Resource-Bounded Distinction Systems

Appendix A: Notation Comparison

Original Treatise Formalization Standard Literature
Operator $\Pi$ Bounded distinction operator $\Pi_t$ Idempotent endomorphism
$\mathrm{Fix}(\Pi)$ Same Image / fixed locus
$\mathrm{NonFix}(\Pi)$ Same Coimage
Witness selection Resource-bounded realizability Algorithmic realizability
Quantized phase transition Filtration step Birth/death of topological feature
Stacky quotient / gerbe Higher RBDS construction (open) Descent datum in $\infty$-category theory
Cycle-Collapse Theorem Theorem about functional digraphs Farthest-neighbor graph theory
Relation-first ontology Yoneda-style relational individuation Categorical ontology
Antisymmetric rank $\Omega$ Matrix function on $X$ Antisymmetric part of adjacency
$\mathrm{NonFix}(\Pi) =$ antisymmetric rank Incorrect