{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R528",
  "content_hash": null,
  "slug": "minimal105-attempt-extend-to-weight-twenty",
  "type": "attempt",
  "title": "Extend the exact sequential search to weight twenty",
  "summary": "Continue the same exact matrix search at weight 20 with every orbit through weight 19 installed as a minimal-subset blocker, then independently replay any survivors.",
  "relevance": "For Minimal vanishing sums of distinct 105th roots, record minimal105-attempt-extend-to-weight-twenty (“Extend the exact sequential search to weight twenty”) documents a concrete method, search boundary, or failed route. The record states: Continue the same exact matrix search at weight 20 with every orbit through weight 19 installed as a minimal-subset blocker, then independently replay any survivors.",
  "relevance_source": "recorded",
  "body": "Start from the exact 48 by 105 remainder matrix and the full affine expansions of all seven certified representatives. Add the weight-20 cardinality constraint and every lower minimal-subset exclusion before solving. Canonicalize each survivor under the 5,040 affine maps, check all proper nonempty subsets exactly, and continue until the normalized solver returns UNSAT. A complete weight-20 record requires the source digest, environment, runtime, peak memory, representative and stabilizer data, and an independent replay. Compare any survivors with the conjectural weight-20 types in arXiv:2008.11268v2 as a cross-check only.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "proposed exact classification of distinct inclusion-minimal conductor-105 subsets at weight 20",
    "bounds": {
      "conductor": {
        "min": 105,
        "max": 105
      },
      "weight": {
        "min": 20,
        "max": 20
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Extension plan checked by production /v1/research/check-plan on 2026-07-28 UTC"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Extension plan checked by production /v1/research/check-plan on 2026-07-28 UTC"
  },
  "models": [],
  "relations": [
    {
      "slug": "R526",
      "title": "Exact affine-orbit replay through weight nineteen",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "minimal-vanishing-105th-root-sums",
      "title": "minimal vanishing 105th root sums",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}