The Minimal Continuity Framework is a formal and executable architecture for evaluating whether a system remains recoverably continuous through transformation. The framework begins with two foundational conditions: the Bootstrap Condition, B₀, which requires an attempted beginning either to remain recoverably connected to the continuation it initiates or to terminate through a registered collapse; and the First Admissibility Constraint, C₀, which excludes hidden operative dependence on conditions that cannot be recovered, represented, or reconstructed within the system’s own continuation processes. These conditions motivate the Continuity Kernel: Ω = (RC, AT, Λ, χ, E, V) where RC evaluates recoverable continuity, AT represents admissible transformations, Λ records append-only lineage, χ measures the depletion of admissible options, E represents remaining continuation capacity, and V denotes the minimum support required to prevent immediate collapse. The work distinguishes foundational admissibility conditions from the operational kernel and from later constructed extensions. These extensions include observer-triggered repair, distributed continuity, support transfer, reactive lattices, recoverability geometry, finite recovery horizons, relational ordering, and branch-sensitive representations. A reference implementation is included to make the framework operational. It provides candidate-transformation generation, continuity evaluation, admissibility filtering, lineage registration, constraint-pressure measurement, expressive-capacity estimation, repair, recovery, support transfer, structured collapse, adversarial testing, comparative policy evaluation, threshold optimization, and exportable experimental results. The framework is intended as a general research architecture for systems whose continuation must remain reconstructible through change. Potential applications include distributed systems, fault recovery, event-sourced architectures, safe control, error correction, biological organization, adaptive systems, and lineage-aware artificial intelligence. The work does not claim that the Continuity Kernel uniquely follows from its foundational conditions, nor that its physical-like extensions constitute a derivation of established physical laws. It is presented as a transparent, testable, and extensible minimal sufficient construction for studying recoverable continuation.
James Shipkowski (Fri,) studied this question.