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bef48acee4
- 42/42 unique matrix hashes (100%) - 42/42 unique canonical hashes (no collisions) - 42/42 unique spectral gaps (full diversity) - Rank estimate: 5 distinct values, range [4, 8] - Laplacian zero count: 3 distinct values, range [1, 3] - 1 outlier: omega_double classified as CadForceProbeReceipt (rank=4) - Classifier still collapses to LogogramProjection for rank>=5 Conclusion: spectral features are diverse. Classifier thresholds need training, not hand-tuning.
42 lines
47 KiB
JSON
42 lines
47 KiB
JSON
{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "rfl_one", "equation_text": "rfl one", "normalized_equation": "one_rfl", "operators": [], "variables": ["rfl", "one"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n = n := by rfl", "proof_script": "theorem t (n : Nat) : n = n := by rfl", "imports": [], "dependencies": [], "source_hash": "2eb9f6a59233beb416395ad25d3a7e0211b824fc5c6c801ebc9a5bb3f62a2373", "environment_hash": "2026-05-26T07:04:40.496742+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 6933, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 37, "proof_chars": 37, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "rfl_add", "equation_text": "rfl add", "normalized_equation": "add_rfl", "operators": [], "variables": ["rfl", "add"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n + 0 = n := by rfl", "proof_script": "theorem t (n : Nat) : n + 0 = n := by rfl", "imports": [], "dependencies": [], "source_hash": "22c02658d595ec0476ff1995168b381605e930801de2ebeba2b55b832a7e090a", "environment_hash": "2026-05-26T07:04:43.551803+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2658, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 41, "proof_chars": 41, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "rfl_succ", "equation_text": "rfl succ", "normalized_equation": "rfl_succ", "operators": [], "variables": ["rfl", "succ"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n.succ = n.succ := by rfl", "proof_script": "theorem t (n : Nat) : n.succ = n.succ := by rfl", "imports": [], "dependencies": [], "source_hash": "ddd5d29d3dd1e40329ac7be84711110606576b827c3a84e6b6509be99042e1ca", "environment_hash": "2026-05-26T07:04:47.023868+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 3179, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 47, "proof_chars": 47, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "simp_add_zero", "equation_text": "simp add zero", "normalized_equation": "add_simp_zero", "operators": [], "variables": ["add", "zero", "simp"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n + 0 = n := by simp", "proof_script": "theorem t (n : Nat) : n + 0 = n := by simp", "imports": [], "dependencies": [], "source_hash": "efb25179cb114978eda7f987a9388e2949cb17627a5512edde87cd9d3366f244", "environment_hash": "2026-05-26T07:04:50.184553+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2491, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 42, "proof_chars": 42, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "simp_mul_one", "equation_text": "simp mul one", "normalized_equation": "mul_one_simp", "operators": [], "variables": ["mul", "one", "simp"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n * 1 = n := by simp", "proof_script": "theorem t (n : Nat) : n * 1 = n := by simp", "imports": [], "dependencies": [], "source_hash": "c0089d5d19cb00aa15510683a51ec87b58def6c5233d2a002ac6e946eec38be8", "environment_hash": "2026-05-26T07:04:53.674048+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 3048, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 42, "proof_chars": 42, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "simp_add_comm", "equation_text": "simp add comm", "normalized_equation": "add_comm_simp", "operators": [], "variables": ["add", "comm", "simp"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : a + b = b + a := by simp [add_comm]", "proof_script": "theorem t (a b : Nat) : a + b = b + a := by simp [add_comm]", "imports": [], "dependencies": [], "source_hash": "6eea1a572785dabf171f1fa04a26e8e643911bda3c289c1c2b7589e082748f7e", "environment_hash": "2026-05-26T07:04:56.590911+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2539, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 59, "proof_chars": 59, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "simp_add_assoc", "equation_text": "simp add assoc", "normalized_equation": "add_assoc_simp", "operators": [], "variables": ["assoc", "add", "simp"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (a b c : Nat) : (a + b) + c = a + (b + c) := by simp [add_assoc]", "proof_script": "theorem t (a b c : Nat) : (a + b) + c = a + (b + c) := by simp [add_assoc]", "imports": [], "dependencies": [], "source_hash": "bba6095c94ebaf9b4ada297727ed1a8f1e1a7657daf44738a5b56d238ae6dd0e", "environment_hash": "2026-05-26T07:04:59.147580+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2196, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 74, "proof_chars": 74, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "simp_mul_comm", "equation_text": "simp mul comm", "normalized_equation": "comm_mul_simp", "operators": [], "variables": ["mul", "comm", "simp"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : a * b = b * a := by simp [mul_comm]", "proof_script": "theorem t (a b : Nat) : a * b = b * a := by simp [mul_comm]", "imports": [], "dependencies": [], "source_hash": "c9db3bace941af4cf587ccc65acda72b3e82d2411f3ee3f450530410208c9569", "environment_hash": "2026-05-26T07:05:01.619450+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2124, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 59, "proof_chars": 59, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "omega_add", "equation_text": "omega add", "normalized_equation": "add_omega", "operators": [], "variables": ["add", "omega"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b c : Nat) : a + b + c = a + c + b := by omega", "proof_script": "theorem t (a b c : Nat) : a + b + c = a + c + b := by omega", "imports": [], "dependencies": [], "source_hash": "e5e03b1835a771571f0bb3ca99b4f38bd2779162fcbfc5a0510ce3457c2b8a1a", "environment_hash": "2026-05-26T07:05:03.946229+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2042, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 59, "proof_chars": 59, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "omega_mul", "equation_text": "omega mul", "normalized_equation": "mul_omega", "operators": [], "variables": ["mul", "omega"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : (a + b) * 2 = a*2 + b*2 := by omega", "proof_script": "theorem t (a b : Nat) : (a + b) * 2 = a*2 + b*2 := by omega", "imports": [], "dependencies": [], "source_hash": "a7737e85b1ccbd4a0b85ba6836c81e02669877ed433134e699a580e39df97625", "environment_hash": "2026-05-26T07:05:06.043353+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 1801, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 59, "proof_chars": 59, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "omega_ineq", "equation_text": "omega ineq", "normalized_equation": "ineq_omega", "operators": [], "variables": ["omega", "ineq"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) (h : a \u2264 b) : a + 1 \u2264 b + 1 := by omega", "proof_script": "theorem t (a b : Nat) (h : a \u2264 b) : a + 1 \u2264 b + 1 := by omega", "imports": [], "dependencies": [], "source_hash": "166370fcdff586c946fd291776c046865ddf3c55a338a7e5cf4c74d006ed06e3", "environment_hash": "2026-05-26T07:05:09.977301+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 3650, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 61, "proof_chars": 61, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "omega_mod", "equation_text": "omega mod", "normalized_equation": "mod_omega", "operators": [], "variables": ["omega", "mod"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a : Nat) : a % 2 < 2 := by omega", "proof_script": "theorem t (a : Nat) : a % 2 < 2 := by omega", "imports": [], "dependencies": [], "source_hash": "002bb6698e3e20497d0351dff4865cba42aa3a2c4a8841eb1d58824a7e0bb89f", "environment_hash": "2026-05-26T07:05:12.765953+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2491, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 43, "proof_chars": 43, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "omega_double", "equation_text": "omega double", "normalized_equation": "double_omega", "operators": [], "variables": ["omega", "double"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n + n = 2 * n := by omega", "proof_script": "theorem t (n : Nat) : n + n = 2 * n := by omega", "imports": [], "dependencies": [], "source_hash": "e919b215f798e5896c82730431d647b20c9bf009072d693602c176795bb08872", "environment_hash": "2026-05-26T07:05:16.072745+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2989, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 47, "proof_chars": 47, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "ring_sq", "equation_text": "ring sq", "normalized_equation": "ring_sq", "operators": [], "variables": ["ring", "sq"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (x y : Nat) : (x + y)^2 = x^2 + 2*x*y + y^2 := by nlinarith", "proof_script": "theorem t (x y : Nat) : (x + y)^2 = x^2 + 2*x*y + y^2 := by nlinarith", "imports": [], "dependencies": [], "source_hash": "3ac022380b181532654d377184b8ee39b42d3801205a690f1ee3785c62207f3c", "environment_hash": "2026-05-26T07:05:18.544426+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2129, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 69, "proof_chars": 69, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "ring_cube", "equation_text": "ring cube", "normalized_equation": "cube_ring", "operators": [], "variables": ["ring", "cube"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (x : Nat) : (x+1)^3 = x^3 + 3*x^2 + 3*x + 1 := by nlinarith", "proof_script": "theorem t (x : Nat) : (x+1)^3 = x^3 + 3*x^2 + 3*x + 1 := by nlinarith", "imports": [], "dependencies": [], "source_hash": "a889eba9fbad22397e4c371dc84fcf6fac29460cf05fe9f3564bb23936a5b747", "environment_hash": "2026-05-26T07:05:20.812533+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 1981, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 69, "proof_chars": 69, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "ring_expand", "equation_text": "ring expand", "normalized_equation": "expand_ring", "operators": [], "variables": ["expand", "ring"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : (a + b) * (a - b) = a^2 - b^2 := by omega", "proof_script": "theorem t (a b : Nat) : (a + b) * (a - b) = a^2 - b^2 := by omega", "imports": [], "dependencies": [], "source_hash": "50d7d00d3728a11c12e1456bafbacf8b4693e2e08bbee213103e9dbd5941a927", "environment_hash": "2026-05-26T07:05:23.770462+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2625, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 65, "proof_chars": 65, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "induct_add_zero", "equation_text": "induct add zero", "normalized_equation": "add_induct_zero", "operators": [], "variables": ["add", "zero", "induct"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : n + 0 = n := by induction n with k IH; rfl; simp [add_succ, IH]", "proof_script": "theorem t (n : Nat) : n + 0 = n := by induction n with k IH; rfl; simp [add_succ, IH]", "imports": [], "dependencies": [], "source_hash": "f9b7198b67b168ec39bb1530c3e85bb771ebe58030620cf76445942750c045e6", "environment_hash": "2026-05-26T07:05:27.078876+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2911, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 85, "proof_chars": 85, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "induct_add_succ", "equation_text": "induct add succ", "normalized_equation": "add_induct_succ", "operators": [], "variables": ["add", "succ", "induct"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (n m : Nat) : n + m.succ = (n + m).succ := by induction n with k IH; rfl; simp [add_succ, IH]", "proof_script": "theorem t (n m : Nat) : n + m.succ = (n + m).succ := by induction n with k IH; rfl; simp [add_succ, IH]", "imports": [], "dependencies": [], "source_hash": "e69e8b26359660beaac38538e3367fc00a89c5ce0761cda17ae2c81b41b0214a", "environment_hash": "2026-05-26T07:05:30.338345+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2713, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 103, "proof_chars": 103, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "induct_mul", "equation_text": "induct mul", "normalized_equation": "induct_mul", "operators": [], "variables": ["mul", "induct"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (n m : Nat) : n * m = m * n := by induction n with k IH; simp; simp [mul_add, IH, add_comm, add_left_comm, add_assoc]", "proof_script": "theorem t (n m : Nat) : n * m = m * n := by induction n with k IH; simp; simp [mul_add, IH, add_comm, add_left_comm, add_assoc]", "imports": [], "dependencies": [], "source_hash": "6a8b09e11b16cfb98d2acdcb10340f966da6a10c6e40cebcbdacefaf44f7b4e0", "environment_hash": "2026-05-26T07:05:32.767739+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2068, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 127, "proof_chars": 127, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "rw_add_comm", "equation_text": "rw add comm", "normalized_equation": "add_comm_rw", "operators": [], "variables": ["add", "rw", "comm"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : a + b = b + a := by rw [add_comm a b]", "proof_script": "theorem t (a b : Nat) : a + b = b + a := by rw [add_comm a b]", "imports": [], "dependencies": [], "source_hash": "50959668e0de82e8ee3b31f6440d9ebe50481e754bfc54c8ec584ddcf89162df", "environment_hash": "2026-05-26T07:05:35.189413+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2119, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 61, "proof_chars": 61, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "rw_mul_comm", "equation_text": "rw mul comm", "normalized_equation": "comm_mul_rw", "operators": [], "variables": ["mul", "rw", "comm"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : a * b = b * a := by rw [mul_comm]", "proof_script": "theorem t (a b : Nat) : a * b = b * a := by rw [mul_comm]", "imports": [], "dependencies": [], "source_hash": "8dd01b69a6bffa2a232f04205a992f14ba3f79f83a05372e5ea6f4fd59f0b455", "environment_hash": "2026-05-26T07:05:37.878995+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2384, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 57, "proof_chars": 57, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "rw_add_assoc", "equation_text": "rw add assoc", "normalized_equation": "add_assoc_rw", "operators": [], "variables": ["assoc", "add", "rw"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (a b c : Nat) : a + b + c = c + b + a := by rw [add_comm a b, add_comm (a+b) c, add_comm b a]; rfl", "proof_script": "theorem t (a b c : Nat) : a + b + c = c + b + a := by rw [add_comm a b, add_comm (a+b) c, add_comm b a]; rfl", "imports": [], "dependencies": [], "source_hash": "555692a15d74dca0d81ded8b21d2a8a1bb24409e6d4db7366a716b91eb66a73d", "environment_hash": "2026-05-26T07:05:40.267007+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 1938, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 108, "proof_chars": 108, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "with_import_list", "equation_text": "with import list", "normalized_equation": "import_list_with", "operators": [], "variables": ["list", "import", "with"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "import Mathlib.Data.List.Basic\ntheorem t (l : List Nat) : l.reverse.reverse = l := by simp", "proof_script": "theorem t (l : List Nat) : l.reverse.reverse = l := by simp", "imports": ["Mathlib.Data.List.Basic"], "dependencies": ["Mathlib.Data.List.Basic"], "source_hash": "5d583ea6-4968-4b95-9a0a-90db64b7e375", "environment_hash": "2026-05-26T07:06:44.339154+00:00", "status": "timeout", "kernel_checked": false, "returncode": -1, "elapsed_ms": 60000, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 90, "proof_chars": 59, "dependency_count": 1, "import_count": 1, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "with_import_nat", "equation_text": "with import nat", "normalized_equation": "import_nat_with", "operators": [], "variables": ["import", "with", "nat"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "import Mathlib.Data.Nat.Basic\ntheorem t (a b : Nat) : a.gcd b = b.gcd a := Nat.gcd_comm a b", "proof_script": "theorem t (a b : Nat) : a.gcd b = b.gcd a := Nat.gcd_comm a b", "imports": ["Mathlib.Data.Nat.Basic"], "dependencies": ["Mathlib.Data.Nat.Basic"], "source_hash": "028e78b689bcf7872cf3a639298b25238c6e3d2e766df395a0761118745e223b", "environment_hash": "2026-05-26T07:06:57.612502+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 16798, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 91, "proof_chars": 61, "dependency_count": 1, "import_count": 1, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "with_import_int", "equation_text": "with import int", "normalized_equation": "import_int_with", "operators": [], "variables": ["import", "with", "int"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "import Mathlib.Data.Int.Basic\ntheorem t (a b : \u2124) : a + b = b + a := by omega", "proof_script": "theorem t (a b : \u2124) : a + b = b + a := by omega", "imports": ["Mathlib.Data.Int.Basic"], "dependencies": ["Mathlib.Data.Int.Basic"], "source_hash": "eaaabd69e5af6b5e64e1f77dec878e82bbac6bab80a976b1271d3f8ecdebc07e", "environment_hash": "2026-05-26T07:07:05.835735+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 7893, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 77, "proof_chars": 47, "dependency_count": 1, "import_count": 1, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "with_import_set", "equation_text": "with import set", "normalized_equation": "import_set_with", "operators": [], "variables": ["import", "with", "set"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "import Mathlib.Data.Set.Basic\ntheorem t (s : Set Nat) : s \u222a s = s := Set.union_self s", "proof_script": "theorem t (s : Set Nat) : s \u222a s = s := Set.union_self s", "imports": ["Mathlib.Data.Set.Basic"], "dependencies": ["Mathlib.Data.Set.Basic"], "source_hash": "135e40eb-3f0d-494b-bfa1-390d3b216e4e", "environment_hash": "2026-05-26T07:08:09.972964+00:00", "status": "timeout", "kernel_checked": false, "returncode": -1, "elapsed_ms": 60000, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 85, "proof_chars": 55, "dependency_count": 1, "import_count": 1, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "algebra_id", "equation_text": "algebra id", "normalized_equation": "algebra_id", "operators": [], "variables": ["algebra", "id"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (x : Nat) : x * 1 = x := by simp", "proof_script": "theorem t (x : Nat) : x * 1 = x := by simp", "imports": [], "dependencies": [], "source_hash": "649dffcb03e5fc917b53e5c72aaabb454b1d3f554030bb205b7db3d8bec72cbd", "environment_hash": "2026-05-26T07:08:13.461439+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 7056, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 42, "proof_chars": 42, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "algebra_distrib", "equation_text": "algebra distrib", "normalized_equation": "algebra_distrib", "operators": [], "variables": ["algebra", "distrib"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b c : Nat) : a * (b + c) = a * b + a * c := by omega", "proof_script": "theorem t (a b c : Nat) : a * (b + c) = a * b + a * c := by omega", "imports": [], "dependencies": [], "source_hash": "a9ae5c52840e562ace840a72fa7ae8b73a4584e51ba6dbc5d569b745de3f82b3", "environment_hash": "2026-05-26T07:08:16.640999+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2823, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 65, "proof_chars": 65, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "algebra_sq_diff", "equation_text": "algebra sq diff", "normalized_equation": "algebra_diff_sq", "operators": [], "variables": ["algebra", "sq", "diff"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (x y : Nat) : x^2 - y^2 = (x - y) * (x + y) := by omega", "proof_script": "theorem t (x y : Nat) : x^2 - y^2 = (x - y) * (x + y) := by omega", "imports": [], "dependencies": [], "source_hash": "d421b2a324a40e0708fa5bda0ab0ff8635ed3dfc391039008b2998b8d2aaa7a3", "environment_hash": "2026-05-26T07:08:19.425076+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2497, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 65, "proof_chars": 65, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "logic_and", "equation_text": "logic and", "normalized_equation": "and_logic", "operators": [], "variables": ["logic", "and"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (A B : Prop) : A \u2227 B \u2192 A := by intro h; exact h.1", "proof_script": "theorem t (A B : Prop) : A \u2227 B \u2192 A := by intro h; exact h.1", "imports": [], "dependencies": [], "source_hash": "1f3ccaf31a3bebda25e8d91a537fa431529bc85c2f77bc26b01c4b6d6ba5db2c", "environment_hash": "2026-05-26T07:08:22.317543+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2480, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 59, "proof_chars": 59, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "logic_or", "equation_text": "logic or", "normalized_equation": "logic_or", "operators": [], "variables": ["logic", "or"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (A B : Prop) : A \u2228 B \u2192 B \u2228 A := by intro h; cases h; right; exact h; left; exact h", "proof_script": "theorem t (A B : Prop) : A \u2228 B \u2192 B \u2228 A := by intro h; cases h; right; exact h; left; exact h", "imports": [], "dependencies": [], "source_hash": "a2174f6ba40eeff557ca78145ffcc3a367b3682bc7fc41d428b65ddc1739de31", "environment_hash": "2026-05-26T07:08:24.920977+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2313, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 92, "proof_chars": 92, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "logic_not_not", "equation_text": "logic not not", "normalized_equation": "logic_not_not", "operators": [], "variables": ["logic", "not"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 0.9183}, "domain": "unknown", "theorem_statement": "theorem t (P : Prop) : P \u2192 \u00ac\u00acP := by intro hp hnp; exact hnp hp", "proof_script": "theorem t (P : Prop) : P \u2192 \u00ac\u00acP := by intro hp hnp; exact hnp hp", "imports": [], "dependencies": [], "source_hash": "050d95459a1cf9d98b30f3527689dc2f1370651fb27c05ab0542de2941003427", "environment_hash": "2026-05-26T07:08:28.089960+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2869, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 63, "proof_chars": 63, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "logic_impl_trans", "equation_text": "logic impl trans", "normalized_equation": "impl_logic_trans", "operators": [], "variables": ["logic", "trans", "impl"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (A B C : Prop) : (A \u2192 B) \u2192 (B \u2192 C) \u2192 (A \u2192 C) := by intro h1 h2 ha; exact h2 (h1 ha)", "proof_script": "theorem t (A B C : Prop) : (A \u2192 B) \u2192 (B \u2192 C) \u2192 (A \u2192 C) := by intro h1 h2 ha; exact h2 (h1 ha)", "imports": [], "dependencies": [], "source_hash": "68857ebebe49bc03f579829e6ea9f1c338e683cc190f36cc6b78d5fb653a5a46", "environment_hash": "2026-05-26T07:08:30.581772+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2069, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 93, "proof_chars": 93, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "order_refl", "equation_text": "order refl", "normalized_equation": "order_refl", "operators": [], "variables": ["refl", "order"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a : Nat) : a \u2264 a := Nat.le_refl a", "proof_script": "theorem t (a : Nat) : a \u2264 a := Nat.le_refl a", "imports": [], "dependencies": [], "source_hash": "4451970253c55225249e60e79a2c463554d742f0d2f31ab503c742b14b857626", "environment_hash": "2026-05-26T07:08:33.035101+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2074, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 44, "proof_chars": 44, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "order_trans", "equation_text": "order trans", "normalized_equation": "order_trans", "operators": [], "variables": ["trans", "order"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b c : Nat) (h1 : a \u2264 b) (h2 : b \u2264 c) : a \u2264 c := Nat.le_trans h1 h2", "proof_script": "theorem t (a b c : Nat) (h1 : a \u2264 b) (h2 : b \u2264 c) : a \u2264 c := Nat.le_trans h1 h2", "imports": [], "dependencies": [], "source_hash": "eddfed86b40133580f4ee090cf5b3283eee4b49b7696fa9f0f047543455c5866", "environment_hash": "2026-05-26T07:08:35.378814+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 2054, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 79, "proof_chars": 79, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "order_antisymm", "equation_text": "order antisymm", "normalized_equation": "antisymm_order", "operators": [], "variables": ["antisymm", "order"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) (h1 : a \u2264 b) (h2 : b \u2264 a) : a = b := Nat.le_antisymm h1 h2", "proof_script": "theorem t (a b : Nat) (h1 : a \u2264 b) (h2 : b \u2264 a) : a = b := Nat.le_antisymm h1 h2", "imports": [], "dependencies": [], "source_hash": "fc360c68b6c6689532747e1dd5cea507ba19d27554af137ca52406638e8662aa", "environment_hash": "2026-05-26T07:08:37.473978+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 1697, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 80, "proof_chars": 80, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "expect_fail_type_mismatch", "equation_text": "expect fail type mismatch", "normalized_equation": "expect_fail_mismatch_type", "operators": [], "variables": ["fail", "mismatch", "expect", "type"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 7, "depth": 4, "branching_factor": 1, "symbol_entropy": 2.0}, "domain": "unknown", "theorem_statement": "theorem t : Nat \u2192 String := \u03bb n => n", "proof_script": "theorem t : Nat \u2192 String := \u03bb n => n", "imports": [], "dependencies": [], "source_hash": "d2b89c30b2bda98be6007f4f3b2c5be60fdce7f90389881cd90bc6717ccd50fd", "environment_hash": "2026-05-26T07:08:39.503463+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 1638, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 36, "proof_chars": 36, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 4}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "expect_fail_unsat", "equation_text": "expect fail unsat", "normalized_equation": "expect_fail_unsat", "operators": [], "variables": ["fail", "expect", "unsat"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t (x : Nat) : x < x := by omega", "proof_script": "theorem t (x : Nat) : x < x := by omega", "imports": [], "dependencies": [], "source_hash": "33046326f037bf6e04615b517b9e7103947ecb57a39ae8f15720b04f8f49d402", "environment_hash": "2026-05-26T07:08:42.308024+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2464, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 39, "proof_chars": 39, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "expect_fail_axiom", "equation_text": "expect fail axiom", "normalized_equation": "axiom_expect_fail", "operators": [], "variables": ["fail", "axiom", "expect"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 5, "depth": 3, "branching_factor": 1, "symbol_entropy": 1.585}, "domain": "unknown", "theorem_statement": "theorem t : 1 = 0 := by native_decide", "proof_script": "theorem t : 1 = 0 := by native_decide", "imports": [], "dependencies": [], "source_hash": "ce18b9609d303aa9916c645780867424c1180632a645dc5783815d6a7cda471d", "environment_hash": "2026-05-26T07:08:44.806237+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 2076, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 37, "proof_chars": 37, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 3}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "expect_fail_timeout_like", "equation_text": "expect fail timeout like", "normalized_equation": "expect_fail_like_timeout", "operators": [], "variables": ["fail", "timeout", "expect", "like"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 7, "depth": 4, "branching_factor": 1, "symbol_entropy": 2.0}, "domain": "unknown", "theorem_statement": "theorem t (a b : Nat) : a^10 + b^10 = (a+b)^10 := by nlinarith", "proof_script": "theorem t (a b : Nat) : a^10 + b^10 = (a+b)^10 := by nlinarith", "imports": [], "dependencies": [], "source_hash": "c53ad7593bd30250685a22d696f8df307ede2614051b09119c731874e72f32bb", "environment_hash": "2026-05-26T07:08:47.046562+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 1837, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 62, "proof_chars": 62, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 4}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "complex_fib", "equation_text": "complex fib", "normalized_equation": "complex_fib", "operators": [], "variables": ["fib", "complex"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "def fib : Nat \u2192 Nat | 0 => 0 | 1 => 1 | n+2 => fib (n+1) + fib n\ntheorem t (n : Nat) : fib (n+2) = fib (n+1) + fib n := by rfl", "proof_script": "theorem t (n : Nat) : fib (n+2) = fib (n+1) + fib n := by rfl", "imports": [], "dependencies": [], "source_hash": "2948b3fa1252d481d7e0c71e2a99f66c48b34e6b3756b74e08e19de1ae2acd74", "environment_hash": "2026-05-26T07:08:49.068247+00:00", "status": "verified_empty_output", "kernel_checked": true, "returncode": 0, "elapsed_ms": 1737, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 126, "proof_chars": 61, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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{"receipt_version": "rrc-proof-receipt-v2", "theorem_name": "complex_sum", "equation_text": "complex sum", "normalized_equation": "complex_sum", "operators": [], "variables": ["complex", "sum"], "constants": [], "operator_counts": {"adjusted": 0, "overflow": 0, "gate": 0, "offload": 0, "mapping": 0, "projection": 0, "loss": 0}, "ast_metrics": {"node_count": 3, "depth": 2, "branching_factor": 1, "symbol_entropy": 1.0}, "domain": "unknown", "theorem_statement": "theorem t (n : Nat) : \u2211 k in Finset.range n, k = n*(n-1)/2 := by sorry", "proof_script": "theorem t (n : Nat) : \u2211 k in Finset.range n, k = n*(n-1)/2 := by sorry", "imports": [], "dependencies": [], "source_hash": "8dbeb0edbae0dce8f194707e612ebc4de2f3e8439a998bb53c4a2eabe35d1e07", "environment_hash": "2026-05-26T07:08:51.187621+00:00", "status": "failed", "kernel_checked": false, "returncode": 1, "elapsed_ms": 1779, "proof_metrics": {"tactic_count": 2, "dependency_count": 1, "rewrite_count": 2, "simp_count": 4}, "metrics": {"statement_chars": 70, "proof_chars": 70, "dependency_count": 1, "import_count": 0, "tactic_count": 2, "ast_depth_estimate": 2}}
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