The Continuity Stack — Foundations I: Unified Structural Ontology

This paper fixes the ontological ground upon which any continuity‑conditioned or identity‑bearing architecture must stand, and does so by stating, with a certain austerity and without the usual academic evasions, that structure cannot be understood without first naming the differentiated Field, the patterned Structure that stabilises relation across it, the Local\ Structuration through which organisation becomes legible, and the execution substrate (H, E, M) from which all realised patterns arise. The argument proceeds by identifying the invariants—differentiation, boundary, gradient, persistence, perturbation, viability—that any structural account must honour, and by introducing the mapping: (H, E, M) PatternSpace as the hinge through which substrate behaviour becomes structurally intelligible. A taxonomy of operator classes is then fixed to constrain the admissible space of transformation, ensuring that later continuity‑native mechanisms cannot drift beyond the ontology that grounds them. Structural adequacy is defined minimally, not as a dynamic variable but as the threshold at which stabilisation becomes real rather than accidental, and the substrate‑rooted commitments are made explicit to prevent the field from collapsing into phenomenological looseness. The result is an ontology that cannot be revised downstream without dissolving the architecture itself, and which therefore serves as the necessary foundation for the information‑continuity theory, substrate‑rooted identity, execution‑rooted provenance, and continuity‑native operator stack developed in the subsequent papers.