{
  "trace_id": "e2e_master_E_equals_mc2_v2",
  "trace_version": "2.0",
  "equation_text": "E = mc^2",
  "equation_shape": {
    "n_vars": 3,
    "n_ops": 2,
    "max_depth": 1,
    "n_quantifiers": 0,
    "n_relations": 1
  },
  "sidon_address": [
    4,
    16,
    16,
    1,
    16,
    1,
    16,
    8
  ],
  "chaos_basin": "q_braid",
  "chaos_steps": 1390,
  "finsler_alpha": "\u03b1(Fisher) = {sqrt(v\u00b7G_Fisher\u00b7v)} \u2014 base cost 0.4167 from verification=1.0",
  "finsler_beta": "\u03b2(torsion drift) = \u03b2\u00b7v \u2014 drift strength 0.1500 from q_braid basin",
  "qubo_variables": 8,
  "qubo_couplings": 36,
  "qaoa_depth": 2,
  "qaoa_qubits": 8,
  "hachimoji_state": "\u03a6",
  "hachimoji_regime": "beautifulTopologicalFolding",
  "hachimoji_phase": 0,
  "hachimoji_chirality": "ambidextrous",
  "hachimoji_direction": "forward",
  "steps": [
    {
      "step_name": "Equation text \u2192 EquationShape",
      "step_number": 1,
      "input_desc": "\"E = mc^2\"",
      "output_desc": "\u27e8vars=3, ops=2, depth=1, quant=0, rels=1\u27e9",
      "theorem_used": "step1_shape_eq (E2EMasterTrace.lean) \u2014 PROVEN by rfl",
      "status": "PROVEN",
      "proof_note": "Parser counts variables (E,m,c=3), operators (=,^=2), depth (exponentiation=1), quantifiers (0), relations (1).",
      "computation_time_ms": 0.02
    },
    {
      "step_name": "Spectral profile \u2192 Sidon address [4,16,16,1,16,1,16,8]",
      "step_number": 2,
      "input_desc": "\u27e83, 2, 1, 0, 1\u27e9",
      "output_desc": "address=[4, 16, 16, 1, 16, 1, 16, 8]",
      "theorem_used": "step2_sidon_valid + step2_address_length (E2EMasterTrace.lean) \u2014 PROVEN by simp",
      "status": "PROVEN",
      "proof_note": "All 8 elements are in Sidon set {1,2,4,8,16,32,64,128}. Address length is exactly 8.",
      "computation_time_ms": 0.0
    },
    {
      "step_name": "Sidon address \u2192 Chaos game basin q_braid (1390 steps)",
      "step_number": 3,
      "input_desc": "address=[4, 16, 16, 1, 16, 1, 16, 8]",
      "output_desc": "basin=q_braid, converged=True, steps=1390, coord=0.076172",
      "theorem_used": "step3_chaos_convergence (E2EMasterTrace.lean) \u2014 STATED sorry",
      "status": "COMPUTED",
      "proof_note": "IFS contraction factor 0.5 guarantees convergence by Banach fixed-point theorem. Basin q_braid verified by chaos_game_16d.py. Formal basin membership proof requires 8D simplex analysis (sorry).",
      "computation_time_ms": 0.15
    },
    {
      "step_name": "Finsler metric F = \u03b1(Fisher) + \u03b2(torsion drift)",
      "step_number": 4,
      "input_desc": "basin=q_braid",
      "output_desc": "\u03b1_base=0.416667, \u03b2_strength=0.15",
      "theorem_used": "TransportTheory.RandersMetric + step4_randers_strong_convexity (E2EMasterTrace.lean) \u2014 STATED sorry",
      "status": "STATED",
      "proof_note": "Randers metric defined in TransportTheory.lean. Strong convexity holds because Fisher information is positive definite and drift 0.15 is bounded by spectral gap. Formal proof requires empirical Fisher matrix analysis (sorry).",
      "computation_time_ms": 0.07
    },
    {
      "step_name": "QUBO encoding of Finsler path cost (8 variables, 36 couplings)",
      "step_number": 5,
      "input_desc": "\u03b1=\u03b1(Fisher) = {sqrt(v\u00b7G_Fisher\u00b7v)} \u2014 base cost 0.416...",
      "output_desc": "QUBO n=8, couplings=36",
      "theorem_used": "step5_qubo_preserves_cost + step5_qubo_ground_state (E2EMasterTrace.lean) \u2014 STATED sorry",
      "status": "STATED",
      "proof_note": "QUBO has 8 binary variables (one per Hachimoji state). Diagonal terms encode \u03b1 cost, off-diagonal encode \u03b2 drift. Formal proof of cost preservation requires discretization error bounds (sorry). Ground state is \u03a6-dominant (trivial regime).",
      "computation_time_ms": 0.04
    },
    {
      "step_name": "QAOA circuit (p=2, 8 qubits)",
      "step_number": 6,
      "input_desc": "QUBO n=8",
      "output_desc": "bitstring=[0, 0, 0, 0, 0, 0, 0, 0], energy=0.0, approx_ratio=1.0",
      "theorem_used": "step6_qaoa_approximation (E2EMasterTrace.lean) \u2014 STATED sorry",
      "status": "COMPUTED",
      "proof_note": "p=2 QAOA with 8 qubits. Approximation ratio 1.0 verified by comparison with brute-force optimal. Formal proof requires QAOA performance bound formalization (sorry).",
      "computation_time_ms": 282.17
    },
    {
      "step_name": "Hachimoji state: \u03a6 (beautifulTopologicalFolding, trivial regime)",
      "step_number": 7,
      "input_desc": "QAOA bitstring=[0, 0, 0, 0, 0, 0, 0, 0]",
      "output_desc": "state=\u03a6, phase=0\u00b0, regime=beautifulTopologicalFolding",
      "theorem_used": "step7_phi_phase + step7_phi_regime (E2EMasterTrace.lean) \u2014 PROVEN by rfl",
      "status": "PROVEN",
      "proof_note": "\u03a6 state: phase 0\u00b0, forward direction, beautifulTopologicalFolding regime. E=mc\u00b2 is above \u03c6_GCP (trivial regime): all constants known, no contradictions, q_braid basin (ordered), small \u03b2 drift.",
      "computation_time_ms": 0.02
    },
    {
      "step_name": "Receipt Merkle hash (all 7 witnesses chained)",
      "step_number": 8,
      "input_desc": "all 7 step witnesses",
      "output_desc": "sha256=c8ad995a0fdd9bd0160ae5e20ca27b89...",
      "theorem_used": "step8_merkle_computable (E2EMasterTrace.lean) \u2014 PROVEN by rfl",
      "status": "COMPUTED",
      "proof_note": "Merkle tree over 7 witnesses with non-commutative mixHash. Root is deterministic from all step outputs. Final SHA-256 from canonical JSON.",
      "computation_time_ms": 0.14
    }
  ],
  "sha256": "c8ad995a0fdd9bd0160ae5e20ca27b89a5ca759ef0465b7d0472d0901b3efcfa",
  "total_sorry": 2,
  "total_proven": 3,
  "total_computed": 3,
  "computation_time_ms": 282.72,
  "schema": "e2e_master_trace_v2",
  "timestamp": "2026-06-21T04:42:41.496217+00:00"
}