Spacetime, Derived - Second Edition

This is the Second Edition of Spacetime, Derived, continuing the work first published as Spacetime, Derived: Density Under Structural Flow (First Edition DOI: 10.5281/zenodo.19373768). The paper asks what structural relation spacetime bears to an object derived without assuming spacetime in advance. Its theorem is: At current domain authority and declared physical scope, qualifying physical Density and spacetime are co-extensive at the relevant carrier / localization level. Co-extension is an extension claim, not total property identity. The Second Edition substantially revises the derivation architecture of the First Edition. Density is re-derived at a weaker universal minimum as non-empty common interaction support among plural incorporated interaction-conditioned distinctions. Physical Density is then admitted independently through physics-owned physical objects and relations before spacetime is introduced as the comparison target. Physics independently fixes the spacetime object. The manuscript then audits the full physical spacetime structure for any additional portable spacetime-specific Structural Flow remainder and tests the independently admitted physical extensions for separation in both directions at fixed level and scope. Major revisions include removal of the former space-face / time-face architecture from minimum Density; removal of F/H/L, temporal accumulation, Recognition, and Coherence from the constitutive spacetime proof; independent physical admission of Density; independent fixation of the physics-owned spacetime target; a portable-remainder audit; explicit same-level / same-scope necessity and exclusivity tests; and replacement of the earlier structural-identity formulation with a theorem of co-extension at the relevant carrier / localization level. The theorem is explicitly falsifiable. A physically established same-level, same-scope case of spacetime without qualifying Density would break necessity. A physically established same-level, same-scope case of qualifying Density without spacetime would break exclusivity. The Second Edition also separates standing spacetime from realized physical history. Carried consequence and provenance remain physically important but are relocated downstream rather than treated as constitutive faces of standing spacetime. The work does not derive metric distance, dimensionality, topology, manifold structure, Lorentzian signature, causal cones, curvature, field equations, quantum ontology, physical constants, or measured physical content. Those remain physics-owned burdens. This Second Edition supersedes the First Edition as the current statement of the Density–spacetime derivation while preserving the First Edition as part of the public derivational record.