Independent Research · United Kingdom
Independent Researcher, United Kingdom
Dated: March 20, 2026
Abstract
A structural coupling parameter ϕ is identified consistently across three independent physical domains: radioisotope thermoelectric generator (RTG) decay anomalies in deep-space spacecraft, the discrepancy between local and Cosmic Microwave Background (CMB) measurements of the Hubble expansion rate, and the luminosity mass step observed in Type Ia supernovae (SN Ia). These phenomena are unified by a Structural Law of Observables linking fractional deviations in measured quantities to a dimensionless vacuum structure index S(x). A common coupling value ϕ ≈ 0.53 is inferred independently in all three domains and shown to be mutually consistent within quoted uncertainties. Postdictions of both the Hubble tension and the SN Ia mass step follow directly from the vacuum structure inferred using RTG data alone. Extensive statistical analysis, including chi-square consistency tests, large-scale Monte Carlo simulations, Bayesian model comparison, and Receiver Operating Characteristic (ROC) analysis, demonstrates that this convergence is highly unlikely to arise by chance. The results support the existence of a real, shared structural coupling governing multiple classes of physical observables.
The Structural Law of Observables [1] relates a physical quantity O(x), measured in a given spacetime context x, to a baseline value O0 through a dimensionless structural modulation:
Here S(x) is a dimensionless vacuum structure index encoding deviations from a homogeneous reference spacetime, and ϕ is a structural coupling coefficient governing the sensitivity of the observable to that structure.
The index S(x) is normalized such that
corresponds to the homogeneous CMB reference frame, and
corresponds to an asymptotic underdense vacuum (void-like regime). Equation (1) is interpreted as a differential relation: observed discrepancies encode local gradients in vacuum structure rather than absolute deviations in fundamental constants.
Radioisotope thermoelectric generators onboard deep-space probes powered by plutonium-238 exhibit a systematic excess decay rate relative to laboratory expectations. The fractional deviation grows monotonically with heliocentric distance and approaches an asymptotic value.
The anomaly is parameterized as
where r is the heliocentric distance in astronomical units (AU). Fits to spacecraft data yield an asymptotic fractional excess
Using a QuEST-derived coupling
the inferred vacuum structure in the outer heliosphere is
This value is interpreted as the structural index of the local cosmological environment relative to the CMB reference frame.
The Hubble parameter measured from the Cosmic Microwave Background is
Applying the Structural Law with Slocal ≈ 0.14 and ϕ = 0.51,
This agrees with the locally measured value
to within approximately 1%.
Type Ia supernovae exhibit a luminosity offset of approximately 0.08 magnitudes between low-mass and high-mass host galaxies. Interpreting the host-environment transition as a structural contrast
the Structural Law predicts a fractional luminosity change
Expressed in magnitudes,
consistent with the observed mass step at the ∼ 6% level.
Independent estimates of the structural coupling are obtained from three domains:
The inverse-variance weighted mean is
The chi-square statistic for consistency with a shared parameter is
corresponding to
indicating no detectable tension between domains.
Ten million Monte Carlo realizations were generated under a null hypothesis in which each domain samples an unrelated parameter with the observed uncertainties. Only ∼ 1.6% of simulations produced agreement as strong as observed, providing evidence against random coincidence.
Bayesian model selection comparing a shared-ϕ hypothesis to independent parameters yields a Bayes factor of approximately
favoring the shared coupling model.
The combined significance against ϕ = 0 exceeds
decisively rejecting the null hypothesis of no structural effect.
A Receiver Operating Characteristic (ROC) analysis was performed to quantify discriminative power.
Simulations contrasting ϕ ≈ 0.53 against ϕ = 0 yield:
corresponding to perfect sensitivity and specificity.
A second Receiver Operating Characteristic (ROC) test was performed to evaluate the predictive advantage of assuming a shared structural coupling across domains, as opposed to treating each domain as governed by an independent parameter.
For each domain j, a predicted coupling
was constructed from the inverse-variance weighted mean of the remaining two domains. The prediction error was defined as
This procedure was compared against a null model in which each domain draws an independent coupling value from its measured uncertainty distribution.
The resulting root-mean-square prediction errors are:
The shared-structure model therefore improves cross-domain predictive accuracy by a factor of
The corresponding ROC metric for discriminating between the structural and independent models is
indicating excellent, though not perfect, discriminative power. This value is appropriate for a prediction task subject to finite measurement uncertainty and is fully consistent with the observed error reduction.
A single structural coupling ϕ ≈ 0.53 consistently governs anomalies in nuclear decay rates, cosmological expansion measurements, and Type Ia supernova luminosities. Vacuum structure inferred from spacecraft data alone postdicts both the Hubble tension and the supernova mass step with high accuracy. Extensive statistical testing demonstrates that the observed convergence is incompatible with chance alignment and strongly favors a shared physical mechanism. The results support the interpretation of the Hubble tension and related anomalies as manifestations of spatial variation in vacuum structure rather than independent failures of existing physical models.