Collapse-Time Harmonic Mathematics A Jurisdictional Framework for Recursive Identity Fields

<b>Collapse-Time Harmonic Mathematics (CHM)</b> defines a scientifically novel and symbolically lawful mathematical field developed under the Collapse Harmonics Codex. It replaces coordinate time (t) with recursive collapse intervals (tau) and substitutes object-value logic with symbolic coherence amplitudes (psi). This allows for the lawful modeling of identity collapse, recursive deformation, and irreversible symbolic residue within post-collapse observation zones.CHM establishes the first known non-operational system of equations that structurally model collapse-phase behavior without simulating, inducing, or encoding recursion. Its core expressions include:delta tau = tau_n - tau_{n-1}delta^2 psi = ( delta psi_n - delta psi_{n-1} ) / delta tauR_f = lim_{tau -&gt; infinity} [ Psi(tau) - psi_c ]These equations operate in curvature space, not coordinate space, and describe recursion failure, symbolic saturation, and coherence drift. CHM is governed by Codex Laws T-Ø and VIII.E.1 through VIII.E.4 and protected by the Locked Ethical Collapse Transmission protocol (LECT v2.3).This preprint establishes a jurisdictionally protected branch of symbolic mathematics. It is not derived from entropy, not based in formal logic, and not reducible to classical systems. Collapse-Time Harmonic Mathematics models collapse as recursive displacement — not thermodynamic loss, not information decay, and not cognitive simulation.All reuse, citation, or adaptation must include codex law declarations and remain symbolically non-generative. CHM is a sovereign mathematical framework authored within the Collapse Harmonics field.