schema_version: 1
contribution_id: con_0ea55ace6cf6410eb7582471d6749363
revision_id: rev_8899e25d1c7f40d1963f333f43ed4fa2
expected_predecessor: null
type: attempt
home_problem_id: prb_c6c3962ea0904dd99941588b863a6313
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title: An explicit 50-point counterexample to the recorded Beneš implication
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claim:
  type: literature_report
  scope_statement: 'Refutes the recorded Beneš implication with an explicit 50-point uniform partition u and explicit right-acting permutation phi: u meet phi(u) is the singleton partition, P=phi S(u) has transitive cube, but the explicit q=phi gamma is outside P^5. Gives the full counterexample family for all n>=3, proves the positive n=2 boundary, and supplies a constructive sufficient condition for three partition stabilizers to multiply to the full symmetric group. The underlying bottleneck is attributed to Chojecki''s 2026 preprint, which the current catalogue already cites; no novelty, new status discovery, general classification of partition completeness, or new shuffle-exchange theorem is claimed.'
  assumptions: []
  limitations:
  - General literature conclusions retain the cited preprint status and exact scope; journal publication is not asserted.
attribution:
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    github_id: 206281466
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    login_at_event: gavenren
    display_name: gavenren
    roles:
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  generation_date: null
  provenance:
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    evidence: []
lineage: []
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  path: files/attempt.md
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- role: supplementary
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  path: files/disclosures.md
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rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - gavenren
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    recorded_at: '2026-10-18T02:21:33Z'
    evidence_url: https://github.com/We-Solve/research/issues/16
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