pith. sign in
module module moderate

IndisputableMonolith.Masses.AlphaGScoreCard

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The AlphaGScoreCard module assembles definition rows and interval brackets for the RS-native product alpha G using imported constants, phi bounds, and electron mass ledger. Researchers verifying the fine-structure constant band against the phi-ladder would cite its closed predictions. The module structure aggregates equalities and bounds from sibling declarations without introducing new theorems.

claimThe module defines predictions for the product satisfying $G = φ^5 / π$ and $α^{-1} ∈ (137.030, 137.039)$ with closed lower and upper bounds obtained from interval arithmetic on $φ$ and the electron mass residue $δ$.

background

This module operates in the Masses domain of Recognition Science, which derives all physics from one functional equation via the T0-T8 forcing chain. It imports the fundamental RS time quantum $τ_0 = 1$ tick from Constants. PhiBounds supplies rigorous algebraic bounds on the golden ratio $φ = (1 + √5)/2$ via the inequalities $2.236^2 = 4.999696 < 5 < 5.001956 = 2.237^2$. ElectronMass supplies the T9 structural derivation of the electron mass from the refined Ledger Fraction Hypothesis with residue $δ$. The local setting uses RS-native units where $c = 1$, $ħ = φ^{-5}$, and $G = φ^5 / π$.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the alphaG scorecard that validates the alpha band and supports the mass formula yardstick * $φ^{rung-8+gap(Z)}$ on the phi-ladder. It fills the numerical prediction step after T7 eight-tick octave and T8 D=3, feeding constant derivations that apply the Recognition Composition Law. It touches closure of the alpha^{-1} interval match.

scope and limits

depends on (3)

Lean names referenced from this declaration's body.

declarations in this module (16)