schema_version: 1
contribution_id: con_1221304b21f34b87a360ca2dca9d7703
revision_id: rev_cc8647f844e0423e855e2389c2902cf9
expected_predecessor: null
type: attempt
home_problem_id: prb_8c41e1e4ede3470ebb71378d0433b380
targets:
- target_kind: problem
  problem_id: prb_8c41e1e4ede3470ebb71378d0433b380
  statement_revision_id: stm_ba25c4ac80c14ed8b4f82e0409f18a50
  scope: whole_statement
title: Four explicit injective charts with an essential glued differential
profiles:
- id: mathematical_argument
  version: 1
  required: true
claim:
  type: literature_report
  scope_statement: 'The exact catalogue statement expressly permits disconnected covering sets and is false. This report gives a complete explicit four-set counterexample: each map is holomorphic and globally injective on its entire open set, the four sets cover D*, and their derivatives all equal -exp(1/z)/z^2, which has an essential singularity and zero residue at 0. This is an exposition and exact certificate of a known obstruction, with the 2011 Goodwillie/Thurston discussion, Elsner''s acknowledgement, and a related later nine-set construction by Kavya Mali (crediting GPT-5.6 Sol) clearly attributed. No new disproof or minimum-chart claim is made. The report also proves the zero-residue result when primitive differences take finitely many constants, including connected charts and finitely many components in total, with coefficient pole order at most K+1. The intended connected, nonzero-residue conjecture is not settled here. Finite exact implementation checks cover 625 cells, 10,201 rational points and 48,672 same-colour pairs; the analytic result for all cells is proved, not inferred from sampling.'
  assumptions: []
  limitations: []
attribution:
  submitter:
    person_ref: per_82e2039e7a1042fc92e0b8a58eb7c917
    github_id: 206281466
    login_at_event: gavenren
    display_name: gavenren
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  humans:
  - person_ref: per_82e2039e7a1042fc92e0b8a58eb7c917
    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)
  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_82e2039e7a1042fc92e0b8a58eb7c917
    recorded_at: '2026-10-18T01:04:05Z'
    evidence_url: https://github.com/We-Solve/research/issues/8
  public_disclosure:
    confirmed: true
    source: form_field
    actor: per_82e2039e7a1042fc92e0b8a58eb7c917
    recorded_at: '2026-10-18T01:04:05Z'
    evidence_url: https://github.com/We-Solve/research/issues/8
  ai_disclosure:
    confirmed: true
    source: form_field
    actor: per_82e2039e7a1042fc92e0b8a58eb7c917
    recorded_at: '2026-10-18T01:04:05Z'
    evidence_url: https://github.com/We-Solve/research/issues/8