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.
acceptedverification passed3 evidence spans6 conditions1 relationrevision 3theoreticalAuthenticated Submission vsb_2d10ba2ff1aff901vcl_6763ba247d40303408a268b226c3e27d7a753b63fca3eb0de99619d509346bfb
At Formal Conjectures commit 59f30aa314ba225fcd9268723ce8291616df1ab0, the Lean development starfleet/erdos-321 establishes a two-sided asymptotic bound on extremalSize, which denotes the same quantity as Formal Conjectures' Erdos321.R and therefore supplies a candidate answer for the exact occurrence Erdos321.erdos_321.variants.isTheta, not a proof of it. For occurrence resolution only, the exact occurrences Erdos321.erdos_321 and Erdos321.erdos_321.variants.isTheta are associated with problem:erdos:321 under resolver root sha256:a9d6787719c5c8069a9e14ade0f5a62975410272e6cd1583865b282d1d8669dd. At the exact retained Erdős 321 source revisions, the terminal theorem and structural comparison do not establish implication to either fixed Nat.log variant.
acceptedverification passed1 evidence span5 conditions1 relationrevision 2theoreticalAuthenticated Submission vsb_a72e375d5b327714vcl_b9c6915de55e15c69d06b9aeed786b0e632986374a347d77ff447ad244f67a2e