  Thermonuclear supernovae, or Type-Ia supernovae (SNeIa), are an essential
tool of cosmology. Precise cosmological constraints are extracted from a Hubble
diagram defined by homogeneous distance indicators, but supernova homogeneity
is not guaranteed. The degree of heterogeneity within the SNeIa parent
population is unknown. In addition, event selections and standardization
procedures are based on empirical, optically-measured observables rather than
fundamental thermonuclear properties. Systematics are a natural consequence of
event selection from a diverse parent population. Quantifying the impact of
diversity-driven systematics is crucial to optimizing SNeIa as cosmic probes.
In this work, the empirical observables are used to calibrate previously
unidentified diversity-driven systematic uncertainties. The foundation of this
approach is the concept of "supernova siblings'', two or more supernovae hosted
by the same parent galaxy. Sibling-based calibrations isolate intrinsic
differences between supernovae; they control for source distance and host
galaxy dependencies that can conceal systematics or lead to their
underestimation. Newly calibrated distance modulus uncertainties are
approximately an order of magnitude larger than previously reported. The
physical origin of these uncertainties is plausibly attributed to the diverse
thermonuclear scenarios responsible for SNeIa and the inhomogeneous apparent
magnitudes induced by this diversity. Systematics mitigation strategies are
discussed. Cosmological parameter constraints extracted from a re-analysis of
the Pantheon+ SNeIa dataset are weaker than previously reported. Agreement with
early-Universe parameter estimates is achieved for a $\Lambda$CDM cosmology,
including a reduction of the Hubble Tension from $\sim$5$\sigma$ to <1$\sigma$.
