IDWT

The Standard Model of particle physics is one of the most precisely tested theories in the history of science. It catalogs the electron, the quarks, the W and Z bosons, and every other particle we have found in accelerators, and its predictions match experiment to ten or more decimal places. Yet for all its accuracy, the Standard Model does not explain why the particles it describes have the masses they do. The electron is 0.511 MeV. The muon is 105.7 MeV. The top quark is 172,570 MeV. These numbers are inputs — measured, catalogued, and inserted by hand. No one knows why they are what they are.

Infinite-Dimensional Wave Theory asks: what is the simplest physical object that could, in principle, produce the full spectrum we observe? The answer it proposes is a single complex wave function \(\Psi_\infty\) defined on a manifold of literally infinite dimension — not ten or eleven dimensions in the string-theory sense, but unboundedly many, with no fixed upper limit on the number of spatial directions. From this one object, every particle mass, every coupling constant, and every mixing angle in the Standard Model follows by calculation.

The setup rests on four postulates (P1–P4). We are inside \(M_\infty\) at the \(d=3\) coordinate level — we observe \(\Psi_\infty\) evaluated at our fixed \(\xi^0\) in the \(d>3\) sector coordinates and access only modes that are resonant at that level. The sector dimensions are macroscopic, with particles bound by sector potential wells. What we call mass is the count of sector microstates associated with each mode — specifically, the number of ways to distribute \(n\) quanta across \(d\) sector directions. This count is the combinatorial function \(S(n,d) = \binom{n+d-1}{d}\), a simplex number. Forces couple through two geometric principles: coordinate containment (a particle can only couple to a force if it lives in that force's sector) and the coupling filter (the particle's own sector geometry determines the structure of that coupling, including what interactions are geometrically forbidden). Gravity is curvature of \(M_\infty\) rather than a sector force: \(G_N = G_\infty/(4\pi)\), the \(4\pi\) being the ordinary 3D Green's-function constant (sector-independent), with \(G_\infty\) the remaining open input. There are no gravitons and no Kaluza-Klein tower.

The mass formula is then \(m = m_{\text{scale},d} \times S(n,d)\), where \(m_{\text{scale},d}\) is a sector energy scale fixed by coupling self-consistency equations, and \(n\) is a mode index selecting which particle within a sector we are computing. Every particle in the Standard Model lives in one of six sectors indexed by the dimension \(d \in \{2, 3, 4, 5, 6, 10\}\). These sectors are nested: the photon's two directions are literally inside every other particle, and each sector adds directions that persist upward through every sector above it. This nesting is what determines which particles feel which forces. The only free inputs are three integer seeds — \(n_d = 1\), \(n_u = 3 = \chi(\mathbb{CP}^2)\), and \(n_{\text{top}} = 72 = \chi(\mathbb{CP}^2)\,\chi(\mathbb{CP}^3)\,\chi(\mathbb{CP}^5)\) — together with the measured electron mass \(m_e\) as the single dimensionful unit. The composite \(n_s = n_d + n_u = 4\) and every other mode index then follow. (The electron is the \(d=6\) \(\mathbb{CP}^3\) sector excitation of \(\Psi_\infty\), a genuine 6D object inhabiting six macroscopic spatial dimensions, whose 3D appearance is a projection from sector space.) Everything else — all fifteen particle masses, the three gauge coupling strengths, the Weinberg angle, the Fermi constant, and the Cabibbo angle and all three PMNS mixing angles — follows by calculation.

The accuracy of the predictions is what makes the framework interesting rather than merely speculative. The W and Z bosons come out within 0.012% and 0.05% of their measured values. The Higgs mass is within 0.05%. The muon lifetime is within 0.3%. Every measured mass except the two bare \(d=4\) up-type quarks agrees with PDG to better than 0.8%, with most below 0.1%; charm (+0.93%) and top (+2.20%) are open residues after the removal of a fitted correction (Part 2 §11). The light-quark masses are parameter-free outputs of the derived sector scales, agreeing with PDG 2024 to within the sizable light-quark uncertainties.

The neutrino sector provides the most striking predictions. Neutrinos live in the \(d=5\) sector. The Clifford algebra of five-dimensional spinors has an exact mathematical property: when \(d \bmod 8 = 5\), no Majorana condition can be imposed on the spinor. This means neutrinos must be Dirac fermions in IDWT — the geometry forbids Majorana mass terms and the seesaw mechanism entirely. As a consequence, the neutrinoless double beta decay rate is predicted to be exactly zero. No oscillation experiment was used to calibrate these predictions: the three neutrino masses, all three PMNS mixing angles, the mass ordering, and the beta-decay effective mass all follow from the same three seeds \(\{n_d=1, n_u=3, n_{\text{top}}=72\}\) and electron mass \(m_e\) that fix everything else. The predicted sum \(\Sigma m_\nu = 60.39\) meV satisfies the Planck bound and lies above the detection threshold of the CMB-S4 experiment.

IDWT is falsifiable in specific and testable ways. Any detection of neutrinoless double beta decay — by KamLAND-Zen, nEXO, or any successor experiment — would rule it out completely. A cosmological neutrino mass sum measured outside the 55–65 meV window would equally falsify it. An inverted neutrino mass hierarchy, if established, would be a direct contradiction. Within the framework, every number is a calculation rather than a parameter, and every calculation is reproducible from a publicly available Python script in under a second on a laptop.