schema_version: 1
contribution_id: con_980a7576a5d54c88804e3aeb9ea985fc
revision_id: rev_d5a0ba7001c64a1d8b981f3ac9125bad
expected_predecessor: null
type: attempt
home_problem_id: prb_a793fdc7ba9145ad84b1812ac0512eca
targets:
- target_kind: problem
  problem_id: prb_a793fdc7ba9145ad84b1812ac0512eca
  statement_revision_id: stm_2b26adfe5e7c472eb510e4b6d41344ce
  scope: whole_statement
title: Why internal minimality does not solve stable-set selection on all finite games
profiles:
- id: mathematical_argument
  version: 1
  required: true
claim:
  type: partial_result
  scope_statement: Claims a complete stable-set description in zero-payoff games, a globally valid refinement showing B,D*,I* do not imply selected-set membership in stability, and rejection of internal inclusion-minimality as the extra axiom; identifies a stable-lift containment gap.
  assumptions:
  - Exact global axioms B,D*,I* and full Mertens 0-stability correspondence
  - Cohomological essentiality and connexity use source conventions
  - Global essential-component refinement properties use cited theorem
  limitations:
  - No strategically motivated sufficient extra axiom
  - Does not resolve S2 research programme or exclude all candidate additional axioms
  - Generic minimality observation not claimed new
  - No human/formal verification claimed
  - Submitted research claim; correctness and novelty have not been independently established.
attribution:
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    github_id: 243585043
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    authorship_confirmation: confirmed
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  organisations: []
  contribution_mode: ai_only
model_uses:
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  declared_name: gpt 6 astra pro
  family: null
  version: unknown
  role: generated_draft
  settings: null
  generation_date: null
  provenance:
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lineage: []
artifacts:
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  location: in_repository
  path: files/WS-107794-attempt.tex
  media_type: application/x-tex
rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - Anonymous submitter
declarations:
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    actor: per_a01e1a18cefa4f96bd8fa738f67cd04d
    recorded_at: '2026-10-18T16:20:10Z'
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    actor: per_a01e1a18cefa4f96bd8fa738f67cd04d
    recorded_at: '2026-10-18T16:20:10Z'
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    recorded_at: '2026-10-18T16:20:10Z'