TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/hodge_complement_20261028/result.json
Original file SHA-256: 811d82cbc63efee9551887ba3ddecb70c7330934d322069ae19f10de25025062
Inclusive original lines: 1-200
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000001 | {
000002 |   "checks": 4833,
000003 |   "full_clifford_fock_comparison": {
000004 |     "annihilation_output_dimension": 5,
000005 |     "antipodal_quotient": "Clebsch SRG(16,5,0,2), the already checked v810 object",
000006 |     "conditioned_creation_after_complement": "five Hodge channel",
000007 |     "full_fock_channel": "(1/5) sum_m [Ad(a_m)+Ad(a_m^dagger)]",
000008 |     "grade2_annihilation_probability": "2/5",
000009 |     "grade2_creation_probability": "3/5",
000010 |     "old_stay_identification": false,
000011 |     "population": "Q5/5 on 32 subset states"
000012 |   },
000013 |   "hodge_channel": {
000014 |     "C_m_square": "projector onto pairs not containing m",
000015 |     "choi_rank": 5,
000016 |     "choi_spectrum": {
000017 |       "0": 95,
000018 |       "2": 5
000019 |     },
000020 |     "covariance": "Phi(conj(Lambda2 U) rho conj(Lambda2 U)^dagger)=Lambda2 U Phi(rho) Lambda2 U^dagger for U in SU(5)",
000021 |     "dimension": 10,
000022 |     "effect_sum": "sum C_m^dagger C_m=3 I_10",
000023 |     "hilbert_schmidt_self_adjoint": true,
000024 |     "kraus_operators": "K_m=C_m/sqrt(3), m=0,...,4",
000025 |     "kraus_ranks": [
000026 |       6,
000027 |       6,
000028 |       6,
000029 |       6,
000030 |       6
000031 |     ],
000032 |     "population": "A_Petersen/3",
000033 |     "sl5_infinitesimal_generators_checked": 24,
000034 |     "space": "Lambda^2 C^5",
000035 |     "su5_sectors": {
000036 |       "Phi_sixth_spectrum": {
000037 |         "1": 1,
000038 |         "1/729": 75,
000039 |         "64/729": 24
000040 |       },
000041 |       "Phi_squared": "Pi_1+(4/9)Pi_24+(1/9)Pi_75",
000042 |       "adjoint_identification": "24=dGamma(sl5), with Phi(A)=-(2/3) A^T",
000043 |       "endomorphism_decomposition": "End(Lambda^2 C^5)=1+24+75",
000044 |       "radial_population_shells": [
000045 |         1,
000046 |         3,
000047 |         6
000048 |       ],
000049 |       "radial_population_transfer": "(1/3)*[[0,1,0],[3,0,1],[0,2,2]] in shell-mass column convention",
000050 |       "radial_spectrum": [
000051 |         "1",
000052 |         "1/3",
000053 |         "-2/3"
000054 |       ],
000055 |       "seventy_five_identification": "orthogonal complement of identity plus dGamma(sl5)"
000056 |     },
000057 |     "superoperator_rank": 100,
000058 |     "superoperator_spectrum": {
000059 |       "-1/3": 35,
000060 |       "-2/3": 14,
000061 |       "1": 1,
000062 |       "1/3": 40,
000063 |       "2/3": 10
000064 |     },
000065 |     "trace_preserving": true,
000066 |     "unital": true
000067 |   },
000068 |   "old_J20_comparisons": [
000069 |     {
000070 |       "common_edge_flux": "nontrivial: none of 4^5 baseline choices and 2^5 class signs admits one common diagonal gauge",
000071 |       "common_ten_label_gauge_solutions": 0,
000072 |       "conditional_channel_factorization": "old block = outcome-conditioned Klein phase twirl after one Hodge outcome",
000073 |       "full_channel_equal": false,
000074 |       "group_choi_ranks": [
000075 |         3,
000076 |         3,
000077 |         3,
000078 |         3,
000079 |         3
000080 |       ],
000081 |       "group_effects": "P_m/3 after normalization",
000082 |       "group_sizes": [
000083 |         4,
000084 |         4,
000085 |         4,
000086 |         4,
000087 |         4
000088 |       ],
000089 |       "individual_baseline_two_cycle_flux": "trivial and removable with an m-conditioned diagonal gauge",
000090 |       "intersecting_coherence_witnesses": 60,
000091 |       "mark": 0,
000092 |       "old_choi_rank": 15,
000093 |       "old_hilbert_schmidt_self_adjoint": true,
000094 |       "old_nonzero_choi_eigenvalue": "2/3 (multiplicity 15)",
000095 |       "old_superoperator_rank": 40,
000096 |       "old_superoperator_spectrum_scaled_by_12": {
000097 |         "-4": 15,
000098 |         "-8": 4,
000099 |         "0": 60,
000100 |         "12": 1,
000101 |         "4": 20
000102 |       },
000103 |       "old_trace_preserving": true,
000104 |       "old_unital": true,
000105 |       "phase_factorization": "R_l=D_l C_m on P_m",
000106 |       "population_equal": true,
000107 |       "relative_phase_group": "Klein four projectively; three characters each with multiplicity two"
000108 |     },
000109 |     {
000110 |       "common_edge_flux": "nontrivial: none of 4^5 baseline choices and 2^5 class signs admits one common diagonal gauge",
000111 |       "common_ten_label_gauge_solutions": 0,
000112 |       "conditional_channel_factorization": "old block = outcome-conditioned Klein phase twirl after one Hodge outcome",
000113 |       "full_channel_equal": false,
000114 |       "group_choi_ranks": [
000115 |         3,
000116 |         3,
000117 |         3,
000118 |         3,
000119 |         3
000120 |       ],
000121 |       "group_effects": "P_m/3 after normalization",
000122 |       "group_sizes": [
000123 |         4,
000124 |         4,
000125 |         4,
000126 |         4,
000127 |         4
000128 |       ],
000129 |       "individual_baseline_two_cycle_flux": "trivial and removable with an m-conditioned diagonal gauge",
000130 |       "intersecting_coherence_witnesses": 60,
000131 |       "mark": 1,
000132 |       "old_choi_rank": 15,
000133 |       "old_hilbert_schmidt_self_adjoint": true,
000134 |       "old_nonzero_choi_eigenvalue": "2/3 (multiplicity 15)",
000135 |       "old_superoperator_rank": 40,
000136 |       "old_superoperator_spectrum_scaled_by_12": {
000137 |         "-4": 15,
000138 |         "-8": 4,
000139 |         "0": 60,
000140 |         "12": 1,
000141 |         "4": 20
000142 |       },
000143 |       "old_trace_preserving": true,
000144 |       "old_unital": true,
000145 |       "phase_factorization": "R_l=D_l C_m on P_m",
000146 |       "population_equal": true,
000147 |       "relative_phase_group": "Klein four projectively; three characters each with multiplicity two"
000148 |     },
000149 |     {
000150 |       "common_edge_flux": "nontrivial: none of 4^5 baseline choices and 2^5 class signs admits one common diagonal gauge",
000151 |       "common_ten_label_gauge_solutions": 0,
000152 |       "conditional_channel_factorization": "old block = outcome-conditioned Klein phase twirl after one Hodge outcome",
000153 |       "full_channel_equal": false,
000154 |       "group_choi_ranks": [
000155 |         3,
000156 |         3,
000157 |         3,
000158 |         3,
000159 |         3
000160 |       ],
000161 |       "group_effects": "P_m/3 after normalization",
000162 |       "group_sizes": [
000163 |         4,
000164 |         4,
000165 |         4,
000166 |         4,
000167 |         4
000168 |       ],
000169 |       "individual_baseline_two_cycle_flux": "trivial and removable with an m-conditioned diagonal gauge",
000170 |       "intersecting_coherence_witnesses": 60,
000171 |       "mark": 2,
000172 |       "old_choi_rank": 15,
000173 |       "old_hilbert_schmidt_self_adjoint": true,
000174 |       "old_nonzero_choi_eigenvalue": "2/3 (multiplicity 15)",
000175 |       "old_superoperator_rank": 40,
000176 |       "old_superoperator_spectrum_scaled_by_12": {
000177 |         "-4": 15,
000178 |         "-8": 4,
000179 |         "0": 60,
000180 |         "12": 1,
000181 |         "4": 20
000182 |       },
000183 |       "old_trace_preserving": true,
000184 |       "old_unital": true,
000185 |       "phase_factorization": "R_l=D_l C_m on P_m",
000186 |       "population_equal": true,
000187 |       "relative_phase_group": "Klein four projectively; three characters each with multiplicity two"
000188 |     },
000189 |     {
000190 |       "common_edge_flux": "nontrivial: none of 4^5 baseline choices and 2^5 class signs admits one common diagonal gauge",
000191 |       "common_ten_label_gauge_solutions": 0,
000192 |       "conditional_channel_factorization": "old block = outcome-conditioned Klein phase twirl after one Hodge outcome",
000193 |       "full_channel_equal": false,
000194 |       "group_choi_ranks": [
000195 |         3,
000196 |         3,
000197 |         3,
000198 |         3,
000199 |         3
000200 |       ],