ResonantAxes
plain-language theorem explainer
ResonantAxes defines the three standard basis vectors in three-dimensional space as the resonant axes of the 8-tick cubic voxel. Researchers modeling postural alignment in Recognition Science cite this set when minimizing coupling costs between conscious boundaries and physical hardware. The definition constructs the set explicitly by listing the unit vectors along each coordinate axis.
Claim. The set of resonant axes is the collection of three functions from Fin 3 to the reals, each equal to the standard basis vector with a 1 in one coordinate position and 0 elsewhere.
background
The module formalizes resonant posture in the 8-tick manifold as a geometric configuration that minimizes coupling cost between the conscious boundary and physical recognition hardware. Preferred axes of symmetry reduce metric strain required to maintain the boundary. Upstream structures supply the nuclear density tiers, J-cost calibration from LedgerFactorization and PhiForcingDerived, gauge content and particle generations from SpectralEmergence, convex J-cost minimization from PhysicsComplexityStructure, and packaged alignment maps from RSNative.Alignment.
proof idea
The definition directly enumerates the three unit vectors along the coordinate axes as an explicit set comprehension.
why it matters
This definition supplies the geometric basis for the postural alignment phase and its alignment quality measure. It connects to the eight-tick octave and the forced three spatial dimensions. No downstream theorems yet reference it, but it fills the applied scaffolding for symmetry axes in the 8-tick manifold.
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