IndisputableMonolith.Unification.ConstantsPredictionsProved
This module collects proved predictions for RS constants, centering on positivity and bounds for the fine-structure constant α. Researchers deriving constants from the phi-forcing chain without free parameters would cite these results. The module assembles direct applications of imported lemmas on gap weights and self-similar forcing.
claimThe fine-structure constant satisfies $0 < α < 0.1$ together with the positivity claim $α > 0$, both derived from the gap term $f_{gap} = w_8 · ln(φ)$ and the forced value of $φ$.
background
The module sits inside the unification domain and imports the RS time quantum τ₀ = 1 tick. PhiForcing establishes that φ arises as the self-similar fixed point of a discrete ledger equipped with J-cost. GapWeight supplies the closed-form, parameter-free projection weight w₈ used in the single gap term f_gap = w₈ · ln(φ) that enters the α pipeline.
proof idea
The module contains a collection of short theorems. Each is a direct one-line wrapper that applies the relevant lemma from Constants.Alpha or GapWeight after the phi-forcing results have fixed φ and w₈.
why it matters in Recognition Science
The module supplies the calculated α > 0 and α bounds that close the alpha pipeline inside the unification framework. It thereby supports the broader claim that all constants emerge from the T5–T8 forcing chain and the Recognition Composition Law without adjustable parameters.
scope and limits
- Does not compute a numerical central value for α.
- Does not derive predictions for G or the mass ladder.
- Does not address the eight-tick octave or D = 3 directly.
- Does not contain the Boltzmann-analog formulas proved in sibling declarations.
depends on (4)
declarations in this module (16)
-
theorem
alpha_positive -
theorem
alpha_lt_0_1 -
theorem
alpha_bounds -
theorem
c_eq_one -
theorem
c_positive -
theorem
boltzmann_analog_formula -
theorem
boltzmann_analog_positive -
theorem
boltzmann_analog_lt_half -
theorem
boltzmann_analog_bounds -
theorem
phi_inverse_formula -
theorem
phi_plus_inverse_eq_sqrt5 -
theorem
phi_sq_gt_2_5 -
theorem
phi_sq_lt_2_7 -
structure
ConstantsPredictionsCert -
theorem
constants_predictions_cert_exists -
theorem
constants_calculated_proofs_summary