{
  "timestamp": "20260914T141742_398689Z",
  "scope": "Spatial depth controls, signed canonical states and the bottom two-band constraint.\n\nThe ambient Clifford representation is reduced to one chirality for odd\nsurface dimension. This keeps the actual intrinsic spinor rank, including\nrank one on the circle, without adding physical spatial coordinates.\n",
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    {
      "name": "full canonical eigenstate d4,beta4.5,gamma20.0",
      "error": 1.4516938270141457e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta4.5,gamma20.0",
      "error": 2.6645352591003757e-15,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta4.5,gamma200.0",
      "error": 3.892899908373812e-18,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta4.5,gamma200.0",
      "error": 2.3812063432160357e-12,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta4.5,gamma10000.0",
      "error": 4.0340389815351035e-23,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-4.5,gamma20.0",
      "error": 1.4521324537210857e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta-4.5,gamma20.0",
      "error": 7.105427357601002e-15,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-4.5,gamma200.0",
      "error": 1.6920747479217695e-18,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta-4.5,gamma200.0",
      "error": 1.4266365866433262e-12,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-4.5,gamma10000.0",
      "error": 4.034038981535104e-23,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "equal frequency for both surface signs d4,up",
      "error": 0.0,
      "tolerance": 3e-13,
      "passed": true
    },
    {
      "name": "full product parity d4,up",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta21.5,gamma20.0",
      "error": 3.720018264577254e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta21.5,gamma20.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta21.5,gamma200.0",
      "error": 1.7328576839899412e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta21.5,gamma200.0",
      "error": 5.0182080713057076e-14,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta21.5,gamma10000.0",
      "error": 7.600798772354549e-20,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-21.5,gamma20.0",
      "error": 6.006583054929787e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta-21.5,gamma20.0",
      "error": 6.661338147750939e-16,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-21.5,gamma200.0",
      "error": 5.77210849287112e-18,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta-21.5,gamma200.0",
      "error": 4.6407322429331543e-14,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-21.5,gamma10000.0",
      "error": 7.600798772354548e-20,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "equal frequency for both surface signs d4,charm",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-13,
      "passed": true
    },
    {
      "name": "full product parity d4,charm",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta73.5,gamma20.0",
      "error": 6.41247409370527e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta73.5,gamma20.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta73.5,gamma200.0",
      "error": 3.3551454935018077e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta73.5,gamma200.0",
      "error": 2.220446049250313e-15,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta73.5,gamma10000.0",
      "error": 6.650302594947684e-19,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-73.5,gamma20.0",
      "error": 4.6118189994861376e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta-73.5,gamma20.0",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-73.5,gamma200.0",
      "error": 4.4401835537897344e-17,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "independent singular value d4,beta-73.5,gamma200.0",
      "error": 4.440892098500626e-16,
      "tolerance": 3e-09,
      "passed": true
    },
    {
      "name": "full canonical eigenstate d4,beta-73.5,gamma10000.0",
      "error": 6.650302594930851e-19,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "equal frequency for both surface signs d4,top",
      "error": 3.3306690738754696e-16,
      "tolerance": 3e-13,
      "passed": true
    },
    {
      "name": "full product parity d4,top",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "mixed diagonal phase control d4,beta0.23",
      "error": 7.927034243810861e-18,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "mixed diagonal phase control d4,beta0.83",
      "error": 2.078364307032313e-18,
      "tolerance": 2e-13,
      "passed": true
    },
    {
      "name": "exact bottom Hermitian mixing determinant",
      "error": 0.0,
      "tolerance": 0.5,
      "passed": true
    },
    {
      "name": "constant normal deformation has zero cross-surface matrix",
      "error": 1.2412670766236366e-16,
      "tolerance": 1e-14,
      "passed": true
    },
    {
      "name": "first surface harmonic retains the adjacent grade",
      "error": 1.3877787807814457e-17,
      "tolerance": 1e-14,
      "passed": true
    },
    {
      "name": "odd-depth signed response reversal down",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm down,weight0.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force down,weight0.0,phase0.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm down,weight0.2,phase0.37",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force down,weight0.2,phase0.37",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm down,weight0.5,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force down,weight0.5,phase0.0",
      "error": 8.137025119188923e-19,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm down,weight0.5,phase1.3",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force down,weight0.5,phase1.3",
      "error": 7.193279787233756e-18,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm down,weight1.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force down,weight1.0,phase0.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "odd-depth signed response reversal strange",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm strange,weight0.0,phase0.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force strange,weight0.0,phase0.0",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm strange,weight0.2,phase0.37",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force strange,weight0.2,phase0.37",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm strange,weight0.5,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force strange,weight0.5,phase0.0",
      "error": 3.302562551226203e-18,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm strange,weight0.5,phase1.3",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force strange,weight0.5,phase1.3",
      "error": 5.5605104393866406e-18,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm strange,weight1.0,phase0.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force strange,weight1.0,phase0.0",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "odd-depth signed response reversal bottom lower component",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom lower component,weight0.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom lower component,weight0.0,phase0.0",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom lower component,weight0.2,phase0.37",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom lower component,weight0.2,phase0.37",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom lower component,weight0.5,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom lower component,weight0.5,phase0.0",
      "error": 1.6625164664065211e-18,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom lower component,weight0.5,phase1.3",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom lower component,weight0.5,phase1.3",
      "error": 8.544704396675732e-19,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom lower component,weight1.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom lower component,weight1.0,phase0.0",
      "error": 2.220446049250313e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "odd-depth signed response reversal bottom upper component",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom upper component,weight0.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom upper component,weight0.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom upper component,weight0.2,phase0.37",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom upper component,weight0.2,phase0.37",
      "error": 1.1102230246251565e-16,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom upper component,weight0.5,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom upper component,weight0.5,phase0.0",
      "error": 7.92124969893433e-17,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom upper component,weight0.5,phase1.3",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom upper component,weight0.5,phase1.3",
      "error": 7.538145002360283e-17,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "full two-branch circle norm bottom upper component,weight1.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    },
    {
      "name": "polarized two-branch force bottom upper component,weight1.0,phase0.0",
      "error": 0.0,
      "tolerance": 3e-11,
      "passed": true
    }
  ],
  "results": [
    {
      "depth": 3,
      "surface_dimension": 1,
      "intrinsic_spinor_rank": 1,
      "chirality": -1,
      "unconnected_gap_bound": 1.1892269164304694
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    {
      "depth": 3,
      "surface_dimension": 1,
      "intrinsic_spinor_rank": 1,
      "chirality": 1,
      "unconnected_gap_bound": 1.1892269164304694
    },
    {
      "depth": 4,
      "surface_dimension": 2,
      "intrinsic_spinor_rank": 2,
      "chirality": 1,
      "unconnected_gap_bound": 1.1767450530442147
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    {
      "depth": 5,
      "surface_dimension": 3,
      "intrinsic_spinor_rank": 2,
      "chirality": -1,
      "unconnected_gap_bound": 1.1634957607189742
    },
    {
      "depth": 5,
      "surface_dimension": 3,
      "intrinsic_spinor_rank": 2,
      "chirality": 1,
      "unconnected_gap_bound": 1.1634957607189742
    },
    {
      "depth": 6,
      "surface_dimension": 4,
      "intrinsic_spinor_rank": 4,
      "chirality": 1,
      "unconnected_gap_bound": 1.1514889015006735
    },
    {
      "depth": 10,
      "surface_dimension": 8,
      "intrinsic_spinor_rank": 16,
      "chirality": 1,
      "unconnected_gap_bound": 1.1167032732739914
    },
    {
      "bottom_counts": [
        816,
        969
      ],
      "geometric_mean": 889.2153844822974,
      "difference_frequency": 153,
      "mean_carrier_frequency": 892.5,
      "full_positive_two_branch_mixing_excludes_geometric_mean": true
    },
    {
      "bottom_first_surface_harmonic_vertex": -1647.1047471159789,
      "constant_surface_vertex": 0.0,
      "hopping": 10000.0,
      "scope": "Linear geometric perturbation; the occupied joint shape is unresolved."
    },
    {
      "depth": 3,
      "label": "down",
      "positive_branch_weight": 0.0,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 3294.2306406457506,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "down",
      "positive_branch_weight": 0.2,
      "relative_phase": 0.37,
      "canonical_norm": 0.9999999999999999,
      "full_two_branch_shape_force": 1976.5383843874506,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "down",
      "positive_branch_weight": 0.5,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": -2.6805237471336295e-15,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "down",
      "positive_branch_weight": 0.5,
      "relative_phase": 1.3,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": -2.3696322681843185e-14,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "down",
      "positive_branch_weight": 1.0,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": -3294.2306406457506,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "strange",
      "positive_branch_weight": 0.0,
      "relative_phase": 0.0,
      "canonical_norm": 0.9999999999999999,
      "full_two_branch_shape_force": 3294.229172630264,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "strange",
      "positive_branch_weight": 0.2,
      "relative_phase": 0.37,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 1976.537503578158,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "strange",
      "positive_branch_weight": 0.5,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 1.0879397900685588e-14,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "strange",
      "positive_branch_weight": 0.5,
      "relative_phase": 1.3,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 1.8317595704142597e-14,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "strange",
      "positive_branch_weight": 1.0,
      "relative_phase": 0.0,
      "canonical_norm": 0.9999999999999999,
      "full_two_branch_shape_force": -3294.229172630264,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom lower component",
      "positive_branch_weight": 0.0,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 3294.210717578423,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom lower component",
      "positive_branch_weight": 0.2,
      "relative_phase": 0.37,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 1976.5264305470532,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom lower component",
      "positive_branch_weight": 0.5,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 5.476679561786969e-15,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom lower component",
      "positive_branch_weight": 0.5,
      "relative_phase": 1.3,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 2.8148056802068666e-15,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom lower component",
      "positive_branch_weight": 1.0,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": -3294.210717578423,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom upper component",
      "positive_branch_weight": 0.0,
      "relative_phase": 0.0,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 3294.2082708859452,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
      "depth": 3,
      "label": "bottom upper component",
      "positive_branch_weight": 0.2,
      "relative_phase": 0.37,
      "canonical_norm": 1.0,
      "full_two_branch_shape_force": 1976.5249625315669,
      "scope": "This shape channel only; balanced cancellation is not general decoupling."
    },
    {
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