IndisputableMonolith.Physics.WEndoForcing
The WEndoForcing module defines the endogenous wallpaper count for D-cubes as E_passive plus the forcing term F. Recognition Science researchers deriving spatial dimension selection from the cubic ledger would cite its dimension-specific cases and uniqueness result. The module consists of a sequence of targeted definitions and lemmas that build the count at successive integer dimensions.
claimThe endogenous wallpaper count is defined by $W_{ m endo} = E_{ m passive} + F$ for a D-cube.
background
This module sits in the Physics domain and imports the AlphaDerivation module, whose doc-comment states it supplies a complete constructive derivation of the fine-structure constant from the geometry of the cubic ledger, including the structural derivation of 4π from Gauss-Bonnet via vertex deficits of Q₃. It introduces the endogenous wallpaper count as the sum of passive excitations and the forcing term F. The module then supplies specialized definitions and equalities for this count at D = 1, 2, 3, 4, 5 and for D ≥ 17, together with a decomposition and a uniqueness statement for D = 3.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the wallpaper count that feeds the dimension-uniqueness result inside the Recognition Science forcing chain (T8). It links the alpha derivation upstream to the geometric selection of three spatial dimensions. The sibling declarations W_endo_at_3, dimension_unique_from_W_endo and components_at_D3 are the direct consumers of the central definition.
scope and limits
- Does not derive numerical values of constants such as α⁻¹.
- Does not treat time-like or higher-dimensional extensions beyond the D-cube.
- Does not contain the full T0–T8 forcing chain.
- Does not address applications outside the cubic ledger geometry.