The Principle of Informational Distinction. From Measurable Distinction to Quantum Action and Gravitational Geometry

We introduce the Principle of Informational Distinction (PID) as an operational framework in which information is defined as the capacity of a physical system to sustain stable, measurable distinctions under time evolution. Two platform-dependent observables — a structural momentum Ω ([Ω] = M²LT⁻¹) and a synchronisation velocity Vₛ ([Vₛ] = LT⁻¹) — define a balance capacity P ≡ ΩVₛ ([P] = M²L²T⁻²), treated as conserved on windows diagnosed by an explicit regime gate (Step 0). A causal ceiling vₘₐₓ bounds propagation; the channel aperture w ≡ Vₛ/vₘₐₓ ∈ (0,1] parametrises the operational regime. On diagnosed conservative windows, treating P as window-invariant under the chart-redundancy and uniform-cell contracts fixes a symplectic geometry on the (Ω, Vₛ) plane and thereby induces phase-space structure, areal quantisation, and an action-scale closure — none of which are assumed as independent postulates. In particular, the action-scale closure is tested in its operational domain form ℏstd =? 2κcan·P̂, where κcan is a clock-based estimator with [κcan] = TM⁻¹ and P̂ the exported balance capacity; on closure-eligible platforms neither acquisition chain uses ℏ as input. Five quantitative predictions (P1–P5), each with explicit PASS/FAIL criteria, encode the empirical content. An anticircular dataflow enforces that each prediction is evaluated on disjoint pre-registered datasets, preventing post hoc tuning.