Native Scalar Gravitational Waves from a Discrete Tick Algebra: Parameter-Free Polarization Predictions Confronted with Lunar Laser Ranging and Pulsar Timing

The Unified Scalar Field Theory (USFT v3) treats space as a relational cubic graph (“the Loom”, valence z = 6) and time as an active tick-rate field, with gravity carried entirely by two positive real scalar fields: the gravitational-tension field ΦG and the tick-rate field ΦT. We derive the gravitational-wave sector of this framework from the tick algebra alone — with no metric, no exponential-metric ansatz, no continuum action, and no free parameters — and, for the first time, confront it with data. Linearizing the two coupled discrete equations of motion shows that the only radiative degrees of freedom are the two graph scalars: USFT radiates scalar gravitational waves only, a breathing (B) and a longitudinal (L) mode, and no transverse-traceless tensor (+, ×) polarizations. Because the polarization content of a theory is fixed by its field content, this is a structural fingerprint, and a single confirmed +/×-only event would falsify the framework. The exact discrete dispersion relation reduces to a massless luminal wave equation, marginal leapfrog stability fixes both c and the valence z = 6, and the scalar quadrupole source radiates a power equal in magnitude to the general-relativistic tensor result with a factor-of-two strain fixed to 2 within 2×10−5 by the Cassini bound. In deriving the detector antenna patterns we correct two elements of the original v3 text: the emitted-power expression requires a (m1 + m2) factor, and the scalar response vanishes at the zenith (where the tensor-+ response is maximal), so the true discriminant is the different angular dependence. We then test the prediction on two independent, already-public datasets. First, reducing twenty years (2006–2026) of Apollo-15 lunar-laser-ranging normal points into a geometric observed-minus-computed series, we place a 95% upper limit of 9.2 m on any anomalous range term at the Earth–Moon synodic period — a null result exactly consistent with USFT’s “no-friction” theorem, the undamped tick-rate oscillation that underlies the framework’s w > −1 dark-energy prediction. Second, recognizing that this light-travel-time observable is best realized on a far longer baseline, we derive the pulsar-timing response from the same tick algebra, obtaining the two scalar antenna functions FB(μ) = (1 − μ)/2 and FL(μ) = μ2/2(1 + μ) and a parameter-free overlap-reduction function ΓUSFT = ΓBB − 2γUSFTΓBL + γUSFT2ΓLL with γUSFT = 1; this curve is not Hellings–Downs. Confronted with the published NANOGrav 15-yr and PPTA DR2 polarization analyses, the scalar-only prediction is in mild tension with the observed quadrupolar signal — a genuine headwind, not a falsification at present sensitivity — with the monopole/longitudinal correlation channel identified as the decisive near-future discriminant.