PosturalAxis
plain-language theorem explainer
PosturalAxis encodes a unit vector in R^3 as the alignment of a primary biological axis with the resonant axes of the 8-tick cubic voxel. Applied researchers modeling metric strain between conscious boundary and physical hardware cite it when quantifying postural coupling. The declaration is a direct structure definition imposing the Euclidean norm constraint on a Fin 3 map.
Claim. A postural axis is a function $v : [3] → ℝ$ satisfying $∑_{i=0}^2 v(i)^2 = 1$, representing the alignment vector of the primary biological axis with the resonant axes of the 8-tick voxel.
background
The module sets the local setting in Phase 10a: resonant posture is a geometric configuration minimizing coupling cost between conscious boundary and physical recognition hardware inside the 8-tick manifold. Preferred axes of symmetry exist; alignment of physical structures (spine, limbs) with these axes reduces metric strain. Upstream constants supply the time quantum tick = 1 and length quantum voxel = 1, while PhiForcingDerived supplies the structure of J-cost and DAlembert supplies ledger factorization of (R_+, ×).
proof idea
Structure definition with empty proof body. It directly declares the field vector of type Fin 3 → ℝ together with the field is_unit enforcing the summation identity for unit Euclidean norm.
why it matters
Supplies the input type for alignment_quality, postural_coupling_cost, postural_minimization, SystemStability and posture_increases_stability. It populates the applied postural-alignment layer that connects the eight-tick octave (T7) and forced D = 3 (T8) to concrete stability calculations. Downstream theorems then show that alignment_quality = 1 forces coupling cost to zero and stability to its maximum value of 1.
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