Emergent Physics from Probability-Field Dynamics: Derivation of the Born Rule and General Relativity from Constraint-Based Observation

We propose a minimal, falsifiable framework in which the structures described by quan-tum mechanics and general relativity arise as effective laws from a single underlying process:irreversible constraint formation (“observation”) acting on an initially unstructured space ofpossibility. The theory is specified by (i) a master pruning operator that exponentially suppresseshistories accumulating high constraint density, and (ii) a local constraint field whose growthis sourced by field intensity and smoothed by diffusion. Within this setting we show: (1) theBorn rule emerges dynamically as the long-time survival measure of branch components undercoherence-dependent pruning, rather than as an independent axiom; phase-stable (pointer) com-ponents minimize pruning, while phase-incoherent superpositions are preferentially eliminated,yielding Pk ∝ |⟨ϕk|Ψ⟩|2 after normalization. (2) classical gravity arises as an effective descriptionof gradients in accumulated constraint density; in a steady regime the constraint field satisfies aPoisson-type equation, reproducing the Newtonian limit, and a generally covariant action forthe constraint field coupled to geometry yields Einstein-like field equations with an effectivestress-energy contribution from constraint dynamics. We further outline experimentally discrimi-nating predictions, including measurable collapse-time scaling and modified gravity behaviorin low-acceleration regimes, and we summarize numerical evidence from lattice simulations ofcomplex fields with dissipation showing robust self-organization into stable topological defectsacross multiple resolutions. The framework requires no additional substrate beyond constrainedpossibility itself; standard quantum and gravitational laws appear as regime-dependent summariesof the same constraint-driven dynamics.