TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/elliptic_quillen_response/elliptic_quillen_response.json
Original file SHA-256: 1b4a826b6f36a5d60c647cc1dbb58a723516bead6b3984425f4bf4c6173f18c8
Inclusive original lines: 1-72
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 |   "curve": "E=C/(Z+iZ), original untwisted nontrivial NS/NS spin",
000003 |   "operator": "K_z=(-i partial_x+2 pi v)+i(-i partial_y+2 pi u), z=v+i u; fixed H1_NSNS domain",
000004 |   "positive_spectrum": "K_z* K_z: 4 pi^2[(m+1/2+v)^2+(n+1/2+u)^2]",
000005 |   "relative_log_determinant": "log[det_zeta(K_z* K_z)/det_zeta(K_0* K_0)]=-2 pi u^2+2 log|theta3(z|i)/theta3(0|i)|",
000006 |   "heat_contract": "-integral_0^infinity [Tr exp(-t L_z)-Tr exp(-t L_0)]dt/t; flat UV coefficients cancel; invertible probes only",
000007 |   "probes": [
000008 |     {
000009 |       "z": [
000010 |         0.17,
000011 |         0.23
000012 |       ],
000013 |       "relative_log_determinant": -0.30088246879410896,
000014 |       "heat_integral_error": 1.166815364598964e-61,
000015 |       "gauge_and_quarter_error": 4.667261458395856e-61
000016 |     },
000017 |     {
000018 |       "z": [
000019 |         0.5,
000020 |         0.0
000021 |       ],
000022 |       "relative_log_determinant": -0.34657359027997264,
000023 |       "heat_integral_error": 3.8893845486632136e-62,
000024 |       "gauge_and_quarter_error": 3.8893845486632136e-62
000025 |     },
000026 |     {
000027 |       "z": [
000028 |         0.11,
000029 |         -0.19
000030 |       ],
000031 |       "relative_log_determinant": -0.16060893984255317,
000032 |       "heat_integral_error": 5.83407682299482e-62,
000033 |       "gauge_and_quarter_error": 2.333630729197928e-61
000034 |     }
000035 |   ],
000036 |   "quillen_log_norm_hessian": [
000037 |     [
000038 |       -6.283185307179586,
000039 |       0.0
000040 |     ],
000041 |     [
000042 |       0.0,
000043 |       -6.283185307179586
000044 |     ]
000045 |   ],
000046 |   "vector_dirac_effective_action": "Gamma_vec=-log det_zeta L_z; Hessian at0=2 pi I2; chiral modulus has half this coefficient",
000047 |   "null_divisor": "z=(1+i)/2 modulo Z+iZ; one complex zero mode of K, simple theta zero, quadratic norm zero",
000048 |   "independently_counted_divisor_winding": 1.0,
000049 |   "line_convention": "positive theta/determinant-section line; explicitly dualize if comparing with occupied Berry convention",
000050 |   "line_unitary_frame_connection": "A=2 pi i u dv; F=-2 pi i dv wedge du; (i/2pi) integral F=+1",
000051 |   "frame_transitions": "e_unit(z+1)=e_unit(z), e_unit(z+i)=exp(2pi i v)e_unit(z)",
000052 |   "line_holonomies": "v-cycle exp(-2 pi i u); u-cycle exp(2 pi i v), including endpoint frame identification",
000053 |   "old_counting_q": 0.3333333333333333,
000054 |   "old_relative_winding_determinant": 0.6666666666666666,
000055 |   "full_spectral_large_gauge_ratio": 1.0,
000056 |   "smooth_zero_twist_EM_test": {
000057 |     "condition": "Only if a proposed smooth z(alpha) has z(0)=0 and uses this norm alone",
000058 |     "quillen_first_derivative": 0.0,
000059 |     "old_minimal_transfer_first_derivative": -0.0003007973861406939,
000060 |     "verdict": "They cannot agree up to a constant reference or fixed multiplicity under that condition; no exclusion for a derived nonzero background or additional original insertions"
000061 |   },
000062 |   "conclusion": "Full spectral norm and the old occupation-pair counting determinant have distinct insertions despite sharing the old circle and winding.",
000063 |   "not_derived": [
000064 |     "primitive P1 charged source/measure and cross-face embedding",
000065 |     "finite v472 Berry-to-continuum metric/connection limit",
000066 |     "identification z=z(alpha_EM) or determinant power5/4",
000067 |     "positive CAR/KMS state for arbitrary temporal gauge twist",
000068 |     "physical time, interacting native source, or complete TFPT solution"
000069 |   ],
000070 |   "physical_gates_closed": [],
000071 |   "complete_TFPT_solution": false
000072 | }