Predictions and No-Go Consequences

Abstract

We consolidate the predictive content of Twistor Configuration Geometry (TCG) into a single paper, separating forward predictions from no-go consequences and structural constraints. The framework’s principal forward prediction is the spin-1 entry of the integer-spin coupling tower $Q_s/Q_2 \propto \alpha^{2s-4}$ derived from postulate P6: at $s=1$ this gives $\alpha_Y \equiv \alpha^{-2} \approx 1.88 \times 10^4$ relative to gravity, the only experimentally accessible case at present sensitivity (the $s=0,2$ entries match observations O1 and O2 as anchors; $s=3,4$ entries are effectively decoupled).

Beyond this, one no-go theorem and three structural constraints sharpen the framework’s falsifiability:

(i) the weak-angle relation $\sin^2\theta_W \approx 3/(4\pi)$ cannot be the on-shell weak angle, since this interpretation gives $M_W = 79.56$ GeV against measured $80.37$ GeV at the 60σ level — the relation is constrained to be the low-$Q^2$ effective leptonic mixing angle;

(ii) the cosmological-constant relation $\Lambda \ell_{\rm Pl}^2 \propto (m_e/m_{\rm Pl})^5$ requires an unstated lightest-charged-lepton selection rule, since muon or tau substitution overshoots by $10^{11}$ to $10^{17}$;

(iii) the postulate P5’ (Zhang 2026, Electroweak Boundary), $g_{2,W}^2 = 4/(3\pi)$ (equivalently $M_W/v = 1/\sqrt{3\pi}$), requires any future first-principles derivation to reproduce $4/(3\pi)$ at sub-percent precision from a canonical SU(2)$_L$ gauge-kinetic normalization, with the line-deformation bundle $\mathcal{E} \to G(2,4)$ as the current natural target — replacing the original dimensionful target $\mu_\star \simeq 89.4$ GeV (v1 §3.3), now retired with the closure of the original P5 in TCG v3 §6.2/§7.2;

(iv) any future correction mechanism for the fine-structure relation must produce the specific residual $\Delta_\alpha = -3.046 \times 10^{-4}$ in sign and magnitude, not merely “a small correction.”

We also pre-register a guardrail on the chamber-weighted-volume functional $\mathcal{I}[f]$ to prevent look-elsewhere abuse: only weight functions with structural motivation in the framework should count as legitimate identifications.

The paper’s honest summary: TCG’s predictive profile is mostly defensive (one no-go theorem and three structural constraints, plus an $\mathcal{I}[f]$ guardrail), with a single forward prediction (spin-1 fifth force) at experimentally accessible sensitivity. Strong-form vindication of the framework awaits this prediction’s confirmation.

DOI

https://doi.org/10.5281/zenodo.20076966