Claim Notes for the (3+3) Spacetime Framework: Seventy Derivation Claims from the Book "From One Sphere to All of Physics"

This Claim Notes document is a priority filing that catalogues seventy specific derivation claims extracted from the (3+3) Spacetime Framework presented in the book ‘From One Sphere to All of Physics: Deriving the Standard Model, Quantum Foundations, and Cosmology from S² Geometry with Zero Free Parameters’ (de Haan 2026, DOI 10. 5281/zenodo. 19633127). The (3+3) framework posits that spacetime has three temporal dimensions (t₁, t₂, t₃) in addition to the three familiar spatial dimensions, with t₃ compactified as a discrete 2-sphere S² of radius R₃ = πℏ/ (mₑ c). From this single geometric posit, combined with a self-referential bit condition fixing the foam cell count at N = 2¹⁵², the framework attempts to derive all Standard Model parameters, the quantum-mechanical axioms, and the late-time cosmological observables without adjustable parameters. The Claim Notes does not reproduce those derivations; it catalogues them. Each of the 70 claims is presented in a compact six-field format (claim, inputs, mechanism, book reference, falsifier, cross-links) and grouped into seven physics domains: fundamental constants (CN-01–CN-05), particle masses (CN-06–CN-18), mixing matrices and CP violation (CN-19–CN-30), force and gauge structure (CN-31–CN-38), cosmology and dark sector (CN-39–CN-55), CMB anomalies (CN-56–CN-60), and quantum foundations (CN-61–CN-70). A reading guide at the front offers three entry paths: a 10-minute pass-through of titles only, a one-hour working read of the full catalogue, and a specialist’s guide to the derivations most relevant to a given domain. The document is intended for readers who want a one-hour entry to the framework before deciding whether to read the book, for physicists evaluating specific claims that fall within their expertise, and for anyone checking priority dates on derivations that may appear in subsequent publications. The document’s most important single feature is §8: a consolidated Falsifiability Summary listing fourteen specific near-term experimental tests, each linked to one or more claims and each time-dated to an experiment already running or scheduled (DESI DR2 in 2026–2027 for the w (z) crossing at z = 0. 223; DUNE and Hyper-Kamiokande in the 2030s for δPMNS = 194. 48° and proton stability; NA62 and KOTO in 2025–2030 for the δPMNS/27 = 7. 20° CP phase; Simons Observatory and CMB-S4 in 2028–2032 for Ωₘ h² and nₛ; and others). Unlike most theoretical frameworks, the (3+3) programme makes several absolute predictions — no proton decay at any observable rate, no SUSY particles at any energy, no WIMP or axion as dark matter, no fourth gauge group — any one of which, if violated by experiment, falsifies the framework. This Claim Notes makes those predictions a single-page reference. The full derivations live in the book and the companion preprints; the Claim Notes is the index and the falsifiability dashboard.