Lawful Navigation

Plate XLV encodes the C015 constitutional architecture of lawful navigation across three explanatory jurisdictions. Title block: C015 — Lawful Navigation · Estimation, Integrity, and Constitutional Governance. Governing axiom: Preserving reference before action is a structural principle that appears across multiple jurisdictions while remaining faithful to the methods, evidence standards, and governing principles of each. Corner seals: Reference is first. Law is governing. Then proceed. / I* remains invariant · dI*/dt = 0. Center column — five-step architectural sequence: 1. Preserve Reference — Hold the governing reference constant; 2. Estimate State — Determine the present state from observations; 3. Evaluate Integrity — Determine whether the estimate is trustworthy; 4. Govern Permissibility — Determine whether execution is constitutionally permissible; 5. Execute and Continue — Execute lawful action, acquire new observations, repeat the cycle. Recursive loop shown from step 5 back to step 2. Center top: Invariant Reference I* — The governing constant. The standing truth. I* does not move. It does not drift. It is not estimated. It governs estimation, integrity, and action. dI*/dt = 0. Left column — Three Jurisdictions: I. Estimation (What is my current state?) — examples: Kalman Filter, Extended Kalman Filter, Invariant Kalman Filter; II. Integrity Evaluation (Can this estimate be trusted?) — example: RAIM (Receiver Autonomous Integrity Monitoring); III. Constitutional Governance (Given a trusted estimate, is execution constitutionally permissible?) — Standing State example: I* Guardian; Governance determines whether lawful navigation may continue. Right column top — Three Residuals table: Estimation: Prediction minus Measurement / Is the estimate accurate? / Improve estimation; Integrity: Navigation solution minus Consistency Requirements / Can the estimate be trusted? / Protect navigation integrity; Constitutional: Δ(t) = x(t) − I* / Does development remain constitutionally coherent? / Preserve invariant reference. These residuals are not mathematically interchangeable. Each belongs to a different explanatory domain. Their recurrence is structural, not literal. Right column bottom — Jurisdictional Contributions: GPS / Position and timing observations; Kalman Filtering / Recursive state estimation; RAIM / Integrity monitoring and evaluation; M002 / Invariant constitutional reference (I*); M089 / Constitutional governance through the I* Guardian. Bottom panel — Structural Recurrence: five-node sequence: Reference → Estimation → Integrity Evaluation → Constitutional Governance → Execution. Navigation succeeds when reference is continuously preserved. Lawful action is possible only when estimation is trustworthy, integrity holds, and governance permits execution. Footer: NOT MOTION. NOT CONFIDENCE ALONE. BUT LAW. PRESERVE REFERENCE. THEN PROCEED. Companion to essay C015 (Lawful Navigation: Estimation, Integrity, and Constitutional Governance). Dependency chain: M002 → M089 → C014 → C015 → P045.