Daif Theory: Pregeometric Time-Matter

This paper develops a speculative and falsifiable framework in which temporal succession and spacetime geometry are conjectured to emerge from a pre-geometric quantum substrate termed time-matter. Causal relations among substrate configurations constitute succession, while a Lorentzian metric and universal proper time are required to arise in the infrared. A locally finite acyclic quantum hypergraph carries bosonic timon, antitimon, neutral-binding, and portal modes. Its conditional continuum ansatz is a hidden Abelian gauge theory containing a complex timon field ΦT, a neutral field χ, and a massive mediator AμT. Gauge symmetry, vacuum, mass, bound-state, background-phase, portal-exchange, and extra-dimensional results follow from explicit ansätze. Linearized timon-sector fields provide hypothetical massive scalar and vector waves, whereas the observed gravitational wave remains the massless spin-2 perturbation of the emergent metric. In the minimal homogeneous vacuum these channels do not mix linearly; hidden waves affect the tensor equation only through their transverse-traceless stress or through an explicitly declared inhomogeneous or nonminimal radiative portal. A Hermitian two-channel propagation ansatz then gives a conserved gravitational-to-hidden conversion probability and a waveform transfer function, while current null polarization and residual tests require the effect to be small. The phenomenological core classifies every stationary-independent-increment monotone operational time through its Bernstein exponent. The induced quantum dynamics is an exact completely positive random-unitary semigroup; ordinary double-commutator phase diffusion is only its low-frequency limit. A covariant influence-functional construction relates differential-clock covariance to a smeared field Hadamard kernel and shows that a free massive field in a stationary vacuum has no zero-frequency white-noise component, so nonzero diffusion requires a gapless, excited, nonstationary, or discrete source. Adiabatic elimination of coherence in the Hermitian two-sector portal gives a conditional Lorentzian transport rate and an energy-density source proportional to the sector imbalance; paired continuity equations conserve the exchange term and quantify competition with cosmological dilution. A coordinated three-channel test combines separated frequency references, differential atom interferometry, and long-baseline magnetometers. Under a declared ultralight-halo benchmark, frequency fixes the candidate mass, occupation, coherence length, coherence time, and spatial phase; a universal clock–matter-wave transfer law and rank-one cross-spectral closure then provide joint failure conditions. These algebraically dependent benchmark relations are not counted as independent confirmations, and the magnetometer channel requires a distinct portal coupling. Existing measurements provide null constraints or detector demonstrations rather than a common-band detection. Linear cosmological perturbations, a restricted causal-set curvature bridge, one-loop running, a finite-temperature bounce problem, a conditional baryon portal, and a black-hole shooting-and-stability problem supply further quantitative consistency tests. No parameter fit, graph-derived portal parameters or cross-channel coupling, baryogenesis solution, stable nontrivial black-hole solution, selection of 3+1 dimensions, unique derivation of general relativity, or empirical time-matter signal is obtained. The construction is therefore a conditional effective research program, not evidence that time-matter exists.