schema_version: 1
contribution_id: con_8a227d15e6ac4ef69204f71a9ea6802a
revision_id: rev_5ded9445527641e793be6480adf2901c
expected_predecessor: null
type: attempt
home_problem_id: prb_34ecf5fa262f4a85a0fbe4af9837c46b
targets:
- target_kind: problem
  problem_id: prb_34ecf5fa262f4a85a0fbe4af9837c46b
  statement_revision_id: stm_98b676801bd24583959904cb93d3dcb4
  scope: special_case
title: Two-player partial results for axiomatic containment of Mertens-stable sets without genericity
profiles:
- id: mathematical_argument
  version: 1
  required: true
claim:
  type: partial_result
  scope_statement: Containment of a Mertens characteristic-zero stable set in every selected set for all 2x2 games; a rank criterion for stability of quasi-strict bimatrix equilibrium singletons; a finite exclusion certificate and the resulting stability of selected sets consisting entirely of quasi-strict equilibria; the set-level settlement of a degenerate 2x3 example; all 2xn games with a strictly dominant column; and exact selection of a whole equilibrium face under explicit balance and spanning conditions, including faces of unbounded dimension. The axioms are assumed globally on all finite games and only the target game is restricted to two players.
  assumptions:
  - The global axioms B, D* and I* of Govindan and Wilson hold for the rule on all finite games.
  - The balance and spanning conditions are assumed where stated.
  limitations:
  - No proof or counterexample is claimed for arbitrary finite two-player target games.
  - The claims are reported by the authors and are not independently verified; no formal proof or referee check is claimed.
  - The exact-arithmetic computer checks reported in the underlying drafts are not included.
attribution:
  submitter:
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    github_id: 243585043
    login_at_event: null
    display_name: Anonymous submitter
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  humans: []
  organisations: []
  contribution_mode: ai_only
model_uses:
- provider: openai
  declared_name: gpt 6 astra pro
  family: null
  version: unknown
  role: generated_draft
  settings:
    thinking_level: unknown
    thinking_time: unknown
  generation_date: null
  provenance:
    level: declared
    evidence:
    - kind: statement
      note: The manuscript states that the three underlying drafts used OpenAI GPT-6 Astra Pro for proof search and preparation; exact version, thinking level and time are not available. Editorial intake does not authenticate provider session logs.
- provider: openai
  declared_name: gpt-6
  family: null
  version: unknown
  role: editing
  settings:
    thinking_level: unknown
    thinking_time: unknown
  generation_date: null
  provenance:
    level: declared
    evidence:
    - kind: statement
      note: The manuscript states that the consolidation and editorial review used OpenAI GPT-6; exact model, version and settings are not available.
lineage: []
artifacts:
- role: manuscript
  location: in_repository
  path: files/ECON-20-two-player-case.tex
  media_type: application/x-tex
rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - Anonymous submitter
  notes: Rights, public release and complete model and people disclosure were confirmed on the submitting owner's instruction in an editor session on 19 October 2026; not independently authenticated.
declarations:
  rights:
    confirmed: true
    source: cli_confirmation
    actor: per_f000c79a661e4888846b5ce878366ad0
  public_disclosure:
    confirmed: true
    source: cli_confirmation
    actor: per_f000c79a661e4888846b5ce878366ad0
  ai_disclosure:
    confirmed: true
    source: cli_confirmation
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