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      "31": "-7978937871483813341730985762128168246321915609183673570790460859995587084288/3"
    }
  },
  "references": {
    "secant": {
      "id": "A000364",
      "offset": 0,
      "url": "https://oeis.org/A000364/b000364.txt",
      "checked": "2026-10-29"
    },
    "quartic": {
      "id": "A211212",
      "offset": 0,
      "url": "https://oeis.org/A211212",
      "checked": "2026-10-29"
    }
  },
  "bounds": {
    "reciprocal_spacing": [
      2,
      6
    ],
    "reciprocal_index": [
      0,
      10
    ],
    "reciprocal_parameters": [
      "-2",
      "-1",
      "0",
      "1/2",
      "1",
      "2",
      "3"
    ],
    "addition_spacing": [
      2,
      6
    ],
    "addition_index": [
      0,
      8
    ],
    "quartic_bridge_secant_index": [
      0,
      40
    ],
    "quartic_packet_index": [
      0,
      11
    ],
    "permutation_dp_spacing": [
      2,
      6
    ],
    "permutation_dp_block_count": [
      0,
      8
    ],
    "enumeration_cases": [
      [
        2,
        0
      ],
      [
        2,
        4
      ],
      [
        2,
        6
      ],
      [
        2,
        8
      ],
      [
        4,
        4
      ],
      [
        4,
        8
      ]
    ],
    "euler_polynomial_degree": [
      0,
      12
    ],
    "newton_precision": 32,
    "alternating_power_lengths": [
      0,
      1,
      2,
      3,
      5,
      6
    ],
    "alternating_power_starts": [
      "-1/2",
      "0",
      "1",
      "3/2"
    ],
    "local_charts": [
      1,
      2,
      3,
      5,
      7,
      9
    ],
    "local_even_degree": [
      0,
      20
    ],
    "dyadic_sharp_depth": [
      0,
      9
    ],
    "bernoulli_degree": [
      0,
      20
    ],
    "local_matrix_size": 12,
    "packet_block_size": 6,
    "pascal_matrix_size": 12,
    "sampling_matrix_spacings": [
      1,
      3
    ],
    "sampling_matrix_orders": [
      0,
      3
    ],
    "base_change_charts": [
      2,
      3,
      5,
      7
    ],
    "base_change_matrix_size": 8,
    "base_change_all_triples": true,
    "congruential_family_spacing": [
      1,
      6
    ],
    "congruential_addresses": "every 0<=j<N",
    "congruential_index": [
      0,
      8
    ],
    "fibonacci_polynomial_degree": [
      0,
      12
    ],
    "fibonacci_sequence_length": 16,
    "fibonacci_companion_power": [
      0,
      12
    ],
    "fibonacci_state_index": [
      0,
      14
    ],
    "literature_packet_step": [
      0,
      12
    ],
    "literature_packet_address": [
      0,
      5
    ],
    "literature_packet_index": [
      0,
      8
    ],
    "literature_dyadic_refinement": [
      0,
      4
    ],
    "literature_difference_base": [
      0,
      6
    ],
    "literature_difference_order": [
      0,
      5
    ],
    "literature_binomial_address": [
      0,
      3
    ],
    "literature_binomial_index": [
      0,
      6
    ],
    "literature_calculus_degree": [
      0,
      8
    ],
    "quartic_exact_index": [
      0,
      47
    ],
    "quartic_difference_base": [
      0,
      6
    ],
    "quartic_difference_step": [
      1,
      8
    ],
    "quartic_difference_order": [
      0,
      5
    ],
    "quartic_displacement_base": [
      0,
      8
    ],
    "quartic_displacement_step": [
      1,
      16
    ],
    "quartic_modular_index": [
      0,
      255
    ],
    "quartic_modulus": 8192,
    "residue_permutation_bits": [
      1,
      8
    ],
    "isometry_pair_indices": [
      0,
      31
    ],
    "period_precision": [
      0,
      8
    ],
    "inverse_bits": 6,
    "mode_primes": [
      3,
      5,
      7
    ],
    "mode_full_degree": [
      0,
      24
    ],
    "stirling_degree": 16,
    "log_derivative_input_degree": 17,
    "edge_small_r": [
      1,
      8
    ],
    "edge_small_x": [
      0,
      8
    ],
    "edge_large_r": [
      15,
      31,
      63
    ],
    "edge_large_x": [
      0,
      6
    ],
    "edge_max_full_degree": 138,
    "edge_carry_r": [
      1,
      255
    ],
    "edge_carry_q": [
      0,
      256
    ],
    "difference_spacing": [
      1,
      5
    ],
    "difference_offsets": "all 0 <= s < M",
    "difference_order": [
      0,
      5
    ],
    "composition_spacings": [
      1,
      4
    ],
    "composition_offsets": "all admitted offsets",
    "composition_order": [
      0,
      3
    ],
    "primes": [
      2,
      3,
      5,
      7,
      11
    ]
  },
  "non_claims": [
    "No novelty or exclusive-method claim.",
    "Finite computations are separate from the written universal algebraic proofs.",
    "No numerical error bound, asymptotic law or complexity advantage is established.",
    "No Lean execution. The local truncation theorems are proved separately; finite checks do not certify broader Euler congruences."
  ]
}
