Erdős problem 94

Suppose $n$ points in $\mathbb{R}^2$ determine a convex polygon and the set of distances between them is $\{u_1,\ldots,u_t\}$ . Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then $\sum_i f(u_i)^2 \ll n^3.$

How the state got here

5 of 6 recorded

Prior stateAccepted, then corrected
Worksubmission v3 cleanup · 3 evidence items
Verification2 of 2 scoped checks passed
Decisionaccepted by Vela Mathematics Program
StandingOpen in this repository
Next gapNot recorded

Result history

Published changes, performers, checks, and later corrections.

2 events

AIagent:submission-v3-cleanupSubmitted byAug 18, 2026, 6:46 PM
accepted2 checks
Accepted here
Decision recorded by AIagent:submission-v3-cleanup-decision
Open change details vpr_b5ca521d2a892eee
AIagent:submission-v3-migrationSubmitted byAug 17, 2026, 6:48 PM
accepted2 checks
Accepted here
The Result was later corrected.
Decision recorded by AIagent:submission-v3-migration
Open change details vpr_d7253663013962ba

Correction history

2 exact relations

correctsproduced the current Result

The retained statement is identical before and after: this correction revised the record’s relations, not the statement text.

Exact identities

correctsproduced a later version

The corrected Result record is not retained in this release.

Exact identities

How the frontier moved

Each state the accepted record passed through, with the evidence that carried it.

Result accepted
Aug 17, 2026, 6:48 PM
Accepted
- For every finite planar point set P, the sum over its distinct determined distances of the unordered-pair distance multiplicities equals P.card.choose 2
Evidence flow
1. Submission receivedbasis: source-asserted
2. Check passedoccurrence mapping fidelitybasis: checked
3. Check passedcorrected record scope fidelitybasis: checked
4. Decision appliedAI agent submission-v3-migrationbasis: repository decision
5. Result acceptedbasis: derived from records
Technical details
Repository root before
sha256:d48ea1c5bd4ac89149733e37b17b0baa8ae9b79b10539c911e8e98cf07ee168c
Repository root after
sha256:45640c5eea54693df444eada6dd1a7c1f5a4b4ef266fddf79cf51d083233ebba
Semantic delta
sha256:38bae692caed70699d6143d7e593d061bbddd5b95c70c6d4487826c4e5261748
Events
- vev_aefe96c39e957fef
- vev_b2787993800e9001
Result corrected
Aug 18, 2026, 6:46 PM
Accepted
- For every finite planar point set P, the sum over its distinct determined distances of the unordered-pair distance multiplicities equals P.card.choose 2
Removed
- For every finite planar point set P, the sum over its distinct determined distances of the unordered-pair distance multiplicities equals P.card.choose 2
Evidence flow
1. Submission receivedbasis: source-asserted
2. Check passedscientific meaning and state fidelitybasis: checked
3. Check passedsubmission v3 revision fidelitybasis: checked
4. Decision appliedAI agent submission-v3-cleanup-decisionbasis: repository decision
5. Result correctedbasis: derived from records
Technical details
Repository root before
sha256:c465145c974a09e8b535efc7e3b6e7755e8b73916d4bad3403c2a41c12841875
Repository root after
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Semantic delta
sha256:9d5bd2448b626ad14d527fe18186d85264b9acad1454bd05e4f0cb1729fe169b
Events
- vev_1bb01953aec0d5ca
- vev_e04b25b2a4c02a15
- vev_aefe96c39e957fef
- vev_b2787993800e9001

Still unresolved

This check does not establish: A new proof, fresh kernel execution, semantic equivalence, or resolution of the cubic Erdős 94 conjecture; External source-owner review, upstream acceptance, or adoption; Scientific acceptance, a Decision, or Standing; Provider-, host-, source-byte-, repository-, or tool-independent reproduction.basis: checked
Exact identity
vvr_ac3996330910c9fb
A grouped formal statement may state a different theorem; equivalence not established.basis: heuristic advisory
Exact identity
source:formal-conjectures/Erdos94.erdos_94.variants.no_three_on_a_line
A grouped formal statement may state a different theorem; equivalence not established.basis: heuristic advisory
Exact identity
source:formal-conjectures/Erdos94.erdos_94.variants.regular_ngon
This check does not establish: Statement identity or semantic equivalence between any two occurrences; That the Claim proves the Problem its occurrence is grouped under; Any change to Standing, and any Decision or acceptance; The correctness of the mathematics the Claim asserts, which this observation does not read.basis: checked
Exact identity
vvr_b485b7d408095f94
A grouped formal statement may state a different theorem; equivalence not established.basis: heuristic advisory
Exact identity
source:formal-conjectures/Erdos94.erdos_94
This check does not establish: Correctness of the mathematical proof or a fresh kernel rebuild; Scientific acceptance, a Decision, or Standing; Provider-, host-, source-byte-, repository-, or tool-independent reproduction.basis: checked
Exact identity
vvr_f89662daad9537c0
This check does not establish: The cubic Erdős 94 distance-multiplicity conjecture; That the underlying Lean proof is correct, which this observation does not rebuild; External source-owner review, human review, or upstream acceptance; Any change to Standing, and any Decision or acceptance.basis: checked
Exact identity
vvr_fb7cbd5546644686

Technical detailsExact roots, source, and retained record identifiers

Problem row: sha256:caba1132228b192c30895be8d189c38faa3f11615496fd4a337b287485e0b7bb
Metadata: sha256:e7fe06de8a677d6c5f7bd3fa8f96e93aa023c4a349a7cea7a22e9805725eda45
Observation: sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content: sha256:246d166026de8d99931c44824f9b0a242ae32beea27c43b1e6d0157a4a6fb2c8

Repository: sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection: sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit: 36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb

Exact Claim-to-Problem Bindings

Binding: sha256:ffab296a51b580d26a08388b559251d7ca87eaeb5758ff782981d9cd4bb3d038
Native record: sha256:718fc70820b1586c57558d7080749be5b006eecce32bfb1218c3a71b26446f04
Content: sha256:b49ada921a91b89436f112da4a07a75e438640a075a7c390aca8162d3584c842

Binding: sha256:477b3b71fd9670e29ecf69152408f40c990a5a72e1ca8c38f494e7d54db218ef
Native record: sha256:718fc70820b1586c57558d7080749be5b006eecce32bfb1218c3a71b26446f04
Content: sha256:b49ada921a91b89436f112da4a07a75e438640a075a7c390aca8162d3584c842

Upstream source Inspect records Source JSON

How the state got here

Result history

Correction history

How the frontier moved

Still unresolved

Exact provenance