The
framework.

Phase Differential Theory proposes a single primitive: the differential of phase, Δϕ, between two coupled relational systems. It is a geometric relational quantity rather than an amplitude, a probability or a state.

Every subsequent construction in the framework — coherence, geometry, matter, interactions — is expressed in terms of Δϕ and its evolution.

The framework is grounded in a small number of axioms concerning admissible transport, closure of the phase-differential structure and the finiteness of coherence.

These axioms constrain the constitutive functionals available to the theory and drive the uniqueness results developed in the foundational papers.

Transport in PDT is defined without recourse to a background metric. It is expressed through relational operators acting on scalar phase fields and characterised by transport capacity and completeness theorems.

Coherence describes the degree to which coupled systems maintain phase relations under transport. The framework provides quantitative measures of coherence and studies its monotonicity properties.

When accumulated phase differential crosses a critical coherence threshold the system undergoes a deterministic phase snap: a resolution event that PDT identifies with the phenomenon usually described as wavefunction collapse.

The snap is governed by the underlying phase geometry rather than by a probabilistic postulate.

Measurement is modelled as the phase snap that occurs when an apparatus enters phase coupling with the system under study. The Born rule appears as an effective ensemble statistic over resolutions.

Spatial and metric structure emerge from the pattern of phase resolutions. Transport horizons and boundary geometry are characterised through quasi-local invariants derived within the foundational programme.

Time is treated as the ordering induced by successive phase resolutions rather than as a fundamental parameter. Its role in the dynamics is that of an emergent bookkeeping variable.

Localised defect structures in the phase field yield the effective particle content of the theory. Their interaction dynamics reproduce Yukawa-, Coulomb- and gravitational-type couplings through a common source propagator.