{
  "status": "complete",
  "dimension": 2,
  "slots": 4,
  "butterfly_coin_bits": 4,
  "independent_palindrome_coin_strings": 256,
  "full_group_size": 24,
  "palindrome_support": 24,
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      "permutation": [
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        2,
        3
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      "mass": "1/16",
      "coin_strings": 16
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    {
      "permutation": [
        0,
        1,
        3,
        2
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      "mass": "1/32",
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    {
      "permutation": [
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      "mass": "1/32",
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    {
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    {
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    {
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    {
      "permutation": [
        1,
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        3,
        0
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    {
      "permutation": [
        1,
        3,
        0,
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      "mass": "1/32",
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    {
      "permutation": [
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        0
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    {
      "permutation": [
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    {
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    {
      "permutation": [
        2,
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    {
      "permutation": [
        2,
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        0
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    {
      "permutation": [
        2,
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    {
      "permutation": [
        2,
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    {
      "permutation": [
        3,
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        1,
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    {
      "permutation": [
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    {
      "permutation": [
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        0,
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    {
      "permutation": [
        3,
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    {
      "permutation": [
        3,
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        0,
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    {
      "permutation": [
        3,
        2,
        1,
        0
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      "mass": "1/16",
      "coin_strings": 16
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  ],
  "palindrome_total_variation": "1/6",
  "explicit_minorant": {
    "exponent": 0,
    "mass": "3/4",
    "uniform_floor": "1/32",
    "gap_formula": "1 - mass/(2*2^exponent)",
    "off_invariants_bound": "5/8"
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        1
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        0
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        1
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        0
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    ],
    "symmetric": true,
    "scaled_projection_identity_verified": true,
    "identity_coefficient": "1/4",
    "exact_nonconstant_norm": "1/4",
    "scaled_projection_rank": "2",
    "nonzero_eigenvector": [
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    "eigenvector_verified": true,
    "justification": "A symmetric nonzero B with B^2=cB has eigenvalues 0,c, so its norm is c. The displayed nonzero eigenvector attains c. Zero B has norm zero."
  },
  "physical_sweep_nonconstant_norm_squared": "1/4",
  "finite_source_target_calibration": {
    "exact_operator_bound": {
      "sweeps": 13,
      "total_variation_upper_bound_squared": "23/268435456",
      "source_target_squared": "1/4194304",
      "previous_bound_squared": "23/67108864"
    },
    "explicit_minorant_bound": {
      "sweeps": 37,
      "total_variation_upper_bound_squared": "1673470251262187957763671875/10384593717069655257060992658440192",
      "source_target_squared": "1/4194304",
      "previous_bound_squared": "334694050252437591552734375/1298074214633706907132624082305024"
    },
    "squared_TV_bound_formula": "((n! - 1)/4) * (sweep_nonconstant_norm_squared)^v",
    "scope": "Conservative regular L2-to-TV bound at these two/four slots only; not optimal mixing, the source-selected Classical.choose witness or any universal all-size schedule"
  },
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "source_proof_verification": "not_run",
  "formal_program_verification": "not_run",
  "arithmetic": "exact Python integer/Fraction; no floating eigensolver",
  "interpretation": "Finite independent enumeration and explicit rational witness. Assumes independent fair switches in the mathematical law; certifies no OS or seeded randomness backend. Selected source identities connect physical sweep adjoint to butterfly/palindrome, but their imports/proofs were not executed or independently accepted."
}