Collision Geometry of Joint Spectra

This paper studies collision geometry for a fixed finite joint-spectrum arrangement under a one-parameter family of affine scalar projections. It proves finiteness of the collision set, chamberwise constancy of branch order, and the spectral quotient theorem for exact commuting-Hermitian realizations. For the explicitly declared rational nine-point arrangement P9, the 36 unordered pairs split into 2 parallel, 10 interior, 15 endpoint, and 9 exterior pairs. The interior collision parameters on the unit interval are 2/7, 2/5, 1/2, 2/3, and 4/5, with 2/3 the unique interior parameter of maximal layer-count drop. An exact two-parameter rectangular family supplies an independent control with one interior collision at b/(a+b). Version 2.1 reclassifies the declared complex128 Rubik registration as a source-addressed Computational Certificate and makes exact promotion fail closed. The exact Rubik quotient corollary is available only under the conjunctive assumptions R1--R3: exact operator admissibility, exact labelled joint registration, and the exact averaging identity. A diagonal exact negative control proves that collision adjacency alone does not imply transport adjacency or nonzero projected composition. The Rubik triangle-versus-chain result remains a bounded Computational Observation. The numerical certificate records nine stable registered clusters and a maximum raw-to-P9 table discrepancy below 10^-15 under the declared implementation and tolerance policy. It does not prove exact commutation, exact rational joint eigenvalues, exact primitive idempotents, a moving arrangement, transport or composition from collision data, maximality, or information-flow preservation. Source repository: https://github.com/dooven-prime/rime-lite Paper IV of the Representation-Induced Mechanics and Evolution (RIME) program. Independent researcher; no institutional affiliation.