bell-algebra-without-bell-violation-ising-kitaev/p5b_m0_targets.json at main · berkay-yueksel-sayim/bell-algebra-without-bell-violation-ising-kitaev · GitHub

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{
  "milestone": "M0-NUMERIC — four locked Bell-algebra targets on the Kitaev-honeycomb fusion qubit",
  "verdict": "GO",
  "provenance": {
    "script": "p5b_cbell_m0_reproduction.py",
    "note": "independent reproduction: mirrored Jordan-Wigner ordering (opposite of the original construction), NOT importing any files from the original construction; own numpy from scratch",
    "date": "2026-06-25 (original independent reproduction); re-run 2026-07-13 for this deposit, identical to machine precision"
  },
  "targets": {
    "P1_ZA_XA_commutator_norm": 2.0,
    "P1_ideal": 2,
    "P2_cross_party_commutator_norm": 0.0,
    "P2_ideal": 0,
    "S_CHSH_ideal_bell_state": 2.828427,
    "S_ideal": 2.8284271247461903,
    "K_commuting_only_control": 1.414214,
    "K_bound": 2
  },
  "adversarial_checks": {
    "chsh_operator_norm": 2.828427,
    "chsh_operator_note": "Tsirelson cap; S can never exceed this on any state",
    "no_third_majorana_max_S": 1.414214,
    "no_third_majorana_note": "falsifiability control: without the 3rd Majorana the 2nd setting commutes with Z_A, so max|S| stays <=2 (1D-trap collapse)",
    "XA_is_static_observable_not_braid": true,
    "bell_state_schmidt": [
      0.7071067811865476,
      0.7071067811865476,
      0.0,
      0.0
    ],
    "entanglement_entropy_bits": 1.0
  },
  "superselection": {
    "Ptot_expectation": 1.0,
    "psi_is_Ptot_eigenstate": true,
    "sector_weight_plus1": 1.0,
    "S_in_plus1_sector": 2.828427,
    "note": "no SSR reduction: Bell state has unit weight in its own parity sector, so the physical parity projection acts as identity on it"
  },
  "algebra_representation_independence": {
    "method": "combinatorial set-overlap rule (-1)^(|S||T|-|S intersect T|) checked against explicit matrix representation",
    "all_sampled_pairs_agree": true
  },
  "lattice_realization": {
    "source": "original construction scripts m0_numeric.py and m3b_kitaev_realspace.py (reproduced for this deposit as p5b_cbell_m5_lattice_sweep.py dependency p5b_m3b_kitaev_realspace.py)",
    "lattice_size": [
      28,
      16
    ],
    "n_vortices": 8,
    "gram_error": 2.2e-14,
    "alice_mode_left_weight_pct": 91.7,
    "footprint_leak_point_value_pct": 8.3,
    "split_over_gap_pct": 7.3,
    "finite_size_leak_series_pct": [
      17.01,
      10.176,
      2.301
    ],
    "finite_size_lattice_L1_series": [
      24,
      32,
      44
    ],
    "bulk_gap_range": [
      0.75,
      0.8
    ],
    "note": "leak series confirms P2 -> 0 exactly as L -> infinity; not a from-scratch re-derivation of the Kitaev honeycomb solution, but an independently cross-checked instantiation of the M0 algebra on it"
  }
}