IndisputableMonolith.Relativity.Lensing.ShadowPredictions
This module defines phase fringe density and related shadow predictions for lensing effects in the Recognition Science framework. It supplies the interference pattern at event horizons as a sinusoidal function of local tick time scaled to the eight-tick period. Researchers modeling black hole shadows or PBH detectability would cite these objects. The module consists of definitions and trivial lemmas that import metric and spherical symmetry results without internal proofs.
claimThe phase fringe density at the event horizon boundary is defined by $ρ_{fringe} = sin(2π t / (8 τ_0))$, where $τ_0$ is the fundamental RS time quantum and $t$ is the local tick coordinate.
background
Recognition Science derives relativity from the unified forcing chain with time quantized as the tick τ₀ = 1 from the Constants module. This module imports the metric geometry and static spherical solutions to treat compact object shadows and lensing boundaries. The eight-tick octave (period 2³) supplies the scaling in the fringe formula, linking local tick coordinate t to interference density at the horizon.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the foundational objects for shadow fringe predictions and observability conditions in RS lensing. It aligns with the eight-tick structure from the forcing chain and supports downstream calculations of fringe frequency and PBH shadow detectability. No direct parent theorems appear in the dependency graph, but the definitions feed sibling results on fringe existence and wavelength conditions.
scope and limits
- Does not derive the full lensing metric from first principles.
- Does not compute numerical shadow diameters for specific masses.
- Does not incorporate ray-tracing or general relativistic propagation.
- Does not prove fringe observability, only defines the density function.
depends on (3)
declarations in this module (11)
-
def
PhaseFringeDensity -
def
LensingCorrection -
theorem
shadow_fringe_exists -
theorem
shadow_diameter_correction -
theorem
pbh_shadow_detectable -
def
H_ShadowFringeObservable -
theorem
shadow_fringe_wavelength_exists -
theorem
shadow_fringe_observable_trivial -
def
ShadowFringeFrequency -
theorem
shadow_fringe_frequency_identity -
theorem
fringe_frequency_grounded