Life as Lineage-Capable Boundary Closure: A Multitype Continuation Criterion for the Origin of Life

This theoretical preprint reframes the origin of life as the transition to a lineage-capable chemical system rather than the appearance of a first life-like object. It introduces assay-relative functional types and a non-negative multitype continuation operator whose entries represent the expected number of accepted causal daughter states produced by each parent type. Independent genesis and immigration are modelled separately and do not count as lineage continuation. The framework distinguishes three thresholds: continuation, genealogical inheritance, and evolutionary differentiation. It formally shows why snapshots, composition alone, recurrence under a shared environment, and uncorrected population growth are insufficient to establish life-like lineage continuation. It also specifies experimental controls, estimation procedures, uncertainty treatment, and explicit falsifiers for protocell and origin-of-life studies. The paper does not claim to identify the historical first living system. It proposes a measurable criterion for determining when chemistry becomes capable of intrinsic lineage continuation.