{
  "schema_version": 1,
  "title": "Semiprime algorithm proof explorer",
  "repository_url": "https://github.com/dbsanfte/RiemannGaussian",
  "pages_path": "/RiemannGaussian/semiprime-proof/",
  "publication_packet": "docs/research-evidence/semiprime-boundary-hybrid-20261029",
  "intro": "The boundary hybrid now has exact original-binary factor-byte correctness, a deterministic half-exponent checked leaf, and a closed quantitative bound for its own mixed native report. The complete primitive-machine bit-complexity theorem remains open.",
  "target": "2^(C\u00b7\u2113/\u221alog(\u2113+2)) \u00b7 (\u2113+1)^d",
  "target_scope": "For every semiprime N from its canonical binary input, \u2113 = \u2308log\u2082(N+1)\u2309, with fixed C and d chosen before N. This is a target, not an achieved running-time theorem.",
  "pipeline_disclaimer": "This is a curated algorithm reading order, not a Lean-extracted dependency graph. Native hybrid gains and historical physical components retain their distinct cost scopes; adjacent stages do not assert complete physical caller joins.",
  "evidence_disclaimer": "Finalized means recorded historical component gates with their original scope. New native results are classified separately as mathematical proofs; compiled integration audits are separate evidence. The inventory and explorer check source/evidence hashes and do not themselves run Lean or certify whole primitive-bit running time.",
  "status_labels": {
    "finalized-machine": "Finalized machine component",
    "proved-math": "Proved mathematical result",
    "draft": "Draft / not finalized",
    "legacy-unclassified": "Legacy source / unclassified"
  },
  "glossary": [
    {
      "term": "Mathematical correctness",
      "meaning": "A theorem identifies the specified algorithm\u2019s output. It does not by itself establish a primitive machine\u2019s total running time."
    },
    {
      "term": "Finalized component",
      "meaning": "A fixed physical program and its stated local contract passed the recorded focused gates. Read its input boundary: a prepared operand is not automatically acquired from N."
    },
    {
      "term": "Caller join",
      "meaning": "A physical program passes actually acquired words to the next program, paying for copies, parsing, cleanup, memory and returns."
    },
    {
      "term": "Whole bit-complexity theorem",
      "meaning": "One deterministic original-input program factors every semiprime within the displayed bound, including preprocessing, recursive coefficients, storage and factor recovery."
    }
  ]
}