IndisputableMonolith.Mathematics.KnotInvariantsFromRS
This module introduces definitions for knot invariants derived from Recognition Science. Mathematicians exploring topological structures in RS-derived physics would cite it. The module consists of definitions building directly on the imported RS constants module.
claimThe module defines $\text{KnotInvariant}$ and $\text{KnotInvariantCert}$ as RS-derived objects on knots, together with counting functions $\text{knotInvariant_count}$ and certification predicates.
background
The module imports Mathlib for standard mathematical structures and IndisputableMonolith.Constants. The Constants module supplies the fundamental RS time quantum $\tau_0 = 1$ tick. No further definitions or theorems are supplied in the module header; the listed sibling declarations establish the main objects.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the mathematical objects needed to express knot invariants inside the Recognition Science framework. It sits downstream of the Constants module and provides tools that later results in the mathematics domain can reference when linking RS to topology.
scope and limits
- Does not derive explicit values of knot invariants for any concrete knot.
- Does not prove invariance under Reidemeister moves.
- Does not connect the invariants to physical observables or the forcing chain T0-T8.
- Does not import or reference the J-cost or phi-ladder constructions.