PhaseFringeDensity
plain-language theorem explainer
PhaseFringeDensity supplies the explicit sinusoidal formula for interference fringe density at the event horizon boundary under the eight-tick cycle. Researchers deriving ILG-corrected black hole shadow observables would cite this expression when constructing phase patterns from the local tick coordinate. The definition is a direct one-line wrapper that applies the sine function to twice pi times t scaled by the reciprocal of eight tau0.
Claim. The phase fringe density is given by $ρ_{fringe}(t) = sin(2π t / (8 τ_0))$, where $τ_0$ is the fundamental tick duration and $t$ is the local tick coordinate.
background
This module formalizes ILG-corrected lensing predictions for black hole shadows, with the objective of showing that the eight-tick cycle produces a detectable phase fringe at the event horizon. The upstream definition of tick sets the fundamental RS time quantum to 1 in native units, with the explicit note that one octave equals eight ticks as the fundamental evolution period. Related tau0 definitions supply the same quantity either as a direct alias to tick or via a derivation involving hbar, G, and c in RS-native units.
proof idea
The definition is a one-line wrapper that applies the sine function to twice pi times the local tick coordinate scaled by the reciprocal of eight tau0.
why it matters
This definition supplies the fringe density function required by the downstream theorem shadow_fringe_exists, which establishes that the eight-tick cycle forces a non-zero phase fringe at the event horizon of any Schwarzschild-like black hole. It directly implements the eight-tick octave (T7) from the forcing chain and supports the module goal of proving detectable fringes in black hole shadows. The parent result uses the definition to witness both the functional equality and the existence of a non-zero value.
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