LensingCorrection
LensingCorrection supplies the ILG-adjusted deflection angle by scaling the general-relativistic value with a fringe factor drawn from the eight-tick cycle. Researchers modeling black-hole shadows or phase-fringe observables in Recognition Science would cite it when converting classical lensing results into the discrete-time framework. The definition is a direct one-line multiplication that encodes the stated scaling without further lemmas.
claimThe ILG lensing correction is given by $δθ_{ILG} = δθ_{GR} ⋅ (1 + ε_{fringe})$, where $δθ_{GR}$ is the deflection angle computed in general relativity and $ε_{fringe}$ is the phase-fringe correction generated by the eight-tick cycle.
background
The definition sits inside the module on black-hole shadow and phase-fringe predictions, whose stated objective is to prove that the eight-tick cycle produces a detectable non-zero phase fringe at the event horizon of any Schwarzschild-like black hole. The eight-tick cycle supplies the fundamental evolution period of eight ticks, with discrete phases $kπ/4$ for $k = 0,…,7$, as supplied by Foundation.EightTick.phase. The tick itself is the fundamental RS time quantum $τ_0 = 1$, taken from Constants.tick and its RS-native-units counterpart. Upstream structures such as NucleosynthesisTiers.of organize physical quantities into discrete φ-tiers, while LedgerFactorization.of calibrates the J-cost on the positive reals.
proof idea
The definition is a one-line algebraic wrapper that performs the multiplication delta_theta_gr * (1 + epsilon_fringe). No lemmas or tactics are invoked; the expression directly implements the scaling relation given in the doc-comment.
why it matters in Recognition Science
This definition supplies the explicit correction term required for all ILG-adjusted lensing calculations inside the shadow-predictions module. It implements the modification arising from the eight-tick octave (T7 of the forcing chain) and thereby supports the module-level claim that a non-zero phase fringe exists at the horizon. The construction links the continuous GR deflection to the discrete time structure of Recognition Science without altering the underlying metric or the phi-ladder mass formulas.
scope and limits
- Does not derive the numerical value of epsilon_fringe from the Recognition Composition Law or the J-cost equation.
- Does not compute or import the general-relativistic deflection angle delta_theta_gr.
- Does not specify the spacetime metric or coordinate system in which the correction is applied.
- Does not address observational thresholds or signal-to-noise requirements for detecting the fringe.
formal statement (Lean)
27noncomputable def LensingCorrection (delta_theta_gr : ℝ) (epsilon_fringe : ℝ) : ℝ :=
proof body
Definition body.
28 delta_theta_gr * (1 + epsilon_fringe)
29
30/-- **THEOREM: Shadow Fringe Existence**
31 The 8-tick cycle forces a non-zero phase fringe at the event horizon
32 of any Schwarzschild-like black hole in the RS framework. -/