This two-part working draft establishes the axiomatic foundations and the structural particle spectrum of Quantum Action Theory (QAT), a geometric, fluid-dynamic framework of spacetime and particle physics. QAT resolves the incompatibility between macroscopic gravity and discrete quantum states by positing a single ontological premise: the conserved substance of the universe is not energy, but action. By enforcing a strict geometric action capacity (R × X = h, equivalently Eτ = h) across a continuous vacuum of three-axis zero-point spinors, the phenomenological constants and particle masses of the Standard Model are derived as mandatory combinatorial and topological limits. Part 1 develops the continuous foundations — the action axiom, the spacetime-algebra of the vacuum, a time-free metric, gravity, least action, and the master formula. Part 2 catalogues the discrete particle spectrum those foundations generate, read explicitly as a resonant electrical network — the engineering picture that sits underneath the group theory and explains why SU(3) colour, the spin multiplets, and the fractional charges take the values they do. The Master Cubic, the Comb, and the Prediction of α Combining a topological spinor-counting formula with a structural reading of the Rydberg keystone (Ry = (3/2) ms c2 α02), the framework derives a depressed cubic equation governing stable particle resonances. Using only the proton mass (Mp) and the Rydberg constant (R∞) as inputs at the n = 81 spinor closure, the real root of this cubic predicts the inverse fine-structure constant: α0−1 = 137.0359991798 This structural prediction agrees with the direct CODATA 2022 measurement at the 0.12σ level, with a propagated uncertainty roughly 1.5× tighter than the direct measurement; the same single integer fixes the proton-to-electron mass ratio. Every measured quantity entering the framework is taken at its CODATA 2022 value up to this anchor; from the prediction onward, the framework adopts its own derived value of α0. Expanded not in the slant but in the spinor count n, the same master cubic collapses to a straight line — a Dirac comb, M(n) = (1/2) ms(α0−1 − 1) n − ms, whose tooth spacing is the cube of the compression (the three-phase volume) and whose offset is the spinor mass ms = me/3. The polynomial and the comb are one object: the spectrum is the set of closed breaths driven by the zero-point sea, which ticks as an impulse train and therefore generates a frequency comb. Closures lock to its teeth (muon n = 9, pion n = 12, proton n = 81); the electron sits off the comb (n = 3, unamplified), the bare anchor. Fractional Charges and Colour from Algebra The master cubic is structurally missing its linear coefficient. Through Vieta's formulas this forces a “cube-roots-of-unity” geometry on the resonance roots. Geometrically, standing the eight-spinor cube on its (1,1,1) body diagonal — the colourless mass current — the three orthogonal internal axes project onto the perpendicular plane at exactly 120°, and their shadows are the quark charges (+2/3, −1/3, −1/3). Charge is a projection, not an independent label; colour is the same frame's Z3 rotation about the mass axis. Read as a single circuit, the colour-singlet (Kirchhoff current) condition forces integer total charge: confinement quantises charge. The Particle Spectrum as an Electrical Network Part 2 makes the engineering reading exact: mass is reactive (stored) power and width is real (dissipated) power, so a stable particle is a pure, loss-free reactance. A quark is a structured impedance — a self-reactance (its mass), a charge port that fixes its line impedance (Z = Z0/q2), a spin port (a mutual reactance), and a colour phase. A meson is a single-phase loop (its field pulses through zero and can annihilate); a baryon is a balanced three-phase wye (a constant, never-zero rotating field — lossless, which is why the proton is stable). Heavy-quark reactances are read off by single, isospin-free spectator swaps, one quantum change at a time: Xs − Xd = MΛ − Mn = 176 MeV, Xc − Xu = MΛc − Mp = 1348 MeV, Xb − Xd = 4680 MeV. A generation is a pure climb up the reactive axis at a fixed charge rung. The diquark is shown to be a real object only once the quark masses differ — it is the resolution of a frustrated spin triangle, the lightest pair winning the deep singlet well, with Λ versus Σ the direct measurement. A single hyperbolic strain (the mismatch between shell radii) is simultaneously the heavy quark's extra mass, its weaker spin coupling, its displacement off the comb tooth, and the internal gravitational redshift that phase-locks a heavy core to its light shells. Exact Mass Anchors and the Lattice A hadron is a closure that warps the spinor-sea membrane, and its mass is the depth of that warp. Every ground state sits at a closure floor n = 3NN (the electron at 3, the pion at 12, the proton at 81), and heavier and excited states populate a two-axis integer lattice n = 4b·3a+1. This explains why ordinary matter is heavy: the all-light proton outweighs the all-light pion not because its quarks are heavy, but because closing three colours into a singlet costs 33 = 27 against the two-body pion's 22 = 4. The mass of ordinary matter is light-quark colour-closure energy. The whole light spectrum — spin 0, 1, 1/2, 3/2 — follows from one constituent network with a single hyperfine law ΔM = κ/(mimj); the octet and decuplet hyperons close to a few MeV with one spin coupling and one scalar-diquark compactness. The electromagnetic isospin splittings are quantised as exact integer multiples of the electron mass — π+ + π− − 2π0 = 18 me and Σ+ + Σ− − 2Σ0 = 3 me (ratio 6, the compactness) — and the proton–neutron splitting is the competition of the flavour and Coulomb terms, placing the neutron at Mp + (81/32) me (+0.002%). The nucleon magnetic-moment ratio comes out μp/μn = −3/2 exactly. The heavy quarks sit on the same lattice (charm and bottom constituent counts ≈ 144 and ≈ 432 spinors, bottom ≈ 3× charm), and the generations are organised by a single bare-mass Koide relation in which the leptons are anchored at exactly 2/3 and the quarks are displaced outward by their electric charge. Beyond the proton anchor, the entire light-and-strange sector requires only two empirical inputs: the down–up mass difference and the strange-quark mass. The Saturation Cap and the Electroweak Vacuum The reflection coefficient that orders the zoo — the photon at the matched centre (Γ = 0), confined matter near the reflective rim — reaches a hard ceiling at the horizon (|Γ| = 1). Identifying this compression reflection with the Standard-Model Yukawa coupling, every light quark and lepton sits near the matched centre while the top quark alone rides the rim. The cap is the electroweak vacuum, and the vacuum scale itself comes out of the same constants — the electron anchor lifted through the universal compression cubed and the self-compression fold — as v = (3/2) me (α0−1/2)3 ≈ 246.6 GeV, matching the measured value to 0.14%. This is why the top is the heaviest fermion and decays before it can hadronise: there is no comb tooth past the cap. Spacetime, Gravity, and the Time-Free Metric QAT reframes General Relativity as the macroscopic manifestation of action conservation. The metric carries no clock: its invariant is the action Eτ = h, read as a hyperbola in the conjugate plane, and in space it is the optical (Jacobi) metric whose geodesics are Fermat's least time and Maupertuis' least action at once — “least time” and “least energy” are the same path seen from the two conjugate sides. An exponential (bipolar isotropic) metric, forced into its opposite-signed form by the action-capacity phase-lock R × X = h rather than posited as an ansatz, derives gravitational time dilation and spatial curvature from the centroid gradients of local topological deformations. It recovers the classical Solar-System tests (PPN γ = 1), reproduces Einstein–Cartan kinematics, and reduces Newton's constant (G) to a strictly emergent Planck-units conversion factor. Gravity couples to the magnitude of the breath, so matter and antimatter fall the same way while carrying opposite charge. The same metric returns classical mechanics: projecting the action capacity along a closure's worldline expands exactly into the Lagrangian L = T − V, so the principle of least action becomes a survival condition for phase coherence rather than an independent postulate. At the strong-field limit, the Born–Infeld saturation of the vacuum Lagrangian produces a purely absorbing horizon with no reflecting core, yielding a definite, falsifiable gravitational-wave ringdown spectrum for next-generation detectors. The Variable Vacuum and the Recovery of Relativity The topological slant α0 is a local compression of the spinor sea, not a universal constant — a single move that resolves two classic obstacles to any medium theory of spacetime. Because gravity couples only to the deformation gradient ∇ξ and not to absolute mass, the uniform zero-point sea is gravitationally neutral, dissolving the vacuum catastrophe. Because every ruler is built from the same local α0, an observer is conformally blind to it, closing the absolute-rest-frame (“aether”) trap; special relativity then emerges as the mechanical equilibration of a current filter holding R × X = h under load. At cosmological scale, the global constraint ∮ξ d4x = 0 forces rarefied voids (ξ 0); these voids act as repulsive gravitational lenses, identifying dark energy as geodesic repulsion. The same picture reinterprets deep inelastic scattering without a virtual sea: the proton is a compressed region of the ambient substrate, and the parton “sea” is its refractive resolution.
Ashley Craig (Fri,) studied this question.