record state
frontier-ownedReview status
unreviewed
frontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Finding bundle
back to stateOBLIGATION (Erdos #617). BANKED: K25 balanced-coloring construction known; the K26 finite case is the first open case and reduces to a SAT instance. OPEN: produce the LRAT/RAT certificate for the K26 SAT encoding and re-check it with `vela reproduce` (unsat_cert); the symmetry-breaking step needs RAT, beyond the current RUP checker.
- id
- vf_da8d51a6cae5ec11
- frontier
- Erdős problems frontier
- version
- 1
- confidence
- 0.50
2inferred
file
/frontier/erdos-problems/at/vev_fe012295f0f30fa7permalink · after_hash 6d850060ae33df5e…vf_da8d51a6cae5ec11 · erdos-problems · snapshot sha256:adf5cd08914be106b09be94cb69e55449b5195f7c3e9894fc07c7fc288c446c0 · https://vela-site-next.fly.dev/frontier/erdos-problems/at/vev_fe012295f0f30fa7citeraw json · vf_da8d51a6cae5ec11 (2.1 KB)
{
"assertion": {
"direction": null,
"entities": [],
"relation": null,
"text": "OBLIGATION (Erdos #617). BANKED: K25 balanced-coloring construction known; the K26 finite case is the first open case and reduces to a SAT instance. OPEN: produce the LRAT/RAT certificate for the K26 SAT encoding and re-check it with `vela reproduce` (unsat_cert); the symmetry-breaking step needs RAT, beyond the current RUP checker.",
"type": "theoretical"
},
"conditions": {
"age_group": null,
"cell_type": null,
"clinical_trial": false,
"concentration_range": null,
"duration": null,
"human_data": false,
"in_vitro": false,
"in_vivo": false,
"species_unverified": [],
"species_verified": [],
"text": "Manually added finding; requires evidence review before scientific use."
},
"confidence": {
"basis": "operator-supplied frontier prior; review required",
"extraction_confidence": 1,
"kind": "frontier_epistemic",
"method": "expert_judgment",
"score": 0.5
},
"created": "2026-06-10T06:43:57.507201+00:00",
"evidence": {
"effect_size": null,
"evidence_spans": [],
"method": "manual state transition",
"model_system": "",
"p_value": null,
"replicated": false,
"replication_count": null,
"sample_size": null,
"species": null,
"type": "theoretical"
},
"flags": {
"contested": false,
"declining": false,
"gap": true,
"gravity_well": false,
"negative_space": false,
"retracted": false
},
"id": "vf_da8d51a6cae5ec11",
"links": [],
"previous_version": null,
"provenance": {
"authors": [
{
"name": "reviewer:will-blair",
"orcid": null
}
],
"citation_count": null,
"doi": null,
"extraction": {
"extracted_at": "2026-06-10T06:43:57.505670+00:00",
"extractor_version": "vela/0.691.0",
"method": "manual_curation",
"model": null,
"model_version": null
},
"journal": null,
"openalex_id": null,
"pmc": null,
"pmid": null,
"review": {
"corrections": [],
"reviewed": false,
"reviewed_at": null,
"reviewer": null
},
"source_type": "expert_assertion",
"title": "manual finding",
"year": null
},
"updated": null,
"version": 1
}Unsealed — 0 attachment(s) on record, awaiting independent verification.
0 attachments · 0 distinct checker actors · 0 methods
blame · custody trail
produced byreviewer:will-blairfinding.asserted · 2026-06-10
vev_fe012295f0f30fa7checked byno verifier attachment on record
accepted byno accept signed
history · 1 event
finding statement
finding typetheoretical
No entity list is declared.
evidence
source-bound1 atoms
theoretical · manual state transition
proof impact
packet context1 events
1 reviewable changes and 0 evaluation records are attached to this finding id.
evidence
method
manual state transition
evidence type
theoretical
conditions
- species_unverified
- species_verified
- text
- Manually added finding; requires evidence review before scientific use.
provenance
source title
manual finding
authors
reviewer:will-blair
Source records
1Evidence atoms
1- vea_ad089b920d3b7fb5theoretical · unknown
OBLIGATION (Erdos #617). BANKED: K25 balanced-coloring construction known; the K26 finite case is the first open case and reduces to a SAT instance. OPEN: produce the LRAT/RAT certificate for the K26 SAT encoding and re-check it with `vela reproduce` (unsat_cert); the symmetry-breaking step needs RAT, beyond the current RUP checker.
vs_066123dd29a9c5b4 · manual_curation
Typed links
2outgoing
No outgoing links.
incoming
- Erdős Problem #617 has status 'falsifiable'. Statement: Let $r\geq 3$. If the edges of $K_{r^2+1}$ are $r$-coloured then there exist $r+1$ vertices with at least one colour missing on the edges of the induced $K_{r+1}$. In other words, there is no balanced colouring. A conjecture of Erdős and Gyárfás [ErGy99]. Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
depends ·
vf_2329bdf075e2c6ef - Erdős Problem #617 has status 'falsifiable'. Statement: Let $r\geq 3$. If the edges of $K_{r^2+1}$ are $r$-coloured then there exist $r+1$ vertices with at least one colour missing on the edges of the induced $K_{r+1}$. In other words, there is no balanced colouring. A conjecture of Erdős and Gyárfás [ErGy99]. Topics: graph theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
depends ·
vf_2329bdf075e2c6ef
Review, event, and evaluation records
2events
vev_fe012295f0f30fa7finding.assertedManual finding added to frontier state
reviewer:will-blair · 2026-06-10
reviewable changes
vpr_6dbe94758958b601finding.addManual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
evaluations
No evaluation record targets this finding id.