Clifford geometric algebra G(p,q,r). unifies vectors, bivectors, rotors. rotations, reflections, translations in one algebra over F_p
| Op | Action |
|---|---|
geometric_product(a, b) |
Full Clifford product of multivectors |
inner(a, b) |
Inner (dot) product — grade lowering |
outer(a, b) |
Outer (wedge) product — grade raising |
reverse(a) |
Reverse multivector (conjugation for rotors) |
dual(a) |
Poincaré dual — complement in the algebra |
sandwich(r, x) |
Rotor application: r x r̃ |
grade(a, k) |
Extract grade-k component |
covers Euclidean G(n,0,0), Projective G(n,0,1), Conformal G(n+1,1,0). fixes the Arc → SVG compilation gap: Arc provides topology, Ren provides spatial embedding, compiler produces vector output. STARK-provable now — geometric product is F_p algebra with extra structure. compiles to Trident
see cyb/languages for the complete language set. see cyb/multiproof for the proving architecture