# Overview This record releases **Route–T Toolkit Note (v0.3)**, a referee-facing “interface document” that abstracts the**Route–T transport-bypass** mechanism from the SAPZ Navier–Stokes package (v5.6r1). It is designed to be **auditable and reusable**:- TR1–TR3 are stated as a three-step extraction module,- an explicit **object dictionary** prevents symbol-role confusion (envelope residual vs extraction residual),- and an **Approximation Bridge (AB)** gives a checklist contract for passing identities from smooth approximants to weak limits. This note introduces **no new analytic input** beyond the validated statements of the main package. # Related records - Main package (v5.6r1): **10.5281/zenodo.18835992**- Supplementary notes (corollary ledger + suitability/LEI contract, v0.4): **10.5281/zenodo.18843294** # What is included (v0.3) Files:- `SAPZ_RouteT_Toolkit_v5.6r1_v0.3.tex` (and PDF if included) Contents:1) **TR1 (Representation)**: transport residual is rewritten as a localized commutator pairing plus named error budgets. 2) **TR2 (Positivity)**: symmetrization + kernel positivity yield a lower bound by a scale-matched defect \[ \mathsf{T}_\varepsilon(t;\chi)=\varepsilon^{-5}\int_{B_\varepsilon(0)}\int_{\Omega}\chi(x)\,|u(x,t)-u(x-h,t)|^2\,dx\,dh . \]3) **TR3 (Local-to-sup)**: near-maximizer localization promotes local averages to a sup-type defect.4) **Template extraction theorem**: \[ (r^{\mathrm{tr}}_\varepsilon(t))_+\ \ge\ c_{\mathrm{tr}}\mathsf{T}_\varepsilon(t)\ -\ \bigl(\mathrm{Err}^{\mathrm{tr}}_\varepsilon(t)+\mathrm{Err}^{\mathrm{pos}}_\varepsilon(t)\bigr). \]5) **Approximation Bridge (AB)**: checklist stability of TR1–TR3 under \(L^2\) strong / \(H^1\) weak convergence.6) **One-page instantiation snapshot** mapping toolkit labels (A, P, T3, B, LEI) to the v5.6r1 package.7) **New in v0.3:** a **one-page “Failure modes / Referee FAQ”** plus a **quick audit checklist**. # What is new in v0.3 - Added a **Failure modes / Referee FAQ (one page)** documenting common objections: - symbol-role confusion (envelope residual vs extraction residual), - scaling misunderstandings (spurious \(\varepsilon^3\) factors), - concerns about hidden regularity/pressure cancellations in positivity, - measurability of near-maximizers, - approximation-bridge assumptions (no hidden derivatives), - explicit error-budget naming and absorption rules.- Added a **quick audit checklist**: a 5-item referee checklist to mechanically verify TR1–TR3 + AB. # Label-first convention References are **label-first**: components are cited by their names (Gate A, CT3 persistence, Route–T extraction, Gate B),with theorem numbers only as secondary parenthetical metadata. Numbers are **secondary**. # Scope & non-claims - This note is not a turbulence phenomenology paper.- It does not claim Route–T applies verbatim to every transport PDE; it provides an auditable interface designed for adaptation.- It does not replace the main package; it documents a reusable module extracted from it. # Author Lee Byoungwoo