Historical observation note, curated October 21, 2026. The original writing date is not established here. The former title, “Windows in the Lattice: Why NS8 Splits Into Tiles,” suggested a general explanation that the qualified account did not establish.
What the visual language recorded
The original article described apparent windows and repeated motifs in selected renderings. Even/odd contrasts, a “binary heartbeat,” changing motifs across k-phases, and apparent nested order at larger N were exploratory interpretations of those views. This archive retains that history; it supplies no newly specified observation study.
What the arithmetic establishes
The Learn companion gives the exact TLF row and column periods and explains the distinction between arithmetic decomposition and visible motifs. Parity or factorization alone does not fix the shape or visibility of a window.
Scope of the archive
A visual comparison needs a fixed generator, size, phase, orientation, projection or color rule, and layout. The historical descriptions of synchrony, beating, interference and cross-size nesting are not established laws here. The associated research remains parked; consult Research for the current evidence categories.