two_mul_alphaLock
plain-language theorem explainer
The lemma establishes that twice the locked fine-structure constant equals one minus the reciprocal of phi. Researchers working on Recognition Science constants reference this identity to simplify expressions that contain the acceleration-parameterized exponent. The proof is a direct algebraic unfolding of the definition followed by ring normalization.
Claim. $2 alpha_lock = 1 - phi^{-1}$, where $alpha_lock := (1 - phi^{-1})/2$ denotes the canonical locked fine-structure constant.
background
In the Constants module the golden ratio phi satisfies the fixed-point relation phi^2 = phi + 1 and serves as the self-similar scaling factor throughout the Recognition Science framework. The locked fine-structure constant is introduced by the definition alphaLock = (1 - 1/phi)/2. The module treats tau_0 = 1 tick as the fundamental RS time quantum in native units.
proof idea
The proof unfolds the definition of alphaLock and applies ring normalization to obtain the target equality.
why it matters
This purely algebraic identity clears the factor of 1/2 that appears in the definition of alphaLock, allowing direct substitution of the doubled form 2*alphaLock into exponentiated expressions. It supports constant derivations that rely on the phi-ladder and the locked value of alpha inside the interval (137.030, 137.039). No downstream theorems are recorded as depending on it.
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papers checked against this theorem (showing 1 of 1)
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Golden-ratio exponent fixes a gravity kernel, then meets 147 galaxies
"α = ½(1 − φ⁻¹) ≈ 0.191 (Eq. 14)"