IndisputableMonolith.Constants.FineStructureConstant
This module collects definitions and theorems for the fine structure constant in Recognition Science, centered on the locked value α_lock re-exported from Constants. It imports the phi-forcing framework to derive positivity, unit-interval membership, and numerical bounds on the inverse. Researchers calibrating electromagnetic coupling against the golden-ratio ladder would cite these results when placing α within the RS-native alpha band. The module structure consists of direct re-exports plus short bound proofs that apply self-similarity lemmas
claimLet α_lock denote the fine-structure constant in RS-native units. Then α_lock > 0, α_lock ∈ (0,1), and 137.030 < 1/α_lock < 137.039.
background
The module sits inside the Constants domain and imports the fundamental RS time quantum τ₀ = 1 tick from the sibling Constants module. It further imports the PhiForcing module, whose doc-comment states that φ is forced by self-similarity in a discrete ledger with J-cost structure. The local theoretical setting is the derivation of observable constants from the unified forcing chain T0–T8, where the J-cost functional and phi-ladder supply the discrete scale that locks electromagnetic coupling.
proof idea
This is a definition and re-export module. Positivity of α_lock is pulled directly from the Constants module. Unit-interval and numerical-bound siblings apply the phi self-similarity lemmas imported from PhiForcing to constrain the inverse within the documented alpha band (137.030, 137.039). No new tactic sequences appear; each declaration is a one-line wrapper or direct numerical check.
why it matters in Recognition Science
The module supplies the fine-structure constant for all downstream mass-formula and Berry-threshold calculations inside the Recognition framework. It feeds the fine_structure_derived sibling and closes the constants section by linking the phi-ladder (T5 J-uniqueness through T8 D = 3) to the observable alpha band. The parent chain is the RCL identity together with the eight-tick octave that forces the numerical window.
scope and limits
- Does not derive α_lock from first principles without the phi-forcing ledger assumptions.
- Does not address running of the coupling with energy scale.
- Does not supply experimental calibration data outside RS-native units.
- Does not prove uniqueness of the alpha band beyond the supplied numerical interval.