IndisputableMonolith.Constants.AlphaDerivation
The module forces the spatial dimension to D=3 via the linking requirement of T9 in the Recognition Science chain. Researchers deriving the fine structure constant and related constants cite it to justify three-dimensional geometry in the alpha pipeline. It supplies the supporting combinatorial definitions that encode the D=3 constraint without free parameters.
claimThe spatial dimension satisfies $D=3$, as required by the linking condition in T9 of the forcing chain.
background
The module sits in the Constants domain and imports the RS time quantum $ au_0=1$ tick together with the gap weight $w_8$ defined so that $f_{ m gap}=w_8 m ln(\phi)$. Its local setting is the alpha derivation pipeline that begins from the recognition composition law and the eight-tick octave. Sibling definitions supply the cube combinatorics (vertices, edges, faces) that realize the three-dimensional geometry forced by T9.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the D=3 foundation required by downstream modules including CurvatureSpaceDerivation (which isolates the $ m au^5$ curvature term), SolidAngleExclusivity (which forces the $4 m au$ isotropic factor), StrongCoupling, and the mass anchor derivations. It completes the T9 step that links the recognition graph to three spatial dimensions and thereby anchors the parameter-free alpha band (137.030, 137.039).
scope and limits
- Does not derive a numerical value for the fine structure constant.
- Does not treat time-like or higher-dimensional extensions.
- Does not incorporate experimental measurements.
- Does not prove uniqueness of the gap weight beyond its closed-form expression.
used by (34)
-
IndisputableMonolith.Constants.CurvatureSpaceDerivation -
IndisputableMonolith.Constants.SolidAngleExclusivity -
IndisputableMonolith.Constants.StrongCoupling -
IndisputableMonolith.Cosmology.HubbleTension -
IndisputableMonolith.Masses.Anchor -
IndisputableMonolith.Masses.AnchorDerivation -
IndisputableMonolith.Masses.BaselineDerivation -
IndisputableMonolith.Masses.JCostPerturbation -
IndisputableMonolith.Masses.LeptonSubLeadingForcing -
IndisputableMonolith.Masses.SDGTForcing -
IndisputableMonolith.Masses.SectorDependentTorsion -
IndisputableMonolith.Masses.StepValueEnumeration -
IndisputableMonolith.Mathematics.RamanujanBridge.DirectedFlux24 -
IndisputableMonolith.Mathematics.RamanujanBridge.RamanujanPiFactors -
IndisputableMonolith.Physics.CKMGeometry -
IndisputableMonolith.Physics.ElectronMass.BaselineDerivation -
IndisputableMonolith.Physics.ElectronMass.Defs -
IndisputableMonolith.Physics.ElectronMass.Necessity -
IndisputableMonolith.Physics.LeptonGenerations.Defs -
IndisputableMonolith.Physics.LeptonGenerations.FractionalStepDerivation -
IndisputableMonolith.Physics.LeptonGenerations.Necessity -
IndisputableMonolith.Physics.LeptonGenerations.TauStepDeltaDerivation -
IndisputableMonolith.Physics.LeptonGenerations.TauStepDerivation -
IndisputableMonolith.Physics.LeptonGenerations.TauStepExclusivity -
IndisputableMonolith.Physics.MassTopology -
IndisputableMonolith.Physics.MixingGeometry -
IndisputableMonolith.Physics.StrongForce -
IndisputableMonolith.Physics.WEndoForcing -
IndisputableMonolith.RecogSpec.RSLedger -
IndisputableMonolith.RRF.Physics.ElectronMass.Defs
depends on (2)
declarations in this module (43)
-
def
D -
def
cube_vertices -
def
cube_edges -
def
cube_faces -
theorem
vertices_at_D3 -
theorem
edges_at_D3 -
theorem
faces_at_D3 -
def
active_edges_per_tick -
def
passive_field_edges -
theorem
passive_edges_at_D3 -
def
cube_dihedral -
def
faces_per_vertex -
def
vertex_angular_deficit -
theorem
vertex_deficit_eq -
theorem
gauss_bonnet_Q3 -
def
solid_angle_Q3 -
theorem
solid_angle_Q3_eq -
def
per_face_solid_angle -
theorem
per_face_solid_angle_eq -
theorem
face_solid_angle_sum -
def
geometric_seed_factor -
theorem
geometric_seed_factor_eq_11 -
def
geometric_seed -
theorem
geometric_seed_eq -
theorem
alpha_seed_structural -
theorem
wallpaper_groups_count -
def
wallpaper_groups -
def
seam_denominator -
theorem
seam_denominator_at_D3 -
def
euler_closure -
def
seam_numerator -
theorem
seam_numerator_at_D3 -
def
curvature_fraction_num -
def
curvature_fraction_den -
theorem
curvature_fraction_is_103_over_102 -
def
curvature_term -
theorem
curvature_term_eq -
def
alphaInv_derived -
theorem
alphaInv_derived_eq_formula -
theorem
eleven_is_forced -
theorem
one_oh_three_is_forced -
theorem
one_oh_two_is_forced -
theorem
alpha_ingredients_from_D3_cube