schema_version: 1
contribution_id: con_4f3d80d81cee4291b258aceeeaf52c9a
revision_id: rev_841301caa0ad4670971f6cca5a56b58b
expected_predecessor: null
type: attempt
home_problem_id: prb_cd7e030428494885b830747fa685b68f
targets:
- target_kind: problem
  problem_id: prb_cd7e030428494885b830747fa685b68f
  statement_revision_id: stm_0007950797e24b1f87e90bc6b7aee684
  scope: whole_statement
title: 'Finite-difference convolution preserves mesh: the established affirmative answer, with a complete proof'
profiles:
- id: mathematical_argument
  version: 1
  required: true
claim:
  type: literature_report
  scope_statement: 'The full affirmative answer to Math-3461 / Shapiro Conjecture 6: for every integer d ≥ 1 and all catalogue inputs p,q in H_d, their exact forward-difference convolution belongs to H_d. This is an established theorem of Jonathan Leake and Nick Ryder (2017 preprint; 2020 publication). This report gives a complete direct proof, an exact reflection identity matching the catalogue normalization, all lower-degree and zero cases, the closed mesh-one boundary, sharpness, and reproducible exact-arithmetic verification. No historical novelty is claimed. No mathematical gap was found by the same-model audits; editorial review and independent human verification remain pending.'
  assumptions: []
  limitations: []
attribution:
  submitter:
    person_ref: per_c76c88099ec548779d152ad46bc93d56
    github_id: 206281466
    login_at_event: gavenren
    display_name: gavenren
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  humans:
  - person_ref: per_c76c88099ec548779d152ad46bc93d56
    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), primary instance
  generation_date: null
  provenance:
    level: declared
    evidence: []
- provider: OpenAI
  declared_name: codex (gpt-6)
  family: null
  version: unknown
  role: generated_draft
  settings:
    reasoning: unknown
    instance: OpenAI Codex (GPT-6), mathematical 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), separate mathematical reviewer
  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), verifier 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_c76c88099ec548779d152ad46bc93d56
    recorded_at: '2026-10-18T14:41:52Z'
    evidence_url: https://github.com/We-Solve/research/issues/19
  public_disclosure:
    confirmed: true
    source: form_field
    actor: per_c76c88099ec548779d152ad46bc93d56
    recorded_at: '2026-10-18T14:41:52Z'
    evidence_url: https://github.com/We-Solve/research/issues/19
  ai_disclosure:
    confirmed: true
    source: form_field
    actor: per_c76c88099ec548779d152ad46bc93d56
    recorded_at: '2026-10-18T14:41:52Z'
    evidence_url: https://github.com/We-Solve/research/issues/19