TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/elliptic_moduli_response/elliptic_moduli_response.json
Original file SHA-256: 62716bd2aa163d944fb535c4463cabbfac8b1915717965c9340521b858fd2153
Inclusive original lines: 1-93
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_rho: y^2=x^4+i rho x^2-1, rho real, |rho|<2",
000003 |   "fixed_Q_obstruction": "-2*a*x**2",
000004 |   "family_Q_action": "rho -> -rho",
000005 |   "marked_cross_ratio": "lambda(a)=(a+2i)/(a-2i); lambda(0)=-1; partial_a lambda(0)=i; partial_rho lambda(0)=-1",
000006 |   "j_invariant": "16(12+rho^2)^3/(4-rho^2)^2",
000007 |   "real_cuts": "hQkappa,hQ^3kappa remain dividing real forms; fixed oval equations v^2=u^4 +/- rho u^2+1",
000008 |   "free_glide": "hQ^2:(x,y)->(-x,-y) remains free",
000009 |   "limitation": "Q itself is a map between fibers, not the original fixed-fiber quarter clock",
000010 |   "primitive_period_at_square": 3.7081493546027438,
000011 |   "period_ratio_derivative": 0.2284732905222318,
000012 |   "boundary_modulus": "r(rho)=I(-rho)/I(rho), W=r/2; I(rho)=2 integral_0^infinity du/sqrt(u^4+rho u^2+1)",
000013 |   "independent_period": "I(rho)=2K((2-rho)/4); tau=i K(1-m)/K(m); Q gives tau -> -1/tau, not modular T",
000014 |   "covariance": "c_n,alpha(rho)=[1+exp(4 pi r(rho)(n+alpha))]^-1, alpha=1/4,3/4",
000015 |   "derivative_covariance": "c_prime=-4 pi r_prime(0)(n+alpha)c(1-c)",
000016 |   "lowest_positive_mode_at_square": 0.04142383216636283,
000017 |   "lowest_mode_derivative": -0.02850113859783212,
000018 |   "spin_kernel_derivative_at_x2_z4": 0.0007573730912245217,
000019 |   "exact_mixed_four_field": "kappa4=-Var(c); equal diagnostic weights at +/-rho give -(c_plus-c_minus)^2/4",
000020 |   "leading_four_field_coefficient": -0.0008123149013728358,
000021 |   "diagnostic_mixtures": [
000022 |     {
000023 |       "diagnostic_rho": ".1",
000024 |       "period_ratio": 1.0231259764357714,
000025 |       "c_plus": 0.03863316138124663,
000026 |       "c_minus": 0.044337142411000695,
000027 |       "connected_four_field": -8.133849896948562e-06,
000028 |       "coefficient_divided_by_rho_squared": -0.0008133849896948562,
000029 |       "density_eigenvalues": [
000030 |         0.03975600021838226,
000031 |         0.9187588478854941,
000032 |         0.0017291516777414014,
000033 |         0.03975600021838226
000034 |       ]
000035 |     },
000036 |     {
000037 |       "diagnostic_rho": ".05",
000038 |       "period_ratio": 1.0114910955380771,
000039 |       "c_plus": 0.040013858380790045,
000040 |       "c_minus": 0.04286444092838755,
000041 |       "connected_four_field": -2.0314552151668683e-06,
000042 |       "coefficient_divided_by_rho_squared": -0.0008125820860667473,
000043 |       "density_eigenvalues": [
000044 |         0.03971991507527822,
000045 |         0.918840935270133,
000046 |         0.0017192345793105737,
000047 |         0.03971991507527822
000048 |       ]
000049 |     },
000050 |     {
000051 |       "diagnostic_rho": ".025",
000052 |       "period_ratio": 1.0057284159146282,
000053 |       "c_plus": 0.04071510301126794,
000054 |       "c_minus": 0.042140218512285915,
000055 |       "connected_four_field": -5.077385478104305e-07,
000056 |       "coefficient_divided_by_rho_squared": -0.0008123816764966888,
000057 |       "density_eigenvalues": [
000058 |         0.03971090194703625,
000059 |         0.9188614372911869,
000060 |         0.0017167588147406821,
000061 |         0.03971090194703625
000062 |       ]
000063 |     },
000064 |     {
000065 |       "diagnostic_rho": ".0125",
000066 |       "period_ratio": 1.002860028061938,
000067 |       "c_plus": 0.041068521373757334,
000068 |       "c_minus": 0.04178105715963004,
000069 |       "connected_four_field": -1.269268115373086e-07,
000070 |       "coefficient_divided_by_rho_squared": -0.0008123315938387751,
000071 |       "density_eigenvalues": [
000072 |         0.03970864917409217,
000073 |         0.9188665615592141,
000074 |         0.001716140092601518,
000075 |         0.03970864917409217
000076 |       ]
000077 |     }
000078 |   ],
000079 |   "new_premise": "Complex structure may vary along the stated real marked-spin family; fixed-fiber Q is relaxed to its explicit family action",
000080 |   "not_derived": [
000081 |     "primitive P1 measure support on this parameter",
000082 |     "original weight or variance of rho",
000083 |     "full ramified marked-equator trace",
000084 |     "physical time or EM coupling identification",
000085 |     "fixed-fiber Q clock away from rho=0",
000086 |     "full interacting native or spacetime theory"
000087 |   ],
000088 |   "source_scope": "Existing free elliptic Cauchy quantization; equal-time CAR family, not a replacement of the pure Dirac-sea machine",
000089 |   "retained_compiler_scope": "The supplied marked base mu4 and its fixed-fiber Q exclude rho != 0. This reuses the existing square-rigidity result; primitive P1 identification is still conditional.",
000090 |   "local_fixed_Q_consequence": "Marked genus-one parity-cover deformations have one complex cross-ratio; Q sends lambda to 1/lambda. At lambda=-1 its derivative is -1, so no invariant tangent. With fixed spin/connection all remaining compatible metric variations are Weyl and preserve transported free Cauchy/Wick data.",
000091 |   "physical_gates_closed": [],
000092 |   "complete_TFPT_solution": false
000093 | }