Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Two stationary clocks and one radial Rindler ray
A symbolic specialization of the conditional right-wedge Rindler theorem. The numerical parameters are chosen model values, not measured quantities; the instantaneous received-frequency reading is conditional on the theorem's additional adopted local phase-reception model, with its local ray-regime and finite-apparatus qualifications and no numerical accuracy or empirical validation claim.
Example
Specialize Right-wedge Rindler clocks, radial rays and frequency ratio to , emission radius , reception radius , and a future outward radial ray. These are exact model parameters. The one-way coordinate travel time is , and over a shared Rindler-time interval the ideal-clock ratio is . The instantaneous received-frequency ratio is under the theorem's additional adopted local phase-reception rule, with its local ray-regime and short-observation qualifications for finite apparatus and no numerical error bound or empirical validation. No experiment is described.
Facts & Assumptions
Given: The parameter values above and the right-wedge definitions and model readings of the theorem.
Right-wedge Rindler clocks, radial rays and frequency ratio: radial travel has , stationary ideal-clock increments scale as , and the wave-covector contraction functional scales as ; the instantaneous reception interpretation adopts the theorem's [A2] and retains all its qualifications.
Verification
Substitute , into the theorem's travel-time formula. Since both radii are positive and the ray is outward, , which is finite.
The clock-gradient formula gives . The contraction functional gives . By [F1], the latter is the instantaneous received-frequency ratio within the additional adopted local phase-reception model, with its local ray-regime and finite-apparatus limits; no measured accuracy is asserted.