alignment_quality
plain-language theorem explainer
Alignment quality quantifies how closely a postural axis aligns with resonant symmetry directions by taking the largest absolute coordinate of its unit vector. Applied researchers in postural minimization would reference this quantity when deriving coupling costs. The implementation extracts the infinity norm of the three-dimensional vector components.
Claim. For a postural axis $pa$ whose vector $v : Fin 3 → ℝ$ satisfies $∑ v_i^2 = 1$, the alignment quality equals $max(|v_0|, |v_1|, |v_2|)$.
background
PosturalAxis is the structure carrying a three-component real vector of unit Euclidean norm that represents the primary biological axis. The module places this structure inside the 8-tick manifold whose cubic voxels possess preferred symmetry axes; alignment with those axes is asserted to reduce metric strain at the conscious boundary. Upstream cost definitions supply the J-cost and derivedCost primitives that later convert the alignment number into a coupling penalty.
proof idea
Direct definition that returns the maximum of the three absolute component values; no lemmas or tactics are invoked.
why it matters
The definition supplies the scalar fed to postural_coupling_cost = 1 − quality² and thereby to the postural_minimization and posture_increases_stability theorems. It operationalizes the geometric step that realizes cost reduction inside the 8-tick octave with D = 3.
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