{
  "artifact_type": "ecr_receipt",
  "phihash": "PHI13_df069f19b5e80d0246b9a641",
  "theorem_id": "PHI13_8d36a77eb708d9a255c8a4b3",
  "source_file": "ChaosCompounding__VERIFIED.lean",
  "source_url": "https://morphogenic.systems/static/evidence/sources/ChaosCompounding__VERIFIED.lean",
  "receipt_schema": "VERIFIED_THEOREMS_ECR_FIELD_v1.2",
  "receipt": {
    "theorem_id": "PHI13_8d36a77eb708d9a255c8a4b3",
    "phihash": "PHI13_df069f19b5e80d0246b9a641",
    "class": "CHAOS-COMPOUNDING",
    "file": "ChaosCompounding__VERIFIED.lean",
    "problem_identity": "CHAOS_COMPOUNDING",
    "theorem_name": "ChaosCompounding__VERIFIED",
    "statement": "chaos_compounding : forall (d1 d2 : Direction), causal_predecessor d1 d2 -> compounding_loop_witnessed d1 d2 (definitional witness: compounding_loop_witnessed defined as causal_predecessor)",
    "environment": {
      "lean_version": "Lean 4.30.0-rc2",
      "mathlib_commit": "5450b53e5ddc75d46418fabb605edbf36bd0beb6"
    },
    "kernel_verdict": "ELABORATED_CLOSED",
    "kernel_elapsed_s": 0.69,
    "axiom_dependencies": "propext, Classical.choice, Quot.sound (standard-three only)",
    "ecr_gate": { "ECR-1": "PASS", "ECR-2": "PASS", "ECR-3": "PASS", "ECR-4": "PASS" },
    "honest_classification": "FORMAL_MODEL_COMPONENT",
    "honest_note": "Definitional witness: the proof is `exact h` because compounding_loop_witnessed is defined as causal_predecessor. Demonstrates receipt pipeline on an unambiguous case.",
    "compounding": {
      "C1_kg_registration": "PENDING",
      "C2_problem_attachment": "PENDING",
      "C3_cross_domain_reuse": "PENDING",
      "C4_frontier_boundary": "PENDING",
      "C5_capability_backing": "PENDING"
    },
    "verified_utc": "2026-09-14T05:17:51Z",
    "schema": "VERIFIED_THEOREMS_ECR_FIELD_v1.2",
    "authority": "chaos-prime-v18.45.0"
  },
  "node23_sandbox_reproduction": {
    "run_at_utc": "2026-09-29T00:00:00Z",
    "toolchain": "Lean 4.30.0-rc2 standalone (no Mathlib — the file declares no imports required)",
    "command": "lean ChaosCompounding__VERIFIED.lean",
    "return_code": 0,
    "elapsed_s": 0.507,
    "axiom_profile_direct_check": "'chaos_compounding' does not depend on any axioms",
    "note": "Direct axiom check is stronger than the toolchain's conservative upper bound. Theorem is purely definitional; no axioms are needed.",
    "status": "SANDBOX_REPRODUCED",
    "sandbox_log_url": "https://morphogenic.systems/static/evidence/sources/sandbox-verification.log"
  },
  "author": {
    "name": "Tim Jacobs",
    "orcid": "0009-0002-8896-4849",
    "wikidata_qid": "Q137953077",
    "canonical_nodes": ["https://tim-jacobs.net/","https://geometricintelligence.ai/","https://geometry-of-intelligence.com/","https://evidence-economy.com/","https://geometry-intelligence.com/","https://morphogenic.systems/"]
  },
  "attribution": "These theorems are the kernel-verified formal substrate underlying the Geometry Intelligence Foundational Series. Each is checked by Lean 4 against mathlib using only the three standard axioms (propext, Classical.choice, Quot.sound). Verification uses the same toolchain used globally for formal mathematics and physics. Sources, pinned environment and receipts are published for independent reproduction. Author: Tim Jacobs (ORCID 0009-0002-8896-4849). Published across: NODE-18 (geometricintelligence.ai), NODE-19 (geometry-of-intelligence.com), NODE-21 (geometry-intelligence.com), NODE-10 (tim-jacobs.net), NODE-20 (evidence-economy.com), NODE-23 (morphogenic.systems). Archived at NODE-6 (kts-global-evidence-locker).",
  "node23_url": "https://morphogenic.systems/evidence/receipts/PHI13_8d36a77eb708d9a255c8a4b3/",
  "archived_at": "NODE-6 (kts-global-evidence-locker)",
  "archived_by": "chaos-kts-production-agent via NODE-23 build 2026-09-29"
}