TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/claude46-gram-response-results.json
Original file SHA-256: 5fb8567b9195a973d0b65a24bf71d25e5127e05a4d754aee699d81191c1ee896
Inclusive original lines: 1-77
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 |   "derivatives_per_unit_direction": {
000003 |     "actual_Hardy_phase_minus_5pi_over_12": {
000004 |       "fixed_line_coefficient_abs": 16.018006332171137,
000005 |       "fixed_line_fraction_of_frobenius_amplitude": 0.8903010769812001,
000006 |       "fixed_line_fraction_of_frobenius_square": 0.7926360076738848,
000007 |       "frobenius_norm": 17.991673543161824,
000008 |       "operator_norm": 17.880914321899798,
000009 |       "rank": 3,
000010 |       "singular_values": [
000011 |         17.880914321899798,
000012 |         1.9932795875802234,
000013 |         0.007508816405864584
000014 |       ]
000015 |     },
000016 |     "imaginary": {
000017 |       "fixed_line_coefficient_abs": 4.161538576299255e-14,
000018 |       "fixed_line_fraction_of_frobenius_amplitude": 5.045200678423787e-15,
000019 |       "fixed_line_fraction_of_frobenius_square": 2.545404988556784e-29,
000020 |       "frobenius_norm": 8.248509507454113,
000021 |       "operator_norm": 5.83257700740252,
000022 |       "rank": 2,
000023 |       "singular_values": [
000024 |         5.83257700740252,
000025 |         5.832577007402507,
000026 |         5.234897196156207e-16
000027 |       ]
000028 |     },
000029 |     "real": {
000030 |       "fixed_line_coefficient_abs": 61.88882400762415,
000031 |       "fixed_line_fraction_of_frobenius_amplitude": 0.9929744069444577,
000032 |       "fixed_line_fraction_of_frobenius_square": 0.9859981728466976,
000033 |       "frobenius_norm": 62.32670608104195,
000034 |       "operator_norm": 62.319858327655396,
000035 |       "rank": 3,
000036 |       "singular_values": [
000037 |         62.319858327655396,
000038 |         0.9237024794166869,
000039 |         0.017962824632996914
000040 |       ]
000041 |     }
000042 |   },
000043 |   "finite_vs_linear_control": {
000044 |     "finite_response_frobenius_norm": 0.5456360675047863,
000045 |     "kappa_over_gap": 0.49,
000046 |     "linear_response_frobenius_norm": 0.646994963180882,
000047 |     "relative_linearization_error": 0.2264717957784201
000048 |   },
000049 |   "gap_asymptotics": {
000050 |     "cross_frobenius_norm": "|kappa|/(sqrt(3) g)+O(1) at y=2/3",
000051 |     "cross_operator_norm": "|kappa|/(sqrt(6) g)+O(1) at y=2/3",
000052 |     "cross_row_norm_exact": 0.8164965809277264,
000053 |     "fixed_line": "Re(kappa)/(3 g^2) Q exactly",
000054 |     "numeric_g_times_cross_frobenius_norm": 0.57738687522509,
000055 |     "numeric_g_times_cross_operator_norm": 0.40827417483977224,
000056 |     "numeric_test_gap": 0.0001
000057 |   },
000058 |   "gram_eigenvalues": [
000059 |     0.005386002055755119,
000060 |     1.191940562322203,
000061 |     1.1919405623222032
000062 |   ],
000063 |   "hardy_norm_condition_if_direction_is_Vadm": {
000064 |     "kappa_magnitude": "0.3096133626901069/cosh(ell_NS/2)",
000065 |     "required_strict_ell_NS_lower_bound": 5.644618151351245,
000066 |     "uses_original_epsilon_f": "2/3-delta_ph"
000067 |   },
000068 |   "leading_fixed_line_coefficient": 61.88882400762549,
000069 |   "original_gap": 0.07338938653344262,
000070 |   "projector_typing": {
000071 |     "P0_is_not_Pstr": true,
000072 |     "norm_commutator_P0_M0P0": 1.0,
000073 |     "plus_C6_branch_is_not_original_P_Seam_plus": true
000074 |   },
000075 |   "scope": "Unregulated plus-branch Gram derivative for the declared finite direction -kappa M0P0; not a derivation of V_adm or Pstr typing",
000076 | [OMITTED: non-scientific conversation or execution metadata]
000077 | }