Opposition
Entry 3.1.3 · Level 2 · Level 2 — Distinguished Angles
Construction
Two rays, opposite directions (θ = 180°)
Formal Signature (σ)
modify_relation(m₁₈₀, r) → r'Justification
The unique angle at which a relation reverses direction. The only non-trivial involution in the angle group.
Semantic Labels
Related Theorems
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.
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.
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.
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.
Every invertible well-formed expression has a unique inverse under the invert operation. The set of invertible expressions forms a group under composition.
Related Entries
Cite this entry
Jordan Traña. "Opposition" (3.1.3). Cosmic Codex — Universal Symbology, 2026. https://cosmiccodex.app/lexicon/3.1.3