Physical Distinction Theory: From Resource-Bounded Discrimination to Quantum Geometry, Open-System Dynamics, and Thermodynamic Monotones

Physics ordinarily begins by specifying states, observables, fields, Hilbert spaces, or spacetime and then asks what can be observed. Physical Distinction Theory (PDT) reverses that order and starts from a finite-resource operational question: which physical alternatives can actually be discriminated within declared limits of energy, time, control, spatial access, and error? This paper develops PDT as a resource-relative theory of physically accessible distinction and, equally importantly, proves where that primitive is insufficient. A scalar distinction capacity is shown not to determine local geometry, and a strengthened ℓp counterfamily proves that complete erasure and elementary radial resolution alone do not force Euclidean structure. With an explicit reversible-distinction-equivalence assumption, the elementary state body is conditionally forced to an ellipsoid and hence a Euclidean ball. Composite non-uniqueness is then proved, making the subsequent n = 3 Bloch-ball selection an imported reconstruction corollary rather than a PDT-native theorem. Conditional Born-weight and Tsirelson theorems are stated with their assumptions exposed. For dynamics, the paper replaces a metric-only rate with an exact total distinction tensor that separates resource-metric motion from state-flow motion. Controlled environmental records yield exact pure- and mixed-record coherence relations and an operational time-local ADDE representation, while a same-input theorem shows why these relations do not by themselves modify microscopic quantum mechanics. Resource-restricted hypothesis-testing and free-energy monotones, computational audits, real-data stress tests, falsification rules, and a sharply delimited gravity frontier complete a reproducible foundations program.