SystemStability
plain-language theorem explainer
The postural system stability definition computes biological stability as the reciprocal of one plus the coupling cost for a given alignment vector. Applied researchers modeling resonant posture in the Recognition framework would cite this when quantifying how axis alignment affects overall system behavior. The definition is a direct composition of the postural coupling cost.
Claim. For a postural axis given by a unit vector in three dimensions, the stability equals $1/(1+C)$, where $C$ is the coupling cost between the biological axis and the underlying metric grid.
background
The Postural Alignment module formalizes resonant posture as a geometric configuration that minimizes coupling cost between the conscious boundary and physical recognition hardware in the 8-tick manifold. Preferred axes of symmetry exist; alignment of the physical structure with these axes reduces metric strain required to maintain the boundary. PosturalAxis is the structure consisting of a unit vector in Fin 3 to R. The upstream postural coupling cost equals 1 minus the square of alignment quality. This mirrors the stability definition from CoherenceTechnology, which replaces coupling cost with geometric strain.
proof idea
One-line definition that applies the postural coupling cost function to the input postural axis.
why it matters
This definition supplies the stability measure used by the downstream theorem posture_increases_stability, which states that alignment quality of 1 yields stability 1.0, and by resonance_increases_stability in CoherenceTechnology. It fills the applied layer of the forcing chain at the eight-tick octave and D=3 spatial dimensions, where resonant axes minimize strain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.