Published October 29, 2026
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Emergent Time from Helical Motion on a Compact Matter Dimension:Axioms, Derivational Boundaries, and Falsifiable Predictions
Description
We propose and stress-test a framework in which spacetime consists of three spatial dimensions plus one com
pact “matter dimension” (a circle), with no external time coordinate. All elementary motion is right-handed helical
motion subject to the quota constraint (cdϕ) 2 = dm2 +dℓ 2 , and time emerges as helical phase count. We obtain: (i)
a parameter-free derivation of the Lorentz factor; (ii) a gravitational field equation exactly equivalent to the spheri
cally symmetric sector of general relativity, with the frame-dragging coefficient and transverse tensor modes derived
under one selected completion principle, consistent with Gravity Probe B, the LAGEOS and LARES satellites and
the gravitational-wave event GW170817; (iii) a two-winding topological encoding of charge quantization and an
even-winding rule from the spinor double cover; (iv) a rank-one locking of all constants’ variations, whose opera
tional signature is the exact constancy of µ = me/mp; (v) under a holographic pinning condition, a mass quantum
k = p hm¯ PH0/c 2 ≈ 4.2 meV and a pre-registered pure-integer neutrino prediction, m3/m2 = 6, which the first mea
surement of both mass splittings by the Jiangmen Underground Neutrino Observatory now disfavours at 3.9σ; with
verdict thresholds stated in advance. A line-count completion proposed afterwards, m = k(n+1/4π), fits them (ratio
33.79) and is registered as a separate prediction (H0 ≈ 66 km/s/Mpc). We equally delimit the underivable: the hierar
chy number N ≈ 2×1021; the fine-structure constant, identified as a twist-vortex log-impedance whose value requires
a microscopic core scale now in tension with ultra-high-energy neutrino bounds; the mass quantum itself, whose
derivation would require a non-abelian gauge sector the framework lacks; and quantum many-body entanglement, a
hard ceiling.