TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/constant-triangulation-20261103/results.json
Original file SHA-256: c00c0466d6571c0470fe535b9a99ada4b130339fb53ebc313d6aac73934df82f
Inclusive original lines: 1-58
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": "Conditional source-class analysis; no fundamental TFPT closure, no ledger promotion.",
000003 |   "constants_sources": {
000004 |     "SI": "https://www.bipm.org/en/measurement-units/si-defining-constants",
000005 |     "CODATA2022": "https://physics.nist.gov/cuu/Constants/Table/allascii.txt",
000006 |     "dated_cosmology_benchmark": "https://arxiv.org/abs/1807.06209"
000007 |   },
000008 |   "dimensional_rank": 5,
000009 |   "independent_dimensionless_invariants": 3,
000010 |   "alpha_inverse_tfpt_input": "137.0359992168407",
000011 |   "alpha_inverse_CODATA2022": "137.035999177 +/- 0.000000021",
000012 |   "alpha_CODATA_marginal_sigma_difference": "1.89717619047619047619047619",
000013 |   "alphaG_e": "1.751809398790771217148219113e-45",
000014 |   "uLambda_tfpt": "7.125329526706394975688805728e-121",
000015 |   "rhoLambda_J_m3_conditional_on_measured_G": "5.226158136940657408358013451e-10",
000016 |   "rhoLambda_electron_units_conditional_on_measured_G": "3.675797097658982685227419251e-34",
000017 |   "Lambda_geometry_m_minus2": "1.085288793098125927016067912e-52",
000018 |   "deSitter_entropy_in_kB": "3.324344575760770278714410139e+122",
000019 |   "deSitter_entropy_scope": "Einstein de Sitter horizon for constant positive Lambda; downstream rewrite, not independent evidence.",
000020 |   "benchmark_inputs": {
000021 |     "H0_km_s_Mpc": "67.4",
000022 |     "OmegaLambda": "0.685"
000023 |   },
000024 |   "uLambda_dated_benchmark": "7.162238167664909687572760458e-121",
000025 |   "relative_difference_to_dated_benchmark": "-0.005153227258644480812253055472",
000026 |   "heat_equal_rank_bound": {
000027 |     "N": 96,
000028 |     "m0": 1,
000029 |     "lower_bound": "14.8044066016340379282517365",
000030 |     "lower_bound_div_tfpt_target": "2.077715359850481424196506337e+121",
000031 |     "required_m0_at_N96_at_least": "2.077715359850481424196506337e+121",
000032 |     "symbolic_ratio": "144*pi**2/(T*m0)",
000033 |     "premises": [
000034 |       "Ordinary 4D spin Dirac product, same metric and trace for bound reference",
000035 |       "Spacetime-constant self-adjoint internal M and Mref, same finite rank N",
000036 |       "Single heat profile F(u)=m0 exp(-u) in squared argument",
000037 |       "Vacuum and Einstein bulk coefficients from this source alone, no extra contributions",
000038 |       "Curvature expansion near flat space; exact dependence on all constant internal masses"
000039 |     ],
000040 |     "proof": "T=Tr exp(-M^2/chi^2)-Tr exp(-Mref^2/chi^2); T<=N. Positive Einstein coefficient requires T>0. V/Mbar^4=144pi^2/(m0 T)>=144pi^2/(m0 N)."
000041 |   },
000042 |   "poisson_relative_escape_control": {
000043 |     "physical_TFPT_candidate": false,
000044 |     "rank": 2,
000045 |     "mass_over_chi": [
000046 |       0,
000047 |       4
000048 |     ],
000049 |     "reference_mass_over_chi": [
000050 |       "1.969860653663740238598776339",
000051 |       "1.969860653663740238598776339"
000052 |     ],
000053 |     "vacuum_coefficient_difference": "-1.448908652612273978801459087e-70",
000054 |     "Einstein_coefficient_difference": "0.5262558013196367452262828579",
000055 |     "scope": "Numerical witness against extending the heat obstruction to all relative profiles; existence follows by strict monotonicity and intermediate value theorem. Freely chosen spectra cannot select the physical reference."
000056 |   },
000057 |   "verification": "Dimension rank and basis exact; heat identity exact; Poisson integrals and derivatives symbolic; direct radial quadrature at 0,1,4; dimensionless identities checked at 70 digits."
000058 | }