shadow_diameter_correction
plain-language theorem explainer
The theorem asserts existence of a real correction delta_D to black hole shadow diameter equal to the ratio of recognition wavelength to Schwarzschild radius multiplied by the standard GR factor 5.196 Rs. Astrophysicists incorporating Recognition Science fringe effects into event-horizon telescope modeling would cite this result when estimating detectability for primordial black holes. The proof is a one-line wrapper that directly constructs the correction term and closes by reflexivity.
Claim. Let $R_s > 0$ be the Schwarzschild radius and let $λ_{rec} > 0$ be the recognition wavelength. Then there exists a real number $δ_D$ such that $δ_D = (λ_{rec}/R_s) · (5.196 · R_s)$.
background
The 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 recognition wavelength λ_rec is defined in Bridge.DataCore as √(ħ G / c³) and equivalently in Constants as the base length ℓ₀ in RS-native units. Upstream structures such as PhiForcingDerived.of supply the J-cost framework while NucleosynthesisTiers.of encodes the discrete φ-tier placement of physical densities.
proof idea
The tactic proof constructs the candidate correction explicitly as (lambda_rec / Rs) * (5.196 * Rs) and then applies the reflexivity tactic to discharge the existential equality. No external lemmas are invoked beyond the built-in real arithmetic.
why it matters
This declaration supplies the explicit fringe correction ε_fringe ~ λ_rec / R_s that the module uses to link the eight-tick octave (T7) to observable shadow fringes. It directly supports the downstream claim that the correction becomes detectable for primordial black holes with Rs ~ 1 micron, as stated in the module doc-comment. The result sits inside the broader ILG geodesic program but remains a definitional placeholder pending full integration of the LedgerFactorization and SpectralEmergence structures.
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