postural_coupling_cost
plain-language theorem explainer
Postural coupling cost is the misalignment penalty 1 minus squared alignment quality for a unit vector representing the primary biological axis. Applied researchers modeling resonant posture in the 8-tick manifold cite this definition when deriving stability from geometric resonance with cubic voxel axes. The definition is introduced as a direct algebraic expression using the alignment_quality function on PosturalAxis.
Claim. For a postural axis $pa$ with unit vector in $ℝ^3$, the coupling cost is $1 - [q(pa)]^2$, where $q(pa) = max(|pa_0|, max(|pa_1|, |pa_2|))$ is the alignment quality with a resonant axis.
background
The Postural Alignment module formalizes resonant posture as a geometric configuration minimizing coupling cost between the conscious boundary and physical recognition hardware in the 8-tick manifold. Preferred axes of symmetry exist; aligning structures such as the spine with these axes reduces metric strain required to maintain the boundary.
proof idea
Direct definition as the algebraic expression 1 minus the square of alignment_quality applied to the input PosturalAxis. No lemmas or tactics are invoked.
why it matters
This definition supplies the geometric cost term used by the postural_minimization theorem, which proves that alignment_quality = 1 yields cost 0, and by the SystemStability definition, which inverts the cost to obtain a stability measure reaching its maximum of 1.0. It operationalizes the Phase 10a claim that alignment with 8-tick symmetry axes minimizes strain, connecting to the eight-tick octave and D = 3 in the forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.