The Planckon is the object proposed in this work as the fundamental degree of freedom of the Planck region (the ℓP, tP, εP scale): a dimensionless, volumeless, indivisible smallest particle (d0); it carries potential energy of order εP. Within the framework of Dimensional Flow Cosmology (ΨD), the paper presents a construction that builds Planck-scale physics from the quantum interactions of Planckons. The model rests on two principles: time is not a coordinate but an event counter of interactions (τ = n·tP); space is built discretely with a doubling cubic geometry. The aim is to show, at the level of equations, that time is not a dimension but a tick count, and to derive the higher particles from the indivisible Planckon by the doubling theorem (gains: a singularity-free base, zero continuous tuning, predeclared falsifiability). By the finiteness principle, zero and infinity are not physical; the base of the ladder is N(d0) = 2⁰ = 1, d0 is never descended to, and the physical ground state is d1. The cosmological beginning is a doubling cascade that produces dimensions and space together: point (d0), line (d1), area (d2), volume (d3). The d3 cube of eight Planckons, with edge 4ℓP, is the basic building block of the self-similar hierarchy; geometric occupancy is fixed at 1/8 on every scale. The energy budget is formulated in operator language; closed bond patterns correspond to massive particles, open patterns to massless carriers; closure divides into four classes — lepton, baryon, meson, condensate — and the meson mass is the second-order remainder left over from conjugate cancellation (Section 8.5). Space is gained not by filling, but by the opening of vibration cells (of gaps). The diameter law d = 2³ƛ derived for the fully closed baryonic packet agrees with the CODATA 2022 value for the proton within 0.76σ — the prediction is a single equation: r = 4ħ/(mc). Counter dynamics (relativistic relations, the discrete spectrum E = 2³εP/N) and the interaction layer (force law, Thomson cross-section) are derived in the companion papers of the series. The four fundamental loop numbers are derived with zero inserted numbers through the chain of architecture, anchor and closed formulas; the neutrino base has zero-input candidate-derivation status via two pre-declared words (δν = 23/48; Mν = Ml·2⁻³²·e⁻²) (Σmν = 0.0593 eV — Section 8.1); the necessity grades of the backbone equations are given in the Constitutivity Inventory. What remains open are the interacting dynamical layer and the continuum limit. The status separation of the quantitative outputs — retrodiction (post-diction) versus out-of-sample prediction — is given with an explicit inventory in §1.3.
Hamdi Barut (Tue,) studied this question.