IndisputableMonolith.Crystallography.SelectionRules
This module introduces selection rules for crystallographic triads in the Recognition Science framework. It defines Triad structures, legalTriad predicates, neutral8 objects, and countLegal functions to enforce constraints from the eight-tick octave. Researchers deriving lattice symmetries from the J-functional equation would cite these definitions. The module consists entirely of definitions with no theorems or proofs.
claimThe module defines objects $T$ (Triad), the predicate legalTriad$(T)$, the structure neutral8, and the function countLegal that tallies valid configurations under the Recognition Composition Law.
background
Recognition Science derives spatial structure from the J-cost functional and the eight-tick octave (T7). This module sits in the crystallography domain and supplies the basic combinatorial objects needed to select admissible triads. The sibling definitions Triad, legalTriad, neutral8, and countLegal encode the local rules that later connect to D = 3 and the phi-ladder.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the combinatorial primitives that parent theorems on crystal symmetry and defect counting will invoke. It fills the gap between the abstract forcing chain (T5–T8) and concrete lattice models, preparing the ground for downstream results that apply the Recognition Composition Law to periodic structures.
scope and limits
- Does not prove that legalTriad configurations reproduce observed crystal classes.
- Does not compute explicit counts for any material lattice.
- Does not link the selection rules to the mass formula or alpha band.
- Does not address non-periodic or defective structures.