Module Guide: IndisputableMonolith.Constants.AlphaDerivation

Purpose

This module supplies a constructive derivation of the inverse fine-structure constant from the geometry of the cubic ledger Q₃. It assembles the geometric seed 4π·11, the curvature term -103/(102π⁵), and the derived α⁻¹ value using only cube combinatorics, discrete Gauss-Bonnet, wallpaper-group counts, and Euler closure.

Main Declarations

• D sets the spatial dimension to 3.
• cube_vertices, cube_edges, cube_faces define hypercube counts.
• vertices_at_D3, edges_at_D3, faces_at_D3 verify the counts for D = 3.
• active_edges_per_tick = 1 and passive_field_edges yield passive_edges_at_D3 = 11.
• cube_dihedral, vertex_angular_deficit, and gauss_bonnet_Q3 derive total curvature 4π.
• geometric_seed and geometric_seed_eq assemble 4π·11.
• wallpaper_groups = 17, seam_denominator, seam_numerator, seam_numerator_at_D3 = 103, and seam_denominator_at_D3 = 102.
• curvature_term and curvature_term_eq give -103/(102π⁵).
• alphaInv_derived and alphaInv_derived_eq_formula combine the terms.
• Summary theorems: eleven_is_forced, one_oh_three_is_forced, one_oh_two_is_forced, alpha_ingredients_from_D3_cube.

Fit into Recognition Science Forcing Chain

The module sits in the constants layer after dimension forcing. It sets D = 3 and derives all numeric ingredients (11, 103, 102, 4π) from Q₃ geometry and the imported wallpaper-group count, producing the structural inputs to α⁻¹.

What Remains Outside This Module

Higher-order δₙ corrections, the canonical exponential formula, and explicit numeric matching to CODATA are handled in sibling modules. The precise provenance link from the forcing-chain theorems that establish D = 3 is not declared inside this module.