Structural Arithmetic Supporting Results: Recurrence Positivity, Reachable Freshness and Difference Annihilators

This paper connects three supporting-result families in structural arithmetic: positivity of a rational recurrence on a sufficient parameter region, the relationship between orbit injectivity and reachable-state freshness, and conditional annihilation of polynomial-periodic sequences. Nineteen declarations across five included formal modules are accompanied by minimized saved acceptance records from an explicitly selected external proof extension; these are not nineteen native admissions. Finite examples are distinguished from general results. Recurrence necessity, unconditional freshness and coverage, and the required floor/rounding decomposition remain outside the established scope. Actual proof bodies are included for inspection; no fresh compilation or resolution of a parent conjecture is claimed.