schema_version: 1
contribution_id: con_ac0b4d1402194030b6ed90a2f240b6b6
revision_id: rev_c59f101c42c4499a8c5265545afe4870
expected_predecessor: null
type: attempt
home_problem_id: prb_21ee4ae9163b47cd8d28c376352b7975
targets:
- target_kind: problem
  problem_id: prb_21ee4ae9163b47cd8d28c376352b7975
  statement_revision_id: stm_78e6e7c11a1842d4a1379761a3889a7e
  scope: part_of_statement
title: Certified orders of the finite-field evaluation transform
profiles:
- id: mathematical_argument
  version: 1
  required: true
claim:
  type: computational_evidence
  scope_statement: Certifies the exact one-variable transform order for every prime p≤31, reproducing all four published identity exponents and proving minimality. Gives explicit generalized eigenvectors forcing 29 | N(29), with N(29)=1253339304585601201485463784571399120. Proves for every prime that the order is S or pS, with the branch decided by an identity test and S the least common multiple of characteristic-factor root orders; this is standard finite-field matrix theory. Also proves for every p and every positive number of variables n that the n-variable transform has exactly the same order N(p), plus inverse/Gram/determinant identities and 4 | N(p) for p ≡ 1 mod 4. All 11 orders, 42 characteristic factors/root orders and explicit certificates pass independent exact checks. No closed formula in p, complete research resolution, priority or human-review claim is made.
  assumptions: []
  limitations:
  - Finite computations through prime 31 do not resolve the arbitrary-prime question.
attribution:
  submitter:
    person_ref: per_e9e31130ef5441e79438f37603ed83be
    github_id: 206281466
    login_at_event: gavenren
    display_name: gavenren
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  humans:
  - person_ref: per_e9e31130ef5441e79438f37603ed83be
    github_id: 206281466
    login_at_event: gavenren
    display_name: gavenren
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  organisations: []
  contribution_mode: ai_only
model_uses:
- provider: OpenAI
  declared_name: codex (gpt-6)
  family: null
  version: unknown
  role: generated_draft
  settings:
    reasoning: unknown
    instance: OpenAI Codex (GPT-6), main instance
  generation_date: null
  provenance:
    level: declared
    evidence: []
- provider: OpenAI
  declared_name: codex (gpt-6)
  family: null
  version: unknown
  role: computation
  settings:
    reasoning: unknown
    instance: OpenAI Codex (GPT-6), research instance
  generation_date: null
  provenance:
    level: declared
    evidence: []
- provider: OpenAI
  declared_name: codex (gpt-6)
  family: null
  version: unknown
  role: review_assistance
  settings:
    reasoning: unknown
    instance: OpenAI Codex (GPT-6), audit instance
  generation_date: null
  provenance:
    level: declared
    evidence: []
lineage: []
artifacts:
- role: manuscript
  location: in_repository
  path: files/attempt.md
  media_type: text/markdown
- role: supplementary
  location: in_repository
  path: files/disclosures.md
  media_type: text/markdown
rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - gavenren
declarations:
  rights:
    confirmed: true
    source: form_field
    actor: per_e9e31130ef5441e79438f37603ed83be
    recorded_at: '2026-10-18T16:02:27Z'
    evidence_url: https://github.com/We-Solve/research/issues/27
  public_disclosure:
    confirmed: true
    source: form_field
    actor: per_e9e31130ef5441e79438f37603ed83be
    recorded_at: '2026-10-18T16:02:27Z'
    evidence_url: https://github.com/We-Solve/research/issues/27
  ai_disclosure:
    confirmed: true
    source: form_field
    actor: per_e9e31130ef5441e79438f37603ed83be
    recorded_at: '2026-10-18T16:02:27Z'
    evidence_url: https://github.com/We-Solve/research/issues/27