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

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