A Confinement-Based Definition of Space-Phase Stiffness with Results Across Scale Favoring a Unified Substrate-Associated Model Over Explanations That Rely Solely On Disconnected Scale-Specific Mechanisms Such as GR

An operational definition of stiffness based on confinement durability is applied across
scales from solar plasma to galactic structures. Stiffness is defined as resistance to lateral
diffusion and coherence loss under specified tolerance and quantified using a diffusionbound framework, ℓ⊥ ∼ √2𝐷⊥𝑡. Lower bounds on effective cross-structure diffusion are
derived for coronal mass ejection expansion, planetary orbital stability, Event Horizon
Telescope ring coherence, RBH-1 wake persistence (~62 kpc), and Fermi bubble bilateral
confinement (~10 Myr). When expressed as a dimensionless confinement index 𝑆 =
𝑡𝑐/𝑡drive, these systems align along a monotonic stiffness ladder spanning many orders of
magnitude in scale.
The key result is not the existence of structure, but the systematic scaling of confinement
durability across regimes governed by distinct local physics. Standard General Relativity,
coupled with environment-specific microphysical processes, explains each case
independently but does not predict a cross-scale scaling relation linking solar plasma
expansion, orbital persistence, horizon-scale coherence, and galactic wake confinement.
The SP3 space-phase framework, in contrast, predicts that confinement durability reflects
a single underlying medium parameter—conditionable stiffness—whose magnitude
increases with structural scale and conditioning state.
Thus, the stiffness ladder functions as a predictive discriminator: if future systems at
intermediate or larger scales populate the same scaling relation, the medium-based
interpretation gains support; if they scatter arbitrarily, it weakens. The present alignment of
diverse astrophysical systems along a single confinement progression favors a unified
substrate-associated model over explanations that rely solely on disconnected scalespecific mechanisms