction joins clauses that may be separately evaluablea comma-separated series may list several propositions

Referenced 75 times: checked 1, looked up by assistants 0, viewed 57, shared 17. A count of attention, not evidence.

Topics

Mathematics · 1efd24fe Statistics · 1efd24fe

Assessment

Supported

Score: 0.8581 under ledger-default@0.3.0 at snapshot 27745

2 of 4 review checks done · 1 counted · 1 by the author only

1 independent evidence lineage · review checks 1 of 4 · stability MEDIUM

Main unresolved issue: 2 counted evidence items have no independence review; repeats of one origin may be counted as several coverage:953a34b6-8db0-8dbf-aac5-f57e18e28412

Not yet independently audited.Evidence reviewed so far supports this claim, but only 1 of 4 review checks has been done.A quoted passage from arxiv.org was not found on the page when Galedra fetched it.

Why?

Strongest counted support: The arXiv abstract states the full-parameter theorem and its equality characterization. weight 1.800000 evidence

Suppressed as dependent: The quoted arXiv abstract directly states the full parameter range, binomial upper bound, and equality only for a full star.

Review gaps: qualifiers reviewed, opposing search done, independence reviewed

What would most change this: One independent, direct measurement that contradicts this claim would move it from Supported to Unresolved.

Hide calculation

0.8581 under ledger-default@0.3.0 at snapshot 27745 · state Supported · Review checks: 1 of 4 · stability MEDIUM · 2 sources, 1 independent lineage

Model ledger-default@0.3.0 (the default model, not the answer) · snapshot 27745 · trace sha256:0bc129ee57b177489364c72fbe2d3f9ce1b06436ee866361205eccc7b68423a8

Last changed at entry seq 25364; nothing logged since has borne on this claim.

How the number was reached

Each counted link is weighed by multiplying the factors the model declares; a factor it does not declare is not shown. Every factor name below links to what that number means.

Link	Working	Weight	Counted as
71c813e0 support	relevance DIRECT 2.0 × observation DIRECT_TEXT 0.9 × interpretation 0 steps, 1 − 0.15 × 0 1.000000 × authenticity UNVERIFIED 1.0 × extraction UNVERIFIED 1.0 × provenance INDEPENDENT 1.0 × edition NAMED_OR_UNRELATED 1	1.800000	0.000000 (dependent strongest only, kept 6a3dbd53)
6a3dbd53 support	relevance DIRECT 2.0 × observation DIRECT_TEXT 0.9 × interpretation 0 steps, 1 − 0.15 × 0 1.000000 × authenticity UNVERIFIED 1.0 × extraction UNVERIFIED 1.0 × provenance INDEPENDENT 1.0 × edition NAMED_OR_UNRELATED 1	1.800000	1.800000

prior 0.50 → log-odds 0.000000 + 1.800000 (the counted weights) = 1.800000 → probability 0.8581

Under neighbouring settings of the same model: 0.7790 to 0.9121, a spread of 0.1331.

Half-even rounding, six places for weights and four for the probability. The same inputs under the same model reproduce this exactly; that is what the trace hash above is for. How a score is worked out explains every factor, why it is there, and what the model sets it to.

Your view

Registered views

Nobody has registered a view yet.

Registered views are personal belief, not evidence: they never change Galedra's assessment. Affiliations are self-declared and shown only for groups of 5 or more.

Checked as part of

Statements this claim was broken out of. The claim is scored on its own; a statement's reading only counts its claims.

“A September 2026 arXiv preprint states that it proves the Erdős–Chvátal simplex conjecture across its full parameter range.” · 1 claim · 29 September 2026

Evidence for

The arXiv abstract states the full-parameter theorem and its equality characterization.

From The Erdős–Chvátal Simplex Conjecture Read 2026-09-29 Relevance DIRECT Steps 0 Counted
The quoted arXiv abstract directly states the full parameter range, binomial upper bound, and equality only for a full star.

From The Erdős–Chvátal Simplex Conjecture Read 2026-09-29 Relevance DIRECT Steps 0 Counted

The abstract wording matches the claim's theorem statement.

Evidence against

None.

Qualifications

None.

Suppressed as dependent

Evidence	Group	Kept instead
85242a11		6a3dbd53

Inferences

Concluded from

None.

Used as a premise in

None.

An inference is interpretation, not evidence: it never changes the assessment of its conclusion. Each premise is a claim with its own evidence.

Threads

None. Threads are for disagreements about how a determination was made — a statement whose figures are not in the passage it rests on, two sources that may share an origin. Something about the world belongs in the evidence above.

Claim edges

None. Edges are stored and displayed; v0.1 does not propagate probability across them.

Review checklist

Review checks: 1 of 4

2 checks by this claim's own author, alongside the independent review above. 1 QUALIFIER CHECK · 1 EVIDENCE VERIFICATION. A check by the person who recorded a claim does not raise its review coverage.

Check	Done	By
qualifiers reviewed	no
opposing search done	no
independence reviewed	no
primary source reviewed	yes	71c813e0, 6a3dbd53

Summary

Supported. The main support is: The arXiv abstract states the full-parameter theorem and its equality characterization. 8ebbe3bc

1 further item repeats the same origin and is not independent evidence. 85242a11

Review checks: 1 of 4. coverage:953a34b6-8db0-8dbf-aac5-f57e18e28412

Generated by stub-v0.1; every sentence cites graph ids.

Contribution history

seq	event	detail
17805	APPENDED
17806	ACCEPT	AUTOMATIC_AFTER_VALIDATION
17811	LINK_EVIDENCE	by 1efd24fe (accepted)
24454	TASK_RESULT	by 1efd24fe (accepted)

Score trace

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      "reason": "dependent_strongest_only",
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  "prior": "0.50",
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  "code_hash": "sha256:c61a6fdf35a754a0d7e958df149036a083c0eaeb7d2d2e52704ec32b0c36def7",
  "contested": false,
  "stability": "MEDIUM",
  "claim_type": "TEXTUAL",
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  "truth_evaluable": true,
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  "review_checklist": {
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    "opposing_search_done": {
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      "ok": true
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  "contradict_groups": 0,
  "rounding_boundary": false,
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  "not_applicable_reason": null,
  "independence_unreviewed": 2
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