TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ALLMODE-COLLECTIVE-TIME-SOURCE.json
Original file SHA-256: 5b03e3ad72404101a2eae74da923ff50c0e24e5a3bed2549f3c16f8569e1ddcd
Inclusive original lines: 1-170
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 |   "result_id": "R079",
000003 |   "all_passed": true,
000004 |   "checks": {
000005 |     "native_full96_builder_reduces_to_nonredundant_quark36": true,
000006 |     "native_higgs_background_is_actual_radial_derivative": true,
000007 |     "native_forces_Hermitian_and_odd": true,
000008 |     "whole_four_direction_trace_norm_is_3Aq": true,
000009 |     "native_h_squared_0.25": true,
000010 |     "native_positive_energy_covariance_is_positive_0.25": true,
000011 |     "native_h_squared_-0.75": true,
000012 |     "native_positive_energy_covariance_is_positive_-0.75": true,
000013 |     "native_h_squared_4.25": true,
000014 |     "native_positive_energy_covariance_is_positive_4.25": true,
000015 |     "native_full36_radial_time_matches_exact_singular_blocks_0.25": true,
000016 |     "native_full36_radial_smearing_matches_exact_singular_blocks_0.25": true,
000017 |     "native_full36_radial_time_matches_exact_singular_blocks_-0.75": true,
000018 |     "native_full36_radial_smearing_matches_exact_singular_blocks_-0.75": true,
000019 |     "native_full36_radial_time_matches_exact_singular_blocks_4.25": true,
000020 |     "native_full36_radial_smearing_matches_exact_singular_blocks_4.25": true,
000021 |     "all_four_ordered_native_characteristic_approaches_proved_Gaussian": true,
000022 |     "all_four_ordered_covariance_approaches_proved_isotropic_limit": true,
000023 |     "pointwise_radial_variance_retains_nonzero_limit": true,
000024 |     "fixed_nonresonant_time_covariance_decays": true,
000025 |     "unscaled_smeared_variance_converges_nonzero": true,
000026 |     "CLT_scaled_fixed_smearing_vanishes": true,
000027 |     "whole_four_component_two_test_function_ordered_product_converges": true,
000028 |     "whole_smeared_ordered_source_is_nontrivial": true,
000029 |     "native_full36_cumulants_match_exact_singular_pairs_0.25": true,
000030 |     "native_full36_cumulants_match_exact_singular_pairs_-0.75": true,
000031 |     "native_full36_cumulants_match_exact_singular_pairs_4.25": true,
000032 |     "independent_small_Fock_checks_second_third_fourth_cumulants": true,
000033 |     "whole_radial_variance_agrees_with_convergent_smearing_sum": true,
000034 |     "actual_original_smeared_composite_retains_nonGaussian_fourth_cumulant": true
000035 |   },
000036 |   "controls": 30,
000037 |   "scope": "Given constant original circle quark CAR/time; native v252 seed252 inputs, alpha1/4 ell1 Hstar(0,1). Gaussian f_v is a test function, width .05 is not a physical weight or scale prediction. All-N proof is separate. No primitive H/3+1/spin2 identification or Lean/ledger promotion.",
000038 |   "Aq": 16.53819902083108,
000039 |   "equal_time_CLT_variance_limit": 49.61459706249324,
000040 |   "ordered_CLT": [
000041 |     {
000042 |       "N": 16,
000043 |       "ordered_characteristic": [
000044 |         0.9133801965218503,
000045 |         2.304480441693638e-05
000046 |       ],
000047 |       "target": 0.905535140903611,
000048 |       "error": 0.00784508946515457,
000049 |       "covariance_error": 9.670432794304679
000050 |     },
000051 |     {
000052 |       "N": 64,
000053 |       "ordered_characteristic": [
000054 |         0.9076293949173262,
000055 |         3.7117504258895123e-06
000056 |       ],
000057 |       "target": 0.905535140903611,
000058 |       "error": 0.0020942573029724652,
000059 |       "covariance_error": 2.596410476769149
000060 |     },
000061 |     {
000062 |       "N": 256,
000063 |       "ordered_characteristic": [
000064 |         0.9060670213991939,
000065 |         -6.640144491932358e-07
000066 |       ],
000067 |       "target": 0.905535140903611,
000068 |       "error": 0.0005318809100698682,
000069 |       "covariance_error": 0.6603786284119405
000070 |     }
000071 |   ],
000072 |   "same_time_and_timed": [
000073 |     {
000074 |       "N": 16,
000075 |       "equal_time_variance": 40.03767277794681,
000076 |       "same_original_time_point3_covariance": [
000077 |         -5.199009355813358,
000078 |         4.626594809412222
000079 |       ]
000080 |     },
000081 |     {
000082 |       "N": 64,
000083 |       "equal_time_variance": 47.04188165535423,
000084 |       "same_original_time_point3_covariance": [
000085 |         -0.09929014622831386,
000086 |         -1.0522846376799908
000087 |       ]
000088 |     },
000089 |     {
000090 |       "N": 256,
000091 |       "equal_time_variance": 48.9601626394967,
000092 |       "same_original_time_point3_covariance": [
000093 |         -0.1337430767312173,
000094 |         0.28612262384900994
000095 |       ]
000096 |     },
000097 |     {
000098 |       "N": 1024,
000099 |       "equal_time_variance": 49.45028458615387,
000100 |       "same_original_time_point3_covariance": [
000101 |         -0.13897244424856564,
000102 |         -0.022786395841963705
000103 |       ]
000104 |     },
000105 |     {
000106 |       "N": 4096,
000107 |       "equal_time_variance": 49.573474949942806,
000108 |       "same_original_time_point3_covariance": [
000109 |         0.0005845742003181727,
000110 |         -0.01426329025204217
000111 |       ]
000112 |     }
000113 |   ],
000114 |   "smeared_variances": [
000115 |     {
000116 |       "N": 16,
000117 |       "unscaled_variance": 26.085299082466904,
000118 |       "CLT_scaled_variance": 0.8151655963270907
000119 |     },
000120 |     {
000121 |       "N": 64,
000122 |       "unscaled_variance": 26.085299082466918,
000123 |       "CLT_scaled_variance": 0.2037913990817728
000124 |     },
000125 |     {
000126 |       "N": 256,
000127 |       "unscaled_variance": 26.085299082466918,
000128 |       "CLT_scaled_variance": 0.0509478497704432
000129 |     },
000130 |     {
000131 |       "N": 1024,
000132 |       "unscaled_variance": 26.085299082466918,
000133 |       "CLT_scaled_variance": 0.0127369624426108
000134 |     },
000135 |     {
000136 |       "N": 4096,
000137 |       "unscaled_variance": 26.085299082466918,
000138 |       "CLT_scaled_variance": 0.0031842406106527
000139 |     }
000140 |   ],
000141 |   "whole_ordered_smeared_source": [
000142 |     {
000143 |       "N": 8,
000144 |       "value": [
000145 |         0.8587316604241578,
000146 |         -0.02781455454471697
000147 |       ]
000148 |     },
000149 |     {
000150 |       "N": 16,
000151 |       "value": [
000152 |         0.8587315956172239,
000153 |         -0.02781453810395312
000154 |       ]
000155 |     },
000156 |     {
000157 |       "N": 32,
000158 |       "value": [
000159 |         0.8587315956172222,
000160 |         -0.027814538103953165
000161 |       ]
000162 |     }
000163 |   ],
000164 |   "unscaled_radial_cumulants_2_3_4": [
000165 |     26.085299082466907,
000166 |     -61.38989945834513,
000167 |     168.79099147128437
000168 |   ],
000169 |   "ledger_changed": false
000170 | }