Six Birds Foundations V: Endogenous Closure — A Catalog of Structural Laws for Living, Cognitive, and Social Systems

The structural laws of the Six Birds corpus through Foundations IV are stated from the standpoint of an external theorist: the theorist declares a lens, detects an obstruction, installs a repair, prices a residual, and runs the audit. This paper makes the closure apparatus part of the carrier. An endogenous closure system carries its own instruments, ledgers, repair generator, boundary records, and re-audit loop, and its claims of self-repair are admitted only when the relevant records are produced by its own transitions under a closed-loop source policy. Six definitions (D1–D6) and sixteen laws (E1–E16) give the resulting catalog: endogenous repair, bounded reflexivity, self-maintenance, repair compilation and collapse; priced exposure, alarm, control prices, and probe acquisition; stack rewrite, individuation, and repair transport; and reconsolidation, offline reclosure, and adaptability. The contributions are labelled throughout. New: the E-system and closed-loop-scope definitions (D4, D5), the status partitions of E1–E5, E7, E8, and E10–E16, and the carried-source theorem of E1, none of which is stated in an earlier corpus paper (E6 recovers the Karush–Kuhn–Tucker conditions and adds a scope repair; E9 recovers same-family saturation and adds only the allocation–acquisition arbitration record). Sharpened: typed records of inherited notions (D1, D2, D3, D6), exact characterizations, and minimized falsifiers. Recovered: the split-pair descent, no-free-distinction, closure-deficit, adequacy-residual, source-of-truth, top-down-channel, self-audit, and holonomy apparatus of the earlier corpus, and the Karush–Kuhn–Tucker conditions of convex duality, all cited at the result and consumed as certified inputs rather than re-proved. The laws are carrier-side and substrate-independent, so living, cognitive, and social systems enter on equal terms as candidate realizations of the same typed hypotheses, not as metaphors for one another; each candidate becomes an instance only when the bridge data and controls named in the law are supplied, and no domain realization is established here. Each law is stated in the six-part normal form inherited from Foundations IV, with an obstruction or falsifier, an exactly-one status partition where applicable, a proof spine, interaction discipline, and explicit nonclaims. D1–D6 and E1–E16 are represented in the companion Lean 4 development, whose theorems are conditional verification results over host-certified predicates, and in a preregistered finite campaign whose exact counts are implementation receipts; two interpretive corollaries, Alarm Fatigue and Operational Selfhood, remain unformalized and are marked accordingly. The executed particle and neural substrate experiments of the companion life-focused development are transcribed as life-facing null, drive, maintenance, motif, and intervention evidence under explicit nonclaims, and an unrun planarian-regeneration protocol states a concrete biological promotion target and its falsifiers. No definition of biological life, consciousness, death, welfare, or autonomous evolution is claimed.