p-adic and D-FUMT8 Correspondence: Each Prime as a FLOWING Instance, with Lean 4 / Mathlib Formalization

Abstract

Adds a fourth rigorous anchor to the Rei-AIOS D-FUMT8 logic by exhibiting each p-adic completion Q_p as a distinct FLOWING-instance of the same rational. Empirical: 23/25 (92 percent) of representative rationals are FLOWING under the standard prime list. Formal: 11 zero-sorry Lean 4 theorems including two FLOWING-witness inequalities (dfumt8MarkNat 2 27 != dfumt8MarkNat 3 27 and dfumt8MarkNat 13 247 != dfumt8MarkNat 2 247) proved by native_decide via Mathlib padicValNat. Together with Papers 69 (Schnorr), 75-76 (QuTiP), and 77 (LeanDFumt), this completes a QUADRUPLE ANCHOR for D-FUMT8 spanning computability, physics, proof theory, and number theory. To our knowledge the first explicit p-adic ↔ eight-valued logic mapping.