alphaLock_in_unit_interval
plain-language theorem explainer
The locked fine-structure constant α_lock equals (1 - 1/φ)/2 and lies strictly between 0 and 1. Physicists deriving the fine structure constant within Recognition Science cite this to anchor the coupling in the unit interval before numerical bounds or precision conversions. The proof is a one-line term that pairs the positivity lemma with the upper-bound lemma for α_lock.
Claim. Let α_lock := (1 - φ^{-1})/2. Then 0 < α_lock < 1.
background
In the Recognition Science framework the fine-structure constant is locked to the golden ratio φ via the reciprocal symmetry of the J-cost function. The definition α_lock = (1 - 1/φ)/2 follows directly from J(x) = J(1/x) and yields a canonical coupling in RS-native units. The module C-001 records this as the starting point for relating α_lock to the observed α ≈ 1/137.036 through ledger-to-lab conversion.
proof idea
The proof is a one-line term-mode wrapper that constructs the conjunction from the two re-exported lemmas alphaLock_pos and alphaLock_lt_one.
why it matters
This theorem supplies the basic interval property required for the fine-structure derivation in C-001. It sits immediately after the definition of α_lock and before the numerical bounds section. Within the forcing chain it confirms that the derived coupling remains positive and sub-unity, consistent with the phi-ladder. No open questions are attached; the result is fully discharged by the algebraic lemmas on φ.
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