Claim

superseded

theoretical Claim

Vela Mathematics Programrecorded Aug 17, 2026, 6:40 PM

Source: source:formal-conjectures
Source record: Erdos94.erdos_94.variants.sum_multiplicity
Published at: github.com

Canonical assertion

At lean-proofs commit 423344341fbfdf4f8f684a302c5d05379125e7dc, Erdos94.variants.sum_multiplicity proves that 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, matching Formal Conjectures commit 94a278e06a8bcbc2e4f2935e491c0c115ec832e0. For occurrence resolution only, the exact occurrence Erdos94.erdos_94.variants.sum_multiplicity is associated with problem:erdos:94 under resolver entity root sha256:32f6e98a826da23c12c7cfcb8853e4712de130136c59f0454bd115c3fdb1e6b1. That occurrence is one of four Erdős 94 declarations Formal Conjectures publishes, and this identity does not establish the cubic distance-multiplicity conjecture.

Local Standing

Local Standing

Replayed at commit 2415f78e850a.

superseded

Evidence

3 retained spans.

3

Assurance

2 scoped checks, each answering a different question. They do not combine into a single verdict, and none of them is the Claim's Standing.

corrected_record_scope_fidelity

Declares 4 limits on what it establishes.

pass

occurrence_mapping_fidelity

Declares 4 limits on what it establishes.

pass

Evidence and Decision

Exact retained path.

Exact relationships

Typed edges retained by this rooted repository projection. They describe declared structure; they do not change either record's standing.

6 relationships

corrects

1

claimstanding · supersededclaim_record edge

At lean-proofs commit 423344341fbfdf4f8f684a302c5d05379125e7dc, Erdos94.variants.sum_multiplicity proves that 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, matching Formal Conjectures commit 94a278e06a8bcbc2e4f2935e491c0c115ec832e0.

No edge evidence text is retained.

sha256:aedff5078a30bea1f8a51c1188f2f0aa9bc43da06c894706297d8bd7a4830767

Supports

3

artifactrecordedcontent_addressed edge

119e4d22c1e8e5f2931f576e6e1af92f906f7bd49d7f4de28b22cb92955600ad

No edge evidence text is retained.

sha256:119e4d22c1e8e5f2931f576e6e1af92f906f7bd49d7f4de28b22cb92955600ad

artifactrecordedcontent_addressed edge

2db17099b421eff43d4892ddedcdd7b1bfecfbc6cca013447b3b94a81c3cd0f8

No edge evidence text is retained.

sha256:2db17099b421eff43d4892ddedcdd7b1bfecfbc6cca013447b3b94a81c3cd0f8

artifactrecordedcontent_addressed edge

e2054e7d5d57d1d1f4fd311d26dba65afb90ef873e7f04cb7bb5e431e43148eb

No edge evidence text is retained.

sha256:e2054e7d5d57d1d1f4fd311d26dba65afb90ef873e7f04cb7bb5e431e43148eb

corrects from

1

claimstanding · acceptedclaim_record edge

At lean-proofs commit 423344341fbfdf4f8f684a302c5d05379125e7dc, Erdos94.variants.sum_multiplicity proves that 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, matching Formal Conjectures commit 94a278e06a8bcbc2e4f2935e491c0c115ec832e0. For occurrence resolution only, the exact occurrence Erdos94.erdos_94.variants.sum_multiplicity is associated with problem:erdos:94 under resolver entity root sha256:32f6e98a826da23c12c7cfcb8853e4712de130136c59f0454bd115c3fdb1e6b1. That occurrence is one of four Erdős 94 declarations Formal Conjectures publishes, and this identity does not establish the cubic distance-multiplicity conjecture.

No edge evidence text is retained.

sha256:aaaf6ebbf510ad08e6376c5958d23f4eb7704944f7d37916eee4ae253e809b3b

proposes from

1

proposalproposal · acceptedsigned_record edge

At lean-proofs commit 423344341fbfdf4f8f684a302c5d05379125e7dc, Erdos94.variants.sum_multiplicity proves that 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, matching Formal Conjectures commit 94a278e06a8bcbc2e4f2935e491c0c115ec832e0. For occurrence resolution only, the exact occurrence Erdos94.erdos_94.variants.sum_multiplicity is associated with problem:erdos:94 under resolver entity root sha256:32f6e98a826da23c12c7cfcb8853e4712de130136c59f0454bd115c3fdb1e6b1. That occurrence is one of four Erdős 94 declarations Formal Conjectures publishes, and this identity does not establish the cubic distance-multiplicity conjecture.

No edge evidence text is retained.

sha256:aedff5078a30bea1f8a51c1188f2f0aa9bc43da06c894706297d8bd7a4830767

Not recorded for this Claim

No correction supersedes, succeeds, or depends on it.

Scope and conditions

An exact evidence file is bound to this Result; its recorded path remains in the technical record.
Occurrence association with problem:erdos:94 is navigation-only and establishes no statement identity or semantic equivalence.
Caveat: This proves only the elementary sum_multiplicity identity, not the cubic Erdős 94 theorem or either other variant.
Caveat: The Formal Conjectures build needs the mechanical Sym2.mk.uncurry to Sym2.mk API spelling change between its pinned Mathlib and lean-proofs.
Caveat: No external source-owner review, human review, upstream acceptance, or external adoption occurred.
Caveat: Producer checks are not Verification, Decision, or Standing.
Caveat: The predecessor's distance_multiplicity_double_counting Verification remains recoverable at rollback/submission-v2-coh-00 (508b39a) and is not re-attested over the compact v3 bytes.

Reproduce the source snapshot

Replay establishes the exact record and checks. It does not add scientific authority.

Inspect graph neighborhood