SystemStability
plain-language theorem explainer
SystemStability defines stability at scale r as the reciprocal of one plus geometric strain to the nearest resonant neighbor. Applied researchers in coherence technology cite it when quantifying how phi-aligned geometries raise biological or physical stability. The definition is a direct one-line wrapper around the GeometricStrain function.
Claim. Let $S(r)$ denote system stability at scale $r$. Then $S(r) := 1/(1 + Q(r))$, where $Q(r)$ is the geometric strain of $r$ relative to its nearest resonant neighbor on the phi-ladder.
background
The Coherence Technology module formalizes how resonant geometries (phi-spirals, octave-loops) affect stability. The golden ratio phi is the unique positive fixed point of the self-similar cost recursion, so geometries aligned with it are resonant. GeometricStrain at r is computed by finding the nearest rung via floor(log_phi(r) + 1/2) and applying the J-cost to the ratio r over that rung power.
proof idea
The definition is a one-line wrapper that applies GeometricStrain.
why it matters
This definition is invoked by resonance_increases_stability, which proves resonant scales give strictly higher stability than non-resonant ones, and by the postural version in PosturalAlignment. It supplies the applied link between the phi-ladder (T6) and measurable stability in the Recognition framework.
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