PTG Applications - Time Travel, CMB and Predictions

Pure Temporal Geometry (PTG) establishes a discrete, relational, 5-dimensional operator algebra governing all change. This paper consolidates three of the framework’s most significant observational and philosophical consequences. First, we prove the structural impossibility of time travel: the SINK operator irreversibly deposits the present into the Φ-axis; the torsion commutator ̂S, ̂P ≠ 0 permanently twists the geometry of traversed steps; and the Peano Anchor of Volume IV grounds the ordinal sequence such that backward traversal is equivalent to asserting 2 < 1. Hawking’s Chronology Protection Conjecture becomes a theorem, not a conjecture. Second, we reinterpret the Cosmic Microwave Background (CMB) as a Φ-axis reading of photons that have ticked forward 13.8 billion relational steps. The primordial plasma is not a place one could visit; it has been deposited into the universe’s Temporal Context. What instruments detect is the holonomy accumulated in each photon’s imaginary axis — including gravitational redshift, the Sachs-Wolfe effect, and polarisation. Observing the CMB is reading the fossil record, not visiting the Mesozoic era. Third, we derive the asymmetry between prediction and exactitude from the same operator algebra. The invariant grammar of the 5D manifold enables topological and statistical prediction. PUMP noise, torsion-driven chaos, and ontological JUMPs make tick-by-tick exactitude structurally impossible. The universe is a generative grammar: its syntax is fixed and knowable; its sentences are creative and indeterminate.