KnotInvariant
plain-language theorem explainer
The KnotInvariant inductive type enumerates the five canonical knot invariants used in Recognition Science for low-dimensional topology. A knot theorist or topologist working in the RS framework would cite this enumeration to fix configDim D = 5 on the complexity ladder of knot discrimination. The definition proceeds by direct inductive construction of five constructors with automatic derivation of Fintype and equality instances.
Claim. Let $K$ be the inductive type whose constructors are the genus, the crossing number, the Alexander polynomial, the Jones polynomial, and the Khovanov homology.
background
The module Knot Invariants from RS introduces five canonical knot invariant families as corresponding to configDim D = 5. These families are the genus, crossing number, Alexander polynomial, Jones polynomial, and Khovanov homology; each functions as a rung on the complexity ladder of knot-type discrimination. The local theoretical setting treats them as structural elements of low-dimensional topology derived from Recognition Science, with the entire module carrying zero sorries and zero axioms.
proof idea
The declaration is an inductive definition that introduces five constructors, followed by automatic derivation of the DecidableEq, Repr, BEq, and Fintype instances.
why it matters
This definition supplies the base type for the KnotInvariantCert structure and the knotInvariant_count theorem, both of which establish that the cardinality is exactly five. It enumerates the canonical families required by the low-dimensional topology section and aligns with the configDim D = 5 convention on the complexity ladder. No open questions are closed here, but the type enables all downstream finiteness arguments.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.