ORIGIN OF LIFE: THE CLOSURE THRESHOLD - The Origin of Life Is the Onset of Operational Closure — a Transition from Self-Organisation to Self-Reference, Not a Threshold in Complexity or Dissipation

Scope: This article establishes a demarcation thesis for the origin of life: the living/non-living boundary is not a threshold value on any rising scalar — complexity, dissipated work, replication fidelity, kinetic stability — but a change of relational kind, the onset of operational closure. The thesis is stated formally, a closure measure κ is defined and computed, an in-silico model demonstrates that self-maintenance organises along κ independently of complexity and dissipation, and the chemical experiment that would confirm or refute the thesis is specified exactly. The claim concerns the individual, metabolic sense of being alive; its extension to the population and lineage sense is identified as the open frontier. The argument is theoretical; its decisive verification is experimental and is set out in §7. Abstract Theories of life's origin locate the living/non-living boundary on a rising scalar axis: more dissipated work (dissipative structures; dissipative adaptation), greater kinetic stability (dynamic kinetic stability), or higher molecular complexity (autocatalytic sets; assembly index). Against this, the present article argues that the boundary is not a magnitude but an organisation. A driven chemical system becomes alive at the moment it achieves operational closure — when it produces the very constraints that maintain it and gates its own boundary, so that its own persistence becomes the variable it regulates. Complexity, dissipation, and replication are necessary scaffolding and excellent biosignatures, but none is the boundary; closure is. The article names the two regimes the field conflates — self-Organisation without closure (ORG) and self-Reference through closure (REF) — and defines a closure measure κ on reaction networks as the fraction of essential constraints that are internally produced and mutually supporting. Computed on canonical systems, κ is zero for a Bénard cell and for a structurally elaborate vesicle that cannot make its own catalyst, and approaches unity for a self-producing vesicle and a minimal autopoietic network. Across a large ensemble of model networks, the capacity to recover from damage — the operational signature of self-maintenance — tracks κ and remains predicted by κ when complexity and dissipation are held fixed, while complexity and dissipation lose their predictive force once closure is accounted for. The thesis yields sharp, contrary predictions against every rising-axis account and a matched-design chemical experiment that would falsify it. The boundary of the claim — individual metabolic life, not evolutionary lineage — is stated precisely, and the coupling between the two is posed as the central unsolved problem. Keywords: origin of life · operational closure · constraint closure · closure measure κ · autopoiesis · dissipative adaptation · assembly theory · self-maintenance · demarcation of life Method ALGUILAS-AI Dialectical Engine