TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/geometric_sector_response/geometric_sector_response.json
Original file SHA-256: fe35987cd8349b7e9772264da859e05a3582ae4a2acab7320e49464328a3dedf
Inclusive original lines: 1-145
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 |   "scope": "Given Pin Dirac family, same initial sea and its zero-mode particle; relative response only, no primitive source identification",
000003 |   "exact": {
000004 |     "weights_exact": true,
000005 |     "initial_slope": "chi_hg_prime(0)=-k <h_prime g_prime>",
000006 |     "negative_weight": "(E-k)^3/(16 E)",
000007 |     "positive_weight": "(E+k)^3/(16 E)"
000008 |   },
000009 |   "baseline_geometry_response": -0.47394864832401096,
000010 |   "contact": 0.38617274219097286,
000011 |   "retarded_response_at_t1": -0.4054682615132567,
000012 |   "complete_derivative_at_t1": -0.01929551932228385,
000013 |   "original_sea_occupation_coefficient_at_t1": 0.015177917523060008,
000014 |   "direct_commutator_max_error": 3.532729664357248e-13,
000015 |   "direct_family_tests": [
000016 |     {
000017 |       "epsilon": 0.02,
000018 |       "max_force_derivative_error": 0.010675443093587256,
000019 |       "max_occupation_coefficient_error": 0.0004662626179215445,
000020 |       "force_derivative_at_t1": -0.019077424314742353
000021 |     },
000022 |     {
000023 |       "epsilon": 0.01,
000024 |       "max_force_derivative_error": 0.0026922723822765393,
000025 |       "max_occupation_coefficient_error": 0.00011906847678192509,
000026 |       "force_derivative_at_t1": -0.019241194142313733
000027 |     },
000028 |     {
000029 |       "epsilon": 0.005,
000030 |       "max_force_derivative_error": 0.0006744700490086686,
000031 |       "max_occupation_coefficient_error": 2.9931516249268996e-05,
000032 |       "force_derivative_at_t1": -0.019281950733046616
000033 |     },
000034 |     {
000035 |       "epsilon": 0.0025,
000036 |       "max_force_derivative_error": 0.000168704227612837,
000037 |       "max_occupation_coefficient_error": 7.493287002569189e-06,
000038 |       "force_derivative_at_t1": -0.019292127974068762
000039 |     },
000040 |     {
000041 |       "epsilon": 0.00125,
000042 |       "max_force_derivative_error": 4.218146470180706e-05,
000043 |       "max_occupation_coefficient_error": 1.873974370961845e-06,
000044 |       "force_derivative_at_t1": -0.019294671530190044
000045 |     }
000046 |   ],
000047 |   "direct_family_extrapolation_error": 3.2509087199983355e-08,
000048 |   "omitted_contact_control_error": 0.38617277470006006,
000049 |   "pulse": {
000050 |     "epsilon": 0.01,
000051 |     "pulse_duration": 0.5,
000052 |     "measurement_time": 1.0,
000053 |     "steps": 100,
000054 |     "final_operator": "Exactly D0 for pulse and no-pulse histories",
000055 |     "unperturbed_relative_response": -0.4739486483240111,
000056 |     "past_positive_pulse_response": -0.47012535688664536,
000057 |     "past_negative_pulse_response": -0.47803970864576567,
000058 |     "predicted_first_derivative": 0.3956885828128384,
000059 |     "direct_first_derivative": 0.3957175879560154,
000060 |     "recurrence_error": 4.7376415062276906e-14,
000061 |     "actual_index_factor_check": {
000062 |       "z": 0.3333333333333333,
000063 |       "determinant_real": 0.6666666666666671,
000064 |       "determinant_imaginary": -8.585578122180855e-18,
000065 |       "ratio_identity_error": 4.44090606632437e-16
000066 |     }
000067 |   },
000068 |   "index_functional": "On the actual same-history pair P_t=U C0 U*, Q_t=P_t+U Pi U*, the exact relative operator is I-z U Pi U* and its determinant is1-z; no C_t-C0 trace-class assumption is needed",
000069 |   "geometric_weight": "Q_full=e^(-2alpha)R(g,alpha); at fixed alpha, delta log Q_full=delta log R. The original q_min=delta_top e^(-2alpha) equals this only under its retained residual normalization contract",
000070 |   "circle_second_response_bound": "|d_n(t)| <= [sum h_m^2(pi m)^6]/[128 |k_n|^6]",
000071 |   "infinite_cutoff_scope": "Second response summability proved; no all-epsilon trace-class or higher local-field regularity claim",
000072 |   "times": [
000073 |     0.0,
000074 |     0.01,
000075 |     0.02,
000076 |     0.03,
000077 |     0.04,
000078 |     0.05,
000079 |     0.06,
000080 |     0.07,
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000082 |     0.09,
000083 |     0.1,
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000092 |     0.19,
000093 |     0.2,
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000100 |     0.27,
000101 |     0.28,
000102 |     0.29,
000103 |     0.3,
000104 |     0.31,
000105 |     0.32,
000106 |     0.33,
000107 |     0.34,
000108 |     0.35000000000000003,
000109 |     0.36,
000110 |     0.37,
000111 |     0.38,
000112 |     0.39,
000113 |     0.4,
000114 |     0.41000000000000003,
000115 |     0.42,
000116 |     0.43,
000117 |     0.44,
000118 |     0.45,
000119 |     0.46,
000120 |     0.47000000000000003,
000121 |     0.48,
000122 |     0.49,
000123 |     0.5,
000124 |     0.51,
000125 |     0.52,
000126 |     0.53,
000127 |     0.54,
000128 |     0.55,
000129 |     0.56,
000130 |     0.5700000000000001,
000131 |     0.58,
000132 |     0.59,
000133 |     0.6,
000134 |     0.61,
000135 |     0.62,
000136 |     0.63,
000137 |     0.64,
000138 |     0.65,
000139 |     0.66,
000140 |     0.67,
000141 |     0.68,
000142 |     0.6900000000000001,
000143 |     0.7000000000000001,
000144 |     0.71,
000145 |     0.72,