CM Optical Papers II: The Topological Repair of Information Flux and the Deterministic Derivation of the Airy Invariant 1.22

This paper, titled "CM Optical Papers II: The Topological Repair of Information Flux and the Deterministic Derivation of the Airy Invariant 1.22," establishes the second pillar of Cognitional Mechanics (CM) in the field of optics. Building upon the axiomatic derivation of the refractive index in Paper I, this work redefines diffraction not as a wave phenomenon, but as a mandatory computational restoration of truncated unitary information. For centuries, diffraction has been explained through the Huygens-Fresnel principle and the interference of secondary wavelets. However, these models remain phenomenological. By introducing the "Zero-Capacity Domain" (Z) to represent physical apertures, this research demonstrates that diffraction is a "Topological Repair" process on the spacetime manifold. The manifold must interpolate phase discontinuities to maintain global unitary consistency, minimizing the Hilbert-Schmidt logical residual (R). Key breakthroughs presented in this work include: The Deterministic Derivation of 1.22: We prove that the Airy invariant 1.22 (the Rayleigh criterion) is a geometric necessity. It is derived as the ratio of the SU(2) phase volume to its spatial projection (j1,1/pi), arising from the minimization of the logical residual. Subsumption of Huygens' Principle: The "secondary sources" of classical optics are reidentified as "Local Recursive Update Points." Physical distance (z) is redefined as the iteration count of the repair algorithm. SE(2) and Fourier Emergence: The Fourier transform is derived as the irreducible representation of the Euclidean motion group of the aperture, identifying the Fraunhofer limit as a stable computational state. Resolution as a Bandwidth Constraint: The Abbe and Rayleigh limits are reinterpreted as the maximum bandwidth for the manifold to distinguish independent repair processes. Validated against precision laser diffraction data with an error rate of less than 0.03%, this paper provides a rigorous mathematical bridge to the upcoming CM Optical Paper III: Coherence.