Assertions · Vela Mathematics Program
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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.
supersededverification passed3 evidence spans7 conditions1 relationrevision 2Authenticated Submission vsb_d49869f07a7907d4vcl_4cae0d412a95d1965b927e1f7dbaa4245f5b9c3f84c5913e1d6a7880d6349165
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.
supersededno Verification Record2 evidence spans5 conditionsAuthenticated Submission vsb_f43df4adcf653c88vcl_9ba852a45d8bc6f9dd024d85ff19e0b81317945f45e9eb073a89e44760a6b009
The Lean development starfleet/erdos-321 establishes a two-sided asymptotic bound on extremalSize, which denotes the same quantity as Formal Conjectures' Erdos321.R at pages commit 59f30aa3, and which therefore supplies a candidate answer for erdos_321.variants.isTheta rather than a proof of it.
supersededno Verification Record1 evidence span3 conditionsAuthenticated Submission vsb_6cc500cc8153c8f5vcl_1da4282b752192c52c2a985476fc13bfe460da01e4fe26c5543b7acb37d8b120