The Structural Determinant Hypothesis: Existence as Structural Equilibrium

This paper advances the Structural Determinant Hypothesis (SDH): to exist is to be a structural equilibrium, that is, a configuration that holds by virtue of its own self-consistency, so that its law is not imposed from without but is identical with its way of holding. The thesis is given a precise necessary condition: generability from a finite computable basis (K1) together with an admissible partial self-reference bounded by a diagonal limit (K2). A toy model shows that the conjunction has content: it partitions describable structures non-trivially and answers the cardinality form of Newman's objection (unconditionally for K1; conditionally — for a fixed language — for K2). A two-level architecture distinguishes the atemporal structural condition (Level 0) from its physical, temporal projection (Level 1); this removes the objection from heat death and places the problem of Boltzmann brains within the competence of Level 1 physics. Catalogue ontologies certify existence by an external criterion — mathematical consistency, membership in an ensemble, evolutionary history. SDH denies the catalogue as a type of ontological claim: a non-equilibrium configuration is not struck from a list of the real, because it was never a candidate on it. The position is formulated in the grounding literature as ground-identity — a fourth position alongside foundationalism, infinitism and coherentism — on which, at the fundamental level, object and ground are identical. SDH is compatible with any multiplicity of realized configurations — one, many, infinitely many — since its claim concerns the regime of realization, not its quantity. It is compared, without any final ranking, with the Multiverse, the Mathematical Universe Hypothesis, cosmological natural selection, the anthropic principle, primitivism about laws, constructor theory, causal set theory and the Wolfram Physics Project; its robustness to the contested status of the fine-tuning problem is established. The hypothesis is advanced as an inductively motivated postulate with an openly named bridging assumption: it is not falsifiable in Popper's sense, but it is open to rational assessment, and its principled open questions — above all, why this configuration rather than another is realized — are recorded as constitutive boundaries of the position, not disguised. NEW IN VERSION 184 - Appendix A.4: an elementary uniqueness theorem proved in place — a solution of the reflexive domain equation anchored in the tower of approximations is unique up to isomorphism of solutions and coincides with the canonical one. This replaces an external citation with the paper's own proof, all computations given in full. - Section 12: the entry of the two-level architecture is closed by derivation — Level 0 and Level 1 are shown to be one reality in two aspects rather than two independent facts; and closure of the regress is recast as a property of a class of expositions, with the strongest catalogue exposition analysed and its two ungrounded nodes exhibited. - Central Thesis: the transfer of self-consistency from parts to whole is made conditional and precise (a localization lemma under the principle P), the classical counterexample is acknowledged, and the thesis "equilibrium is not eternity" is stated explicitly. - Appendix A.7 (new): the physical edge — type III von Neumann algebras, amenability rather than the trace as the substantive watershed, a splitting lemma with an effective layer showing that the modular flow of canonical trace-free factors is computable together with its presentation, passivity (Pusz–Woronowicz) as a second theorem-level support for equilibrium, and a rule restricting claims about uncomputability to the level of classes of problems. - Clarifications of cardinality throughout, and the principle of methodological similarity named explicitly. Full text in English. The Russian original of this version is available from the author.