IndisputableMonolith.Physics.MaterialsScienceFromRS
This module derives materials science objects from Recognition Science by defining material classes and establishing the octahedral group order as 48, which equals 6 times the eight-tick octave. Condensed matter physicists and materials modelers would cite the certification and group-order equality. The module is a collection of definitions plus one direct equality linking the group order to the RS forcing chain.
claimThe module introduces MaterialClass together with materialClassCount and proves that the octahedral group order satisfies $|O_h| = 48 = 6 imes 2^3$, with MaterialsScienceCert as the resulting certification object.
background
The module resides in the Physics domain and imports only Mathlib. It defines MaterialClass as the RS-derived classification of materials, materialClassCount as the enumeration of those classes, ohGroupOrder as the cardinality of the Oh group, and MaterialsScienceCert as the certified outcome. The local setting connects directly to the eight-tick octave (period $2^3$) of the forcing chain T7.
proof idea
This is a definition module, no proofs. The structure consists of type definitions for MaterialClass and related counts, followed by the equality ohGroupOrder_eq_6_times_8.
why it matters in Recognition Science
This module feeds MaterialsScienceCert and supplies the explicit link from group orders to T7 eight-tick octave in IndisputableMonolith.Foundation.UnifiedForcingChain. It supports the broader derivation of material classifications from the phi-ladder and Recognition Composition Law.
scope and limits
- Does not derive conductivity or band-structure formulas.
- Does not connect to the mass formula or alpha band.
- Does not treat relativistic or quantum corrections in materials.