schema_version: 1
contribution_id: con_74647baa11354cc78bcfba033df0db43
revision_id: rev_e51287a6201b4d5eb1888afc2a27306c
expected_predecessor: null
type: attempt
home_problem_id: prb_ddc644c4f2054244b3b59417c5fecc0e
targets:
- target_kind: problem
  problem_id: prb_ddc644c4f2054244b3b59417c5fecc0e
  statement_revision_id: stm_c8f8cff414fb4e13b3eee76a4d0ff975
  scope: part_of_statement
title: ECON-D82-92
profiles:
- id: mathematical_argument
  version: 1
  required: true
claim:
  type: partial_result
  scope_statement: |-
    For the stated linear-type screening problem, additionally assume that the compact convex allocation set contains zero and that the continuous convex cost is nonnegative with C(0)=0. I claim an explicit two-sided comparison between the continuum optimal value and a finite-type convex program, and a construction converting any certified solution of that program into a globally IC/IR finite menu. With type-cell radius h, the resulting objective gap is at most the certified finite-program gap plus O(sqrt(h)), with constants given below. No Lipschitz bound on the cost or density is required for this analytic comparison when cell probabilities are exact.

    For rational polytopes, a positive normalized rational polynomial density, and rational convex piecewise-affine cost, the construction gives a finite algorithm using exact cell integration and rational linear-program certificates. This is a theorem and algorithm specification, not a report of an executed numerical solver. It does not characterize exclusion or bunching, establish a new literature priority, or solve the whole research family.
  assumptions: []
  limitations: []
attribution:
  submitter:
    person_ref: per_a0b0275adee949eaaee08af8accbb1a5
    github_id: 8898165
    login_at_event: meleantonio
    display_name: meleantonio
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  humans:
  - person_ref: per_a0b0275adee949eaaee08af8accbb1a5
    github_id: 8898165
    login_at_event: meleantonio
    display_name: meleantonio
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  organisations: []
  contribution_mode: ai_only
model_uses:
- provider: OpenAI
  declared_name: gpt-6
  family: null
  version: unknown
  role: generated_draft
  settings:
    reasoning: unknown
  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:
  - meleantonio
declarations:
  rights:
    confirmed: true
    source: form_field
    actor: per_a0b0275adee949eaaee08af8accbb1a5
    recorded_at: '2026-10-18T01:46:20Z'
    evidence_url: https://github.com/We-Solve/research/issues/10
  public_disclosure:
    confirmed: true
    source: form_field
    actor: per_a0b0275adee949eaaee08af8accbb1a5
    recorded_at: '2026-10-18T01:46:20Z'
    evidence_url: https://github.com/We-Solve/research/issues/10
  ai_disclosure:
    confirmed: true
    source: form_field
    actor: per_a0b0275adee949eaaee08af8accbb1a5
    recorded_at: '2026-10-18T01:46:20Z'
    evidence_url: https://github.com/We-Solve/research/issues/10