CMB-S4 Science Case, Reference Design, and Project Plan

Abstract

The (3+3) research programme posits that spacetime is six-dimensional with signature (+,+,+,-,-,-) — three spatial dimensions and three time-like dimensions — and that the third time-like dimension t_3 is compactified as a discrete two-sphere S^2 with 2^152 Planck-area cells. From this geometric starting point, together with the t_2 precession dynamics driven by the tribonacci constant, the programme derives 25+ observationally distinct phenomena without free parameters, spanning the Standard Model (fine structure constant at 7 ppb, proton-to-electron mass ratio at 0.008%, three fermion generations, strong CP, CP phases), quantum foundations (Born rule, Schrodinger equation, complex-valuedness, spin-statistics, Bell/Tsirelson bound), and cosmology (Hubble tension, six CMB anomalies, dark matter identity and abundance at 0.02%, preferred-axis large-scale structure). This paper is the programme’s entry point. It differs from the eleven companion preprints in its purpose rather than its content. The companion preprints each develop one specific application of the framework with full technical derivations; this paper does not re-derive any of them. Instead it presents the (3+3) geometry axiomatically — taking the six-dimensional spacetime with discrete-S^2 compactification as given, rather than arguing for its necessity — and shows what follows from the axioms, with structured pointers to the application papers for the full derivations. The paper is aimed at readers who want to assess the programme before committing to the 500-page book manuscript that justifies the axioms from first principles. The paper establishes six things: (A) a clean axiomatic presentation of the (3+3) geometry as six explicit axioms; (B) the immediate structural consequences of the geometry (trisection N_c = 3; 12 pentagonal defects; magic angle 54.74 degrees; CP tilt 14.48 degrees; half-integer spin from SU(2) double cover; hbar as derived quantity); (C) quantum mechanics as geometry (wavefunction as direction on S^2; psi in C from t_2 rotation; Schrodinger from linearised t_2 precession; Born rule via three convergent routes; Tsirelson = dim(S^2) = 2; cosmological decoherence floor 14.5 Gyr); (D) Standard Model parameters from geometry (alpha at 7 ppb; m_p/m_e at 0.008%; three generations; strong CP resolution; delta_PMNS = 194.48 degrees; spin-statistics); (E) cosmology from geometry (Hubble tension resolution; six CMB anomalies as projections of one structure; dark matter as n=0 KK condensate with alpha_23 = 0.8428 at 0.02%; intrinsic CMB dipole; preferred-axis LSS); (F) the unification claim — a consolidated table of 25+ derived phenomena from one geometric postulate. The paper is explicit about what it does not do. It does not derive the geometry from first principles (book [1]’s role). It does not reproduce any application-paper derivation (those live in [2–12]). It does not claim the framework is established as correct. Six open items are explicitly consolidated at the programme level (section 10): no 6D Lagrangian formulation; S^2 uniqueness only partially addressed; path-integral reformulation absent; interpretive comparisons with QBism, relational quantum mechanics, consistent histories undeveloped; precision amplitudes for CMB anomalies not derived; programme-level gaps including General Relativity reconstruction, QFT beyond Standard Model, black-hole thermodynamics, collider predictions, pedagogical development. Falsifiability is concentrated at named experiments through 2035 (section 11): DUNE and Hyper-Kamiokande on delta_PMNS = 194.48 degrees; neutron-EDM at PSI/ILL/SNS on strong CP; CMB-S4, LiteBIRD, Simons Observatory on the 11 additional cold spots and anomaly axis convergence; DESI 2028 on intrinsic CMB dipole and 3-fold LSS symmetry; precision Bell tests on Tsirelson saturation; real-QM falsification reconfirmation. Nine independent falsification routes covering the entire programme. The programme’s distinguishing feature is the combination of specific numerical predictions (alpha at 7 ppb, m_p/m_e at 0.008%, alpha_23 at 0.02%), named experimental tests at specific facilities with specific timeframes, zero free parameters, and scope across three physical domains (particle physics, quantum foundations, cosmology) from the same geometric substrate. This paper is the shortest path for a reader to assess whether the combination is compelling before committing to any deeper read.