Module pga 

3D PGA motors as dual quaternions — CPU oracle for projector.wgsl Phase 2b+.

Motor { r, d } packs the even subalgebra: rotation (r) + translation (d). When d == 0, sandwich_point reduces to the Phase 1 quaternion path. Phase 2c: bilateral T_pull via motor_translate composed after intrinsic R_w · R_q. Phase 3: v-band topology (R_toroidal, T_radial, T_anchor) inside intrinsic stack.

Structs

Motor

PGA motor — matches WGSL Motor { r: vec4, d: vec4 }.

Functions

bilateral_pull_active

Bilateral T_pull magnitude gate — node lane + authenticated Human-Centric standpoint.

blade4_to_quat

Map motor r or d vec4 (s, e12, e13, e23) → quaternion (w, x, y, z).

cluster_centroid_lattice

Deterministic centroid lattice for boundary cliques — matches WGSL (no extra SSBO in Phase 3).

cluster_id_from_sigma

Boundary-clique cluster slot derived from tensor.sigma (spectral class index).

legacy_rotor_apply_vector

Phase 1 quaternion sandwich — regression baseline when d = 0.

motor_mul

Dual-quaternion product (qr1, qd1) ⊗ (qr2, qd2).

motor_reverse

PGA reversion: flip bivector signs; scalar + pseudoscalar stay positive.

motor_rq

motor_rq_gated

motor_rw

motor_to_mat4_col

Column-major affine mat4 (WGSL mat4x4<f32>) for a rigid motor (rotation + translation). Built by sending the origin (→ translation) and the basis vectors (→ rotation columns) through the sandwich product, so the matrix reproduces sandwich_point exactly. Used as the per-artefact model transform in the mesh shader (Phase 2 kinematic joints).

motor_translate

Pure translation motor — dual part encodes v/2 through quat_to_blade4.

motor_v_band

Phase 3 v-band intrinsic motor: Euclidean / cyclic / hyperbolic / boundary clique.

pull_vector

Pull vector toward camera eye: direction · (0.12 · α · epistemic_q).

quat_to_blade4

Inverse of blade4_to_quat.

rotor_from_axis_angle

rotor_mul

sandwich_point

Null-vector sandwich on euclidean (x, y, z) — P' = Ω P Ω̃.

semantic_motor

semantic_motor_intrinsic

semantic_motor_phase2c

Phase 2c semantic motor: Ω = T_pull · (R_w · R_q).

tensor_deontic_lane

Per-node deontic lane encoded in Tensor10D::mu (metadata carrier).