Analytic statement under ordinary4D product geometry, constant internal masses, squared-argument F(u)=m0 exp(-u), and direct classical bulk matching. Exact in all masses, only the first local curvature coefficient. No claim about full dynamic boson integration, quantum corrections, other original reference maps or the general TFPT source. R044/R045 is retained; new is the joint vacuum test with full constant mass dependence. No ledger promotion.
Read the exact result, assumptions and evidence
Result
In the explicitly chosen ordinary4D Spin Dirac product with arbitrary constant selfadjoint M,Mref and the same covaried metric,trace,rankN, the relative heat response factors: T=Tr exp(-M²/chi²)-Tr exp(-Mref²/chi²)<=N; V=m0chi⁴T/(4pi²), Mbar²=m0chi²T/(24pi²). Positive Einstein response requires T>0 and V/Mbar⁴>=144pi²/(m0N). At N96,m0=1 this gives14.8044 instead of7.12533e-121. T=0 also removes Einstein. All constant masses are resummed. A numerical rank2 relative Poisson witness has DeltaA2=0,DeltaA1=0.5262558>0 and prevents generalization to all relative profiles; its freely chosen spectra are not a TFPT candidate.
Required assumptions
Conditional equal-rank heat product with constant masses
Additionally chosen ordinary4D Spin Dirac product,constant selfadjoint internal M and Mref,same covaried metric and trace,rankN; exactly F(u)=m0 exp(-u),u=D²/chi²; volume and Einstein bulk coefficients solely from this relative classical source without other contributions. No claim that P1/P2 or original S_adm selects these premises.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Exact dimensional statement only for the named inventory; existing alpha/vacuum formula is input, SI numbers use CODATA2022, Planck2018 is only a dated illustration without a current fit or covariance test. No new prediction or source derivation.
Read the exact result, assumptions and evidence
Result
For c,hbar,G,kB,e,me,epsilon0,rho_energy the dimension matrix has rank5 and nullity3, with alpha, Gme²/(hbar c) and rho_energy hbar³/(me⁴c⁵) as a basis. Existing TFPT vacuum u=(8pi)² alphaG_e² I_vac. The Einstein de Sitter rewrite S/kB=24pi²/u=32pi⁴exp(2/alpha) is conditional and not independent evidence. The supplied alpha contract gives u=7.1253295267e-121. SI definitions do not derive a common physical action.
Required assumptions
P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
The reviewed decision record says which approach can be reused, which failed in its scope and what a new attempt would have to change.
What is resolved, and what remains
Open task
Evaluate original volume, curvature and gauge responses together
The same original physical source with bound reference,eta,domain,field integration and time supplies the existing alpha/flavor/clock responses and a tiny positive vacuum response with finite Einstein response without a freely selected profile or reference.
Next investigation: Preserve R112 and the active common-source continuation; compute its actual joint background responses. Do not equate boundary Q with the entire bosonic action or rescan the excluded heat product with different constant masses.
Original historical attempts linked to this question
These are original research records. Their reported verdicts are distinct from the reviewed results above.
constant triangulation 20261103
Can independent constants and existing TFPT readouts determine a common physical source, and can the relative single heat product realize both gravity and vacuum energy?
Recorded verdict: PARTIAL_CONSTANT_TRIANGULATION_WITH_SCOPED_HEAT_OBSTRUCTION
Historical inventory; not independently reviewed by this export.