Route--T Toolkit Note: TR1--TR3 as a Reusable Extraction Module (SAPZ Navier--Stokes v5.6r1, Supplement v0.2)

# Overview This record releases a short **toolkit note** abstracting the *Route–T transport-bypass* mechanism from the main SAPZ Navier–Stokes package: - Main package (v5.6r1): DOI 10.5281/zenodo.18835992 - Supplementary notes (corollary ledger + suitability contract, v0.4): DOI 10.5281/zenodo.18843294 The present toolkit isolates the three-step extraction module **TR1–TR3** and an explicit **Approximation Bridge (AB)** in a reusable, referee-facing “interface” form. # What is included (v0.2) - **Route–T toolkit note (TeX/PDF)**: `SAPZ_RouteT_Toolkit_v5.6r1_v0.2.*` - Object dictionary preventing symbol-role confusion (envelope residual vs extraction residual) - Minimal assumptions for TR1 (representation), TR2 (positivity), TR3 (local-to-sup) - Combined template theorem: positive transport residual ≥ defect − (declared errors) - Checklist-style Approximation Bridge (AB) for passage from smooth approximants to weak limits - **One-page instantiation table** pinning toolkit labels (A,P,T3,B) to the v5.6r1 package # Label-first convention All references are **label-first**: package components are cited by names (Gate A, CT3 persistence, Route–T extraction, Gate B),with theorem numbers only as secondary parenthetical metadata. # Scope & non-claims - This note introduces **no new analytic input** beyond the v5.6r1 package.- It does not claim Route–T applies verbatim to every transport PDE; it provides an auditable interface designed for adaptation. # Author Lee Byoungwoo