Conditional Unlocking Fields: A Necessity-Based Framework for Identity Persistence (Version 2.0)

Version 2. 0 of the Conditional Unlocking Fields (CUF) framework, a necessity-based recursive law for identity persistence derived from a single ontological primitive: Necessitated Update Activity (NUA). This version replaces the informal viability count of Version 1 with a fully specified measurement architecture and introduces formal invariance requirements and an empirical validation programme. The framework defines identity persistence through a canonical system consisting of a state, generative transition, constraint functional, viability bound, and stabilization ledger operator. A strict four-stage update protocol (Propose → Measure → Correct → Record) enforces preledger measurement ordering, making the extraction of pre-ledger overflow K (n) K (n) K (n) structurally non-substitutable. The measurement architecture introduces: Pre-ledger overflow K (n) Block-averaged overflow Kb (b) Kb^ (b) Kb (b) Stabilization burden Mb=CVaR0. 95Mb = CVaR₀. ₉₅Mb=CVaR0. 95 Identity-lock threshold k∗=Q0. 95Kb (b) ∣s=scritk^* = Q₀. ₉₅Kb^ (b) s = s₂ₑ₈ₓk∗=Q0. 95Kb (b) ∣s=scrit Normalized burden M~b=Mb/k∗Mb = Mb / k^*M~b=Mb/k∗ Identity persistence is determined by the condition M~b<1Mb < 1M~b<1, with collapse occurring at M~b≥1Mb 1M~b≥1. This boundary is structurally derived and not an arbitrary normalization. An empirical programme spanning six dynamical system classes (discrete maps, delay differential equations, coupled map lattices, cellular automata, stochastic control, and regime contrasts) demonstrates that persistence collapse follows a universal three-phase structure (plateau → transition → collapse) across deterministic chaotic systems and is absent in stochastic controls. Results are validated under operator perturbations, multiple seeds, and invariant transformations. The framework includes: A formally defined invariance group G=GW×Gb×GgG = GW Gb GgG=GW×Gb×Gg Five structural falsification criteria Four misuse classes (M1–M4) Three certification levels (CUF-A, CUF-B, CUF-C) Version 2. 0 supersedes Version 1 (Zenodo DOI: 10. 5281/zenodo. 18124579) and represents the first operational and empirically grounded formulation of the CUF framework.