{
  "schema": "SOVRIENT_THEOREM_REFERENCE_V1",
  "generated_utc": "2026-05-08T18:03:30Z",
  "generator": "scripts/export_theorem_reference.py",
  "page": {
    "html": "https://www.sovrient.com/theorem-reference",
    "json": "https://www.sovrient.com/theorem-reference.json",
    "title": "ACL2 + Isabelle/HOL Theorem Twins | Sovrient",
    "status": "public_reference_surface"
  },
  "summary": "Public-safe reference surface for Sovrient's current certified ACL2 theorem family, a repo-internal Isabelle/HOL family for session and briefing invariants, and a live Isabelle/HOL pi minimal-period route that is the first live Isabelle theorem-twin route.",
  "claim_boundary": [
    "The current live public claim is that Sovrient has a certified ACL2 theorem family and a bounded public reference surface for it, with three live public raw theorem-twin routes (ACL2 frame, ACL2 ZF gate, and Isabelle pi minimal period).",
    "The Isabelle/HOL session-scope framework (session scope, participant authority, opportunity-brief safety) exists repo-internally and remains repo-internal; those three twins are not live public routes.",
    "The Isabelle/HOL pi framework is a distinct framework; its minimality theorem is the first live Isabelle theorem-twin route and a live public route.",
    "Three raw theorem twins are live public today: ACL2 frame, ACL2 ZF gate, and Isabelle pi minimal period. The rest of the family remains repo/internal unless separately declared.",
    "The theorem reference surface does not replace ACL2 or Isabelle certification or make JSON the authority layer.",
    "No claim is made that every production lane or SSEJ record is already formally theorem-bound.",
    "The canonical surfaced theorem in the live Isabelle route is minimal_shared_period_2pi_trig_complexexp; the shared-period kernel in Pi_Structural_Periodicity is a frozen prerequisite checkpoint, not the surfaced result.",
    "The broader interpretive articulation about pi as a recurrent structural constant across arbitrary oscillatory or Fourier-related formalisms is not a theorem; it is recorded in a companion note only.",
    "The live Isabelle/HOL pi route also serves a non-discovery alternate application/cbor companion encoding. It is descriptive only, not CBOR-LD, and does not replace the JSON-LD twin route.",
    "All three live theorem-twin routes now also serve non-discovery application/cbor companion encodings. These are descriptive transport companions only, not CBOR-LD, and do not replace the JSON-LD twin routes or the prover-specific authority artifacts."
  ],
  "authority_chain": [
    "ACL2 source books (.lisp) and certification artifacts (.cert and .port) for the current public family",
    "Isabelle/HOL source theories (.thy), session root, and build wrapper for the repo-internal second prover family",
    "Published theorem twins with declared hashes for the current public ACL2 twin routes",
    "Public-safe theorem reference surface"
  ],
  "formal_system": {
    "prover": "ACL2",
    "prover_version": "8.6+",
    "warnings_floor": [
      "Guards"
    ],
    "public_surface_scope": "current live public theorem-twin routes remain ACL2 frame, ACL2 ZF gate, and Isabelle pi minimal period. The session-scope Isabelle/HOL framework remains repo-internal."
  },
  "family_summary": {
    "certified_book_count": 3,
    "exported_theorem_count": 35,
    "roles": [
      "frame",
      "core",
      "lane"
    ],
    "live_twin_count": 3,
    "staged_twin_count_pending_deploy": 0,
    "prover_family_count": 2
  },
  "family": [
    {
      "id": "scf_dtau_001_frame",
      "role": "frame",
      "status": "certified",
      "expected_load_marker": ":frame-loaded",
      "exported_theorem_count": 12,
      "summary": "Abstract admission, governance, replay, and durability structure."
    },
    {
      "id": "scf_dtau_001_core1",
      "role": "core",
      "status": "certified",
      "expected_load_marker": ":core1-loaded",
      "exported_theorem_count": 7,
      "summary": "Minimal concrete singleton witness over p-core."
    },
    {
      "id": "scf_dtau_001_zf_gate_core",
      "role": "lane",
      "status": "certified",
      "expected_load_marker": ":zf1-loaded",
      "exported_theorem_count": 16,
      "summary": "First real authoritative singleton path for the ZF release-eligibility latch."
    }
  ],
  "additional_prover_families": [
    {
      "id": "sovrient_isabelle_001",
      "prover": "Isabelle/HOL",
      "prover_version": "Isabelle2025",
      "status": "repo_internal_build_verified",
      "public_route_status": "no_live_public_theorem_twin_routes",
      "planned_publication_state": "not_scheduled_for_public_route_in_current_release",
      "gating_reason": "Repo-internal Isabelle session-scope twins are held until public theorem-twin export reproducibility and route-level claim boundaries are CI-validated; public claims do not depend on them.",
      "summary": "Repo-internal Isabelle/HOL framework for session scope, participant authority, and opportunity-brief safety invariants.",
      "repo_internal_twin_count": 3,
      "public_live_twin_count": 0,
      "exported_theorem_count": 13,
      "roles": [
        "session_scope",
        "participant_authority",
        "opportunity_brief_safety"
      ],
      "family": [
        {
          "id": "sovrient_isabelle_session_scope",
          "role": "session_scope",
          "status": "build_verified",
          "exported_theorem_count": 3,
          "summary": "Declared session envelope scope and mutation-boundary rules."
        },
        {
          "id": "sovrient_isabelle_participant_authority",
          "role": "participant_authority",
          "status": "build_verified",
          "exported_theorem_count": 5,
          "summary": "Advisory and companion participants remain non-authoritative; human review resolves conflicts."
        },
        {
          "id": "sovrient_isabelle_opportunity_brief_safety",
          "role": "opportunity_brief_safety",
          "status": "build_verified",
          "exported_theorem_count": 5,
          "summary": "Likely timing, confirmed release, and award claims remain separated in opportunity briefs."
        }
      ],
      "note": "Theories and repo-internal twins exist and build-verify locally, but no live public theorem-twin routes are published for this framework today."
    },
    {
      "id": "sovrient_isabelle_pi_001",
      "prover": "Isabelle/HOL",
      "prover_version": "Isabelle2025",
      "parent_session": "HOL-Analysis",
      "status": "build_verified_with_live_public_route",
      "public_route_status": "live_public_theorem_twin_route",
      "summary": "Isabelle/HOL framework formalizing pi as the canonical minimal positive shared period of sin, cos, and the complex exponential on the imaginary axis. Shared-period kernel is a frozen prerequisite; the minimality theorem is the canonical surfaced result and the first live Isabelle theorem-twin route.",
      "repo_internal_twin_count": 0,
      "public_live_twin_count": 1,
      "staged_twin_count_pending_deploy": 0,
      "exported_theorem_count": 5,
      "roles": [
        "pi_minimal_period"
      ],
      "family": [
        {
          "id": "sovrient_isabelle_pi_minimal_period",
          "role": "pi_minimal_period",
          "status": "build_verified",
          "publication_status": "live_public",
          "exported_theorem_count": 5,
          "canonical_surfaced_theorem": "minimal_shared_period_2pi_trig_complexexp",
          "frozen_prerequisite": {
            "source_path": "formal/isabelle/pi/Pi_Structural_Periodicity.thy",
            "role": "shared_period_kernel_checkpoint"
          },
          "summary": "Canonical form: 2*pi is the minimal positive shared period of sin, cos, and exp(i*x). Live public Isabelle/HOL theorem-twin route, with the shared-period kernel preserved as a frozen checkpoint.",
          "alternate_encodings": [
            {
              "encoding_format": "application/cbor",
              "content_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor",
              "sha256_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.sha256",
              "manifest_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.manifest.json",
              "profile": "sovrient-cbor-companion-v1",
              "publication_status": "live_public_companion",
              "authority_role": "descriptive_companion_only",
              "not_cbor_ld": true
            }
          ]
        }
      ],
      "note": "First live Isabelle/HOL theorem-twin route, live public route as of 2026-04-16. Authority remains with the .thy source files, ROOT session file, build wrapper, prover identity, and a successful Sovrient_Isabelle_Math session build. The broader interpretive articulation about pi as a structural constant across all Fourier-related formalisms is not a theorem; see docs/PI_STRUCTURAL_PERIODICITY_NOTE_2026-04-16.md."
    }
  ],
  "twin_model": {
    "public_surface_role": "descriptive reference surface",
    "internal_twin_status": "two_live_public_acl2_twins_plus_one_live_isabelle_twin_plus_repo_internal_additional_isabelle_framework",
    "internal_twin_note": "Two live public raw theorem twins today (both ACL2): frame and ZF gate. One live public raw theorem twin today (Isabelle/HOL): pi minimal period. Three additional Isabelle/HOL twins (session scope, participant authority, opportunity-brief safety) remain repo-internal. Authority stays with prover-specific formal artifacts in all cases."
  },
  "first_live_theorem_twin": {
    "id": "scf_dtau_001_zf_gate_core",
    "prover": "ACL2",
    "jsonld": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.jsonld",
    "sha256": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.jsonld.sha256",
    "publication_status": "live_public",
    "alternate_encodings": [
      {
        "encoding_format": "application/cbor",
        "content_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor",
        "sha256_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor.sha256",
        "manifest_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor.manifest.json",
        "profile": "sovrient-cbor-companion-v1",
        "publication_status": "live_public_companion",
        "authority_role": "descriptive_companion_only",
        "not_cbor_ld": true
      }
    ]
  },
  "first_live_isabelle_theorem_twin": {
    "id": "sovrient_isabelle_pi_minimal_period",
    "prover": "Isabelle/HOL",
    "jsonld": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.jsonld",
    "sha256": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.jsonld.sha256",
    "publication_status": "live_public",
    "alternate_encodings": [
      {
        "encoding_format": "application/cbor",
        "content_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor",
        "sha256_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.sha256",
        "manifest_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.manifest.json",
        "profile": "sovrient-cbor-companion-v1",
        "publication_status": "live_public_companion",
        "authority_role": "descriptive_companion_only",
        "not_cbor_ld": true
      }
    ]
  },
  "live_theorem_twins": [
    {
      "id": "scf_dtau_001_frame",
      "prover": "ACL2",
      "jsonld": "https://www.sovrient.com/theorem-twins/scf_dtau_001_frame.jsonld",
      "sha256": "https://www.sovrient.com/theorem-twins/scf_dtau_001_frame.jsonld.sha256",
      "publication_status": "live_public",
      "alternate_encodings": [
        {
          "encoding_format": "application/cbor",
          "content_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_frame.cbor",
          "sha256_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_frame.cbor.sha256",
          "manifest_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_frame.cbor.manifest.json",
          "profile": "sovrient-cbor-companion-v1",
          "publication_status": "live_public_companion",
          "authority_role": "descriptive_companion_only",
          "not_cbor_ld": true
        }
      ]
    },
    {
      "id": "scf_dtau_001_zf_gate_core",
      "prover": "ACL2",
      "jsonld": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.jsonld",
      "sha256": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.jsonld.sha256",
      "publication_status": "live_public",
      "alternate_encodings": [
        {
          "encoding_format": "application/cbor",
          "content_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor",
          "sha256_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor.sha256",
          "manifest_url": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor.manifest.json",
          "profile": "sovrient-cbor-companion-v1",
          "publication_status": "live_public_companion",
          "authority_role": "descriptive_companion_only",
          "not_cbor_ld": true
        }
      ]
    },
    {
      "id": "sovrient_isabelle_pi_minimal_period",
      "prover": "Isabelle/HOL",
      "jsonld": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.jsonld",
      "sha256": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.jsonld.sha256",
      "publication_status": "live_public",
      "alternate_encodings": [
        {
          "encoding_format": "application/cbor",
          "content_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor",
          "sha256_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.sha256",
          "manifest_url": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.manifest.json",
          "profile": "sovrient-cbor-companion-v1",
          "publication_status": "live_public_companion",
          "authority_role": "descriptive_companion_only",
          "not_cbor_ld": true
        }
      ]
    }
  ],
  "ssej_connection": {
    "role": "Justified_support",
    "note": "The formal layer now has a path to support SSEJ Justified references with theorem ids, but no public claim is made that live production SSEJ records already cite theorem ids."
  },
  "related_surfaces": {
    "governance_reconstruction": "https://www.sovrient.com/governance-reconstruction",
    "governance_reconstruction_state": "https://www.sovrient.com/data/governance_reconstruction_state.json",
    "machine_state": "https://www.sovrient.com/machine-state.json",
    "managed_agent_reference": "https://www.sovrient.com/managed-agent-reference",
    "first_live_theorem_twin": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.jsonld",
    "live_theorem_twins": [
      "https://www.sovrient.com/theorem-twins/scf_dtau_001_frame.jsonld",
      "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.jsonld",
      "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.jsonld"
    ],
    "first_live_isabelle_theorem_twin": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.jsonld",
    "glossary_ssej": "https://www.sovrient.com/glossary#ssej",
    "glossary_anatop": "https://www.sovrient.com/glossary#anatop",
    "first_live_isabelle_theorem_twin_cbor": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor",
    "first_live_isabelle_theorem_twin_cbor_manifest": "https://www.sovrient.com/theorem-twins/sovrient_isabelle_pi_minimal_period.cbor.manifest.json",
    "first_live_theorem_twin_cbor": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor",
    "first_live_theorem_twin_cbor_manifest": "https://www.sovrient.com/theorem-twins/scf_dtau_001_zf_gate_core.cbor.manifest.json"
  }
}