Atom
Entry 4.1.2 · Level 3 · Level 3 — Entity-in-Enclosure
Construction
A single point centered in a triangle
Formal Signature (σ)
embed(a₁) → e, with D₃ boundaryJustification
Minimum-polygon enclosure (△, T1) with simplest entity (•, T1). Most fundamental instance of defined existence.
Semantic Labels
AtomElementIrreducible unit
Related Theorems
T3Sort Completeness
The four sorts (G, T, R, C) classify all well-formed expressions without overlap or gap. Every well-formed expression belongs to exactly one sort.
T4Operation Closure
The 11 Σ_UL operations are closed over the set of well-formed expressions. Applying any operation to well-formed inputs always yields a well-formed output.
T6Sort Preservation Under Operations
Each operation signature specifies the sorts of its inputs and output. The sort of the result is fully determined by the operation and the sorts of its arguments.
T9Sort–Operation Compatibility
The sort system and operation system are mutually consistent: no operation can produce a sort violation, and no sort restriction blocks a structurally valid operation.
Related Entries
Cite this entry
Jordan Traña. "Atom" (4.1.2). Cosmic Codex — Universal Symbology, 2026. https://cosmiccodex.app/lexicon/4.1.2