Local Kay–Radzikowski–Wald Obstructions in the Protected Core of Ori's 2007 Time-Machine Spacetime

This preprint studies the local geometric and quantum-field-theoretic behavior of the protected portion H1∘H_1^\circH1∘ of the future chronology horizon in Ori’s 2007 composite vacuum/dust time-machine spacetime.

In the exact periodic pseudo-Schwarzschild core, the closed horizon generators are shown to be past affinely complete and future affinely incomplete, with one circuit multiplying the remaining future affine length by

$$q=\exp [-l/(4\mu )].$$

The manuscript constructs exact future-directed radial null segments lying entirely within the globally hyperbolic development whose endpoints converge to the same quotient-manifold horizon point while becoming intrinsically causally unrelated in every sufficiently small globally hyperbolic neighborhood. Using a single Hamiltonian normalization at launch, the transported endpoint covectors have the common-scale limit

(p,dr; p,−q−1dr),(p,dr;\,p,-q^{-1}dr),(p,dr;p,−q−1dr),

with no independent rescaling at the terminal endpoint.

These calculations directly supply the local geometric input used in Proposition 2 of Kay, Radzikowski, and Wald. The paper formulates a compact-generation-free localized propagator argument, obtaining a mismatch between the causal propagator of the globally hyperbolic development and the intrinsic propagator of a sufficiently small neighborhood. Under the stated free Klein–Gordon assumptions, this yields an obstruction to F-locality for compatible extensions of the standard CCR algebra and a protected-side non-L2L^2L2 Hadamard mismatch.

The result is deliberately local. The manuscript does not claim that Ori’s complete chronology horizon is compactly generated, that the stress-energy tensor universally diverges, that semiclassical backreaction destroys the horizon, or that the formation of Ori’s time machine is impossible. The evolving dust-envelope geometry and the remainder of the full horizon remain unclassified.

This manuscript is a preprint and has not undergone independent peer review. The model-specific synthesis is described only as provisionally novel, and independent specialist verification is invited. OpenAI ChatGPT and Codex were used extensively for mathematical derivation, proof development, source auditing, drafting, and adversarial review. Dakota Rain Lock conceived and directed the research program, curated the resulting argument and audit trail, and assumes responsibility for the decision to publish it.