Proof Path TheoryReading edition

A complete minimal proof-field record

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The wording and mathematics follow the retained manuscript. This reading format does not add a proof review or extend Lean coverage.

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D A complete minimal proof-field record

The following record defines both its premise and its target. It is a complete importable example rather than a schema fragment with an unresolved target reference. The rule is explicitly assumed for this demonstration. Its declared certification must not be mistaken for a proof of an arbitrary implication between the displayed labels.

{
  "schema_version": "1.0",
  "premises": ["A"],
  "targets": ["B"],
  "nodes": [
    {"id": "A", "label": "Premise A", "kind": "premise"},
    {"id": "B", "label": "Target B", "kind": "claim"}
  ],
  "evidence": [
    {
      "id": "e-rule",
      "kind": "assumption",
      "source": "Declared demonstration rule A implies B",
      "scope": "This finite inference model only",
      "certifies": true
    }
  ],
  "justifications": [
    {
      "id": "j1",
      "premises": ["A"],
      "conclusion": "B",
      "rule": "assumed implication",
      "certified": true,
      "evidence_ids": ["e-rule"]
    }
  ]
}

The file examples/minimal_monograph.json contains this record. The public importer checks its identifiers and Boolean fields, and declared closure reaches B. Mathematical soundness still requires the explicit interpretation contract of Section 9.

References

[1] komorebi-space

Komorebi P. Komorebi Space: Coherent Realizations, Obstructions, and Descent. Monograph, 2026. The finite proof-field view construction here is a relative application of its strict coherent realization principle, not a claim of unrestricted semantic completeness.

[2] buss

S. R. Buss, editor. Handbook of Proof Theory. Elsevier, 1998.

[3] cover-thomas

T. M. Cover and J. A. Thomas. Elements of Information Theory. Second edition, Wiley, 2006.

[4] diestel

R. Diestel. Graph Theory. Fifth edition, Springer, 2017.

[5] garey-johnson

M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.

[6] knuth

D. E. Knuth. Literate Programming. CSLI Publications, 1992.

[7] maclane

S. Mac Lane. Categories for the Working Mathematician. Second edition, Springer, 1998.

[8] nemhauser

G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher. An analysis of approximations for maximizing submodular set functions I. Mathematical Programming, 14:265–294, 1978.

[9] troelstra

A. S. Troelstra and H. Schwichtenberg. Basic Proof Theory. Second edition, Cambridge University Press, 2000.

Source and conversion record

Source SHA-256: ce05e88b439e9fd55ef6eb04da708a63ce02e6627424e6daac0dca4177b8ab51

Unsupported prose commands stop the build. The mathematical expression sequence is checked against the source, with manuscript macros expanded for display.

Conversion records

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