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- 24 transition matrices decomposed via power iteration - Verified proofs: rank=4.00 vs Failed: rank=1.25 - Verified density 0.170 vs Failed 0.105 - 7 unique spectral gaps, 7 unique Laplacian zero counts - Features from proof-state transitions, not receipt hashes
24 lines
7.2 KiB
JSON
24 lines
7.2 KiB
JSON
{"name": "apply_chain", "proof_status": "verified", "trace_tags": 6, "unique_states": 6, "matrix_size": 6, "rank": 5, "spectral_gap": -1.434362, "laplacian_zero_count": 6, "density": 0.138889, "eigenvalue_max": 0.900969, "symmetric_eigenvalues": [0.900969], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.236068}
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{"name": "calc_chain", "proof_status": "failed", "trace_tags": 1, "unique_states": 1, "matrix_size": 1, "rank": 0, "spectral_gap": 0.0, "laplacian_zero_count": 1, "density": 0.0, "eigenvalue_max": 0.0, "symmetric_eigenvalues": [0.0], "laplacian_eigenvalues": [0.0], "frobenius_norm": 0.0}
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{"name": "cases_and_elim", "proof_status": "verified", "trace_tags": 6, "unique_states": 6, "matrix_size": 6, "rank": 5, "spectral_gap": -1.434362, "laplacian_zero_count": 6, "density": 0.138889, "eigenvalue_max": 0.900969, "symmetric_eigenvalues": [0.900969], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.236068}
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{"name": "cases_or_swap", "proof_status": "failed", "trace_tags": 7, "unique_states": 7, "matrix_size": 7, "rank": 6, "spectral_gap": -1.752772, "laplacian_zero_count": 7, "density": 0.122449, "eigenvalue_max": 0.920991, "symmetric_eigenvalues": [0.920991], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.44949}
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{"name": "constructor_example", "proof_status": "verified", "trace_tags": 6, "unique_states": 6, "matrix_size": 6, "rank": 5, "spectral_gap": -1.434362, "laplacian_zero_count": 6, "density": 0.138889, "eigenvalue_max": 0.900969, "symmetric_eigenvalues": [0.900969], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.236068}
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{"name": "fail_bad_coercion", "proof_status": "failed", "trace_tags": 2, "unique_states": 2, "matrix_size": 2, "rank": 1, "spectral_gap": 0.05, "laplacian_zero_count": 2, "density": 0.25, "eigenvalue_max": 0.5, "symmetric_eigenvalues": [0.5], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.0}
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{"name": "fail_missing_lemma", "proof_status": "failed", "trace_tags": 1, "unique_states": 1, "matrix_size": 1, "rank": 0, "spectral_gap": 0.0, "laplacian_zero_count": 1, "density": 0.0, "eigenvalue_max": 0.0, "symmetric_eigenvalues": [0.0], "laplacian_eigenvalues": [0.0], "frobenius_norm": 0.0}
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{"name": "fail_type_mismatch", "proof_status": "failed", "trace_tags": 1, "unique_states": 1, "matrix_size": 1, "rank": 0, "spectral_gap": 0.0, "laplacian_zero_count": 1, "density": 0.0, "eigenvalue_max": 0.0, "symmetric_eigenvalues": [0.0], "laplacian_eigenvalues": [0.0], "frobenius_norm": 0.0}
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{"name": "fail_unsat", "proof_status": "failed", "trace_tags": 1, "unique_states": 1, "matrix_size": 1, "rank": 0, "spectral_gap": 0.0, "laplacian_zero_count": 1, "density": 0.0, "eigenvalue_max": 0.0, "symmetric_eigenvalues": [0.0], "laplacian_eigenvalues": [0.0], "frobenius_norm": 0.0}
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{"name": "have_chain", "proof_status": "verified", "trace_tags": 6, "unique_states": 6, "matrix_size": 6, "rank": 5, "spectral_gap": -1.434362, "laplacian_zero_count": 6, "density": 0.138889, "eigenvalue_max": 0.900969, "symmetric_eigenvalues": [0.900969], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.236068}
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{"name": "induct_add_succ", "proof_status": "failed", "trace_tags": 3, "unique_states": 3, "matrix_size": 3, "rank": 2, "spectral_gap": -1.307107, "laplacian_zero_count": 3, "density": 0.222222, "eigenvalue_max": 0.666667, "symmetric_eigenvalues": [0.666667], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.414214}
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{"name": "induct_add_zero", "proof_status": "failed", "trace_tags": 3, "unique_states": 3, "matrix_size": 3, "rank": 2, "spectral_gap": -1.307107, "laplacian_zero_count": 3, "density": 0.222222, "eigenvalue_max": 0.666667, "symmetric_eigenvalues": [0.666667], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.414214}
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{"name": "induct_factorial", "proof_status": "verified", "trace_tags": 2, "unique_states": 2, "matrix_size": 2, "rank": 1, "spectral_gap": 0.05, "laplacian_zero_count": 2, "density": 0.25, "eigenvalue_max": 0.5, "symmetric_eigenvalues": [0.5], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.0}
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{"name": "induct_mul_zero", "proof_status": "failed", "trace_tags": 3, "unique_states": 3, "matrix_size": 3, "rank": 2, "spectral_gap": -1.307107, "laplacian_zero_count": 3, "density": 0.222222, "eigenvalue_max": 0.666667, "symmetric_eigenvalues": [0.666667], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.414214}
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{"name": "intro_all", "proof_status": "verified", "trace_tags": 8, "unique_states": 8, "matrix_size": 8, "rank": 7, "spectral_gap": -1.611768, "laplacian_zero_count": 8, "density": 0.109375, "eigenvalue_max": 0.939693, "symmetric_eigenvalues": [0.939693], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.645751}
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{"name": "intro_apply", "proof_status": "verified", "trace_tags": 8, "unique_states": 8, "matrix_size": 8, "rank": 7, "spectral_gap": -1.611768, "laplacian_zero_count": 8, "density": 0.109375, "eigenvalue_max": 0.939693, "symmetric_eigenvalues": [0.939693], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.645751}
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{"name": "omega_chain_ineq", "proof_status": "verified", "trace_tags": 2, "unique_states": 2, "matrix_size": 2, "rank": 1, "spectral_gap": 0.05, "laplacian_zero_count": 2, "density": 0.25, "eigenvalue_max": 0.5, "symmetric_eigenvalues": [0.5], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.0}
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{"name": "omega_chain_unsat", "proof_status": "failed", "trace_tags": 1, "unique_states": 1, "matrix_size": 1, "rank": 0, "spectral_gap": 0.0, "laplacian_zero_count": 1, "density": 0.0, "eigenvalue_max": 0.0, "symmetric_eigenvalues": [0.0], "laplacian_eigenvalues": [0.0], "frobenius_norm": 0.0}
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{"name": "omega_distrib", "proof_status": "failed", "trace_tags": 1, "unique_states": 1, "matrix_size": 1, "rank": 0, "spectral_gap": 0.0, "laplacian_zero_count": 1, "density": 0.0, "eigenvalue_max": 0.0, "symmetric_eigenvalues": [0.0], "laplacian_eigenvalues": [0.0], "frobenius_norm": 0.0}
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{"name": "omega_reorder_sum", "proof_status": "verified", "trace_tags": 2, "unique_states": 2, "matrix_size": 2, "rank": 1, "spectral_gap": 0.05, "laplacian_zero_count": 2, "density": 0.25, "eigenvalue_max": 0.5, "symmetric_eigenvalues": [0.5], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.0}
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{"name": "rw_chain_3step", "proof_status": "verified", "trace_tags": 6, "unique_states": 6, "matrix_size": 6, "rank": 5, "spectral_gap": -1.434362, "laplacian_zero_count": 6, "density": 0.138889, "eigenvalue_max": 0.900969, "symmetric_eigenvalues": [0.900969], "laplacian_eigenvalues": [0.0], "frobenius_norm": 2.236068}
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{"name": "rw_chain_eq", "proof_status": "verified", "trace_tags": 4, "unique_states": 4, "matrix_size": 4, "rank": 3, "spectral_gap": -1.037132, "laplacian_zero_count": 4, "density": 0.1875, "eigenvalue_max": 0.809017, "symmetric_eigenvalues": [0.809017], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.732051}
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{"name": "rw_chain_mixed", "proof_status": "verified", "trace_tags": 4, "unique_states": 4, "matrix_size": 4, "rank": 3, "spectral_gap": -1.037132, "laplacian_zero_count": 4, "density": 0.1875, "eigenvalue_max": 0.809017, "symmetric_eigenvalues": [0.809017], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.732051}
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{"name": "rw_then_omega", "proof_status": "failed", "trace_tags": 3, "unique_states": 3, "matrix_size": 3, "rank": 2, "spectral_gap": -1.307107, "laplacian_zero_count": 3, "density": 0.222222, "eigenvalue_max": 0.666667, "symmetric_eigenvalues": [0.666667], "laplacian_eigenvalues": [0.0], "frobenius_norm": 1.414214}
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