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Claim

superseded

theoretical Claim

Vela Mathematics Programrecorded Aug 17, 2026, 6:34 PM

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.

Local Standing

Local Standing

Replayed at commit 36c6d0fef71a.

superseded
Evidence

2 retained spans.

2

Evidence and Decision

Exact retained path.

Exact relationships

Typed edges retained by this projection.

4 relationships

Supports

2
artifactrecordedcontent_addressed edge
119e4d22c1e8e5f2931f576e6e1af92f906f7bd49d7f4de28b22cb92955600ad

No edge evidence text is retained.

sha256:119e4d22c1e8e5f2931f576e6e1af92f906f7bd49d7f4de28b22cb92955600ad
Graph
artifactrecordedcontent_addressed edge
e2054e7d5d57d1d1f4fd311d26dba65afb90ef873e7f04cb7bb5e431e43148eb

No edge evidence text is retained.

sha256:e2054e7d5d57d1d1f4fd311d26dba65afb90ef873e7f04cb7bb5e431e43148eb
Graph

corrects from

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. 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
Graph

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.

No edge evidence text is retained.

sha256:8e762a3a7dff021b90d15618d8197ed2454d457416a494ae57e90d2b00688fb4
Graph

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.
  • 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.
Reproduce the source snapshot

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

Reproduce
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Cite this Result

Identifies these exact bytes. A correction or supersession produces a different record.

Vela Mathematics Program. Claim vcl_9ba852a45d8bc6f9dd024d85ff19e0b81317945f45e9eb073a89e44760a6b009. sha256:8e762a3a7dff021b90d15618d8197ed2454d457416a494ae57e90d2b00688fb4. https://problems.science/repositories/math/claims/vcl_9ba852a45d8bc6f9dd024d85ff19e0b81317945f45e9eb073a89e44760a6b009