The Planck Scale: Where the Two Faces Meet

The Planck length is ℓ_P = √(ℏG/c³). Not the collision of two independent theories — the meeting point of two faces of one break. ℏ is the quantum face (Axiom B: minimum action per record). G = 2κ/m_ε² is the gravitational face (AP08 §5). c is the propagation limit (Axiom C). The Planck length is where the minimum record (ℏ) and the curvature scale (G) meet, bounded by c. At this scale, one ε writing one record in one unit of action produces one unit of curvature. The quantum and gravitational sectors are of equal weight. Neither dominates. Neither is perturbative. They are one.

Above the Planck scale (L ≫ ℓ_P): many records, smooth geometry, classical limit (AP13). The gravitational sector dominates; quantum corrections suppressed by (ℓ_P/L)². The world you observe. At the Planck scale (L ~ ℓ_P): δG/G ~ γ, of order unity. The pre-state and the record are equally present; the geometry is not smooth; the monoid is sparse; the discrete structure is exposed. Below the Planck scale (L < ℓ_P): the question is ill-posed. There is no sub-ℓ_P resolution. Geometry IS the accumulated record; below one record there is no geometry, only the pre-state — the white space, the 1:1.