TDRE Final version

We present the final formulation of Resonant Etheric Dynamics (TDRE), a discrete theoretical framework that describes space as a discrete medium, the plenum, made of massless elementary con- stituents (etherons), and all physical entities as collective states of that medium. The formulation replaces and supersedes the versions of November 2025 and July 2026. It is built from explicit pos- tulates, and every result is marked as derived, postulated or hypothetical. The main results are: (i) the algebra of the theory is Sylvester’s nonion algebra M3(C), in which the nine TDRE indices ad- mit an assignment satisfying four structural requirements, and whose nine elements decompose as spin 0 ⊕1 ⊕2; (ii) for a bipartite honeycomb plenum the long-wavelength dynamics is the Lorentz- invariant O(3)/CP1 sigma model, with a single speed c = (3/√2) d ωch fixed by the node spacing and the chronon frequency, so that Lorentz invariance of the wave sector is derived rather than assumed; gamma-ray timing bounds the spacing to d ≲7 ×10−27 m and the chronon to νch ≳3 ×1033 Hz; (iii) matter consists of topological solitons of the same field, with length contraction, time dilation and emergent mass m = hν0/c2; (iv) electromagnetism and weak-field gravitation are written as first-order equations in the nonion algebra with consistent SI units, and the nine nonions correspond one-to-one to the nine independent components of the electromagnetic energy–momentum tensor; (v) gravita- tion is modelled as the effect of an isotropic zero-point flux of the plenum; within the stated pos- tulates the model recovers Newton’s law, the gravitational redshift, the post-Newtonian parameters γ= β= 1 and gravitational waves with the quadrupole formula, consistently with all the bounds ex- amined here; the flux has a second constant, independent of G, the energy throughput per unit mass Γ= 4πGc/β ≳6.6×1042 W kg−1, which is the quantity relevant for any exchange of energy between matter and the plenum; (vi) Koide’s charged-lepton relation is shown to be equivalent to equipartition between the singlet and doublet modes of a Z3 cycle, and predicts mτ = 1776.969 MeV; (vii) as a hypothesis, the return of the flux is carried by self-conjugate (Majorana) excitations of the plenum, whose only static electromagnetic property is a toroidal moment and which carry a magnetic charge alternating in sign over their cycle; this explains the absence of static monopoles and, if these ex- citations are the neutrinos, predicts that neutrinoless double-β decay exists; (viii) the flux exerts on every body a one-sided push g0 = πG/β , of which gravity is the residue g= g0τ, τ being the opti- cal depth of the attracting body; (ix) if the absorption coefficient is fixed by the scale of the plenum (hypothesis H8), Newton’s constant becomes G= 9d2c3/(16π3¯ h): the node spacing is then d ≃7.4 Planck lengths, gravity and the quantum of action enter one formula, and the structure coincides with Sakharov’s induced gravity. The theory differs from general relativity in the strong field: it predicts no event horizons and, with the exponential completion of the spatial metric stated as a hypothesis, a black-hole shadow 4.6% larger than the Schwarzschild value. The work presents a coherent model and its consequences; it does not claim that nature has been shown to work in this way, and it states which observations would falsify it.