Abstract
This paper is the first step of the Dual–Flux programme, which explores how spacetime-like structure may emerge from an extremely minimal pre-geometric ontology. No manifold, metric, topology, or primitive time parameter is assumed. Instead, the framework starts from two informational flux modes, subject to a single global conservation rule.
Part I is structural rather than dynamical. We argue that maintaining compatibility of repeated dual-flux interactions requires a distinguished compatibility locus, interpreted as a present surface P0, together with a stabilising response mode that can retain coherent information. The asymmetric roles of the two fluxes induce a minimal three-step compatibility cycle, encoded as a discrete clock ℤ3t, whose coarse-grained action yields an effective internal complex phase. The chirality of a full cycle induces a projective lift (spin clock) ℤ4t acting on this internal phase sector. Under explicit structural assumptions (reality, associativity, irreducibility, isotropy, and the presence of several internal response channels), the resulting internal algebra closes minimally on the quaternion algebra ℍ, whose imaginary subspace is a three-dimensional isotropic sector. Finally, overlaps between coheron activation patterns on P0 define a positive Gram operator which, generically on a spanning family, induces a positive quadratic form on this sector, yielding a 3D spatial pre-metric.
The aim of Part I is modest: to provide one coherent route from a non-geometric dual-flux ontology to a (1+3) pre-geometric spacetime architecture. Dynamical equations, causal propagation, Lorentzian signature, and curvature require additional dynamical assumptions and will be addressed in later parts of the Dual–Flux programme.
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Dual–Flux Foundations I (Zenodo)
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