The Conservation of Contingency: Relativity's Discrete Completion and the Incompressibility Floor of Physics

Every relativity principle in the history of physics is shown to decompose into two components: an empirical claim that a symmetry holds (equivalently, that an absolute structure is absent), and a one-line selection lemma — no natural (isomorphism-equivariant) construction can select a member of a fixed-point-free orbit. The historical sequence (position, velocity, simultaneity, gauge phase) exhausted the identity component of the relevant symmetry groups. It is proved that the remaining freedom is the component group π0: for the discrete labeling pair (matter vs. antimatter, future vs. past), the CPT theorem canonically gates the diagonal, leaving exactly one Z2 — a single bit that no conjugation-invariant principle can fix. Around this floor, a conservation principle is established: reformulations of physical theory transfer contingency but never reduce it. Three mechanisms are isolated — a conjugation obstruction with two meta-barriers, a multiplicity-starvation identity equating the Chevalley–Weil leading density with the Riemann–Hurwitz density (g−1)/|G|, and a uniqueness-versus-adjustability exclusion — verified across the surveyed classes (curves, vertex operator algebras, positive characteristic, lattices, Shimura milieus, operator algebras) with a complete escape-mode taxonomy (import, symmetry, extinction) and zero surviving counterexamples. Physical dualities audit to zero import and generate the presentation symmetry under which the incompressible core is invariant. The framework yields measure-free readings of anthropic bounds, locates the irreducible core of the quantum measurement problem, and issues pre-registered, dated predictions: JUNO mass ordering at ≥96%, a Σmν triple test near 0.06 eV, and Euclid dark-energy benchmarks for 21 October 2026. All numerical claims are reproducible from self-contained recipes, independently verified by blind reimplementation. The result blocks necessity-type derivations of physical content within all surveyed principle classes; it asserts neither absolute impossibility nor any restriction on typicality- or dynamics-based explanation. Registration note: The verdict rules of Section 8 (Table 10) are frozen as of the posting date of this record — the public posting instrument for the paper's pre-registered, dated predictions. Reference implementations and the machine-audit manifest are available from the author upon reasonable request.