Dynamic Knot Theory from Discrete Informational Consistency. Part I: From the microscopic θ-cell to the mesoscopic language of loops

In classical knot theory, knots are treated as static embeddings S1 →֒R3, with equivalence specified axiomatically via Reidemeister moves. Within the framework of the Tensor Model of Discrete Dynamics (TMDD), knot topology is derived from first ontological principles: a knot emerges as a stable mode of informational tension with Morse index µ = 0 in the consistency configuration space Mcons. This paper is the first part of a series on dynamic knot theory and is exclusively theoretical in scope. We develop a microscopic description in terms of a tensor Iˆ with SU(2) × SU(2) × U(1) symmetry, formulate a mesoscopic loop language in terms of canonical coordinates (Q, C, K, G, S, X), and derive discrete analogues of Reidemeister moves as threshold-driven reactions of the system to local imbalance. Experimental signatures, phenomenological reconstruction, and cross-domain validation will be addressed in subsequent parts of the series. In the continuum limit, we show the reduction of the cross η-term of the action to the Chern–Simons functional and the recovery of the Jones polynomial as an observable of consistency dynamics.