Supplementary Notes to "SAPZ Singularity Principle for Navier–Stokes (v5.6r1)": Corollaries and LEI Contract

# Overview This record releases two **supplementary notes** to the main package: - **Main package (v5.6r1):** “SAPZ Singularity Principle for Navier–Stokes” (Main + Companion + Verification Note), Zenodo DOI: \(10.5281/zenodo.18835992\). These notes are designed to improve **referee-facing clarity** and **verification ergonomics**. They introduce **no new analytic input** beyond the validated statements of the v5.6r1 package. # What is included 1) **Corollary ledger + proof maps (v0.3)**- File: `SAPZ_Corollary_Ledger_v5.6r1_v0.3.tex` (and PDF if included)- Content: a list of downstream consequences that become available once the package-level global regularity theorem is accepted (e.g., emptiness of the singular set, instant smoothing for \(t>0\), higher-regularity propagation, uniqueness in the package class, bounded-domain qualitative dynamics), each with a short “proof map” referencing package checkpoints. 2) **Suitability / LEI contract note (v0.3)**- File: `SAPZ_Suitability_Contract_v5.6r1_v0.3.tex` (and PDF if included)- Content: an explicit, checklist-style sealing of the **local energy inequality (LEI)** contract used at the endpoint continuation (Gate B), restricted to the **solution class covered by the package** (Leray–Hopf limits produced by standard approximation schemes). # Relation to the main package (v5.6r1) These notes are intended to be linked in Zenodo as **“isSupplementTo”** the main package record (DOI \(10.5281/zenodo.18835992\)). - The **main package** contains the proof architecture and the trusted core base (TCB).- The **supplementary notes** provide: - a corollary ledger that answers “what automatically follows if the proof is validated,” and - a standalone LEI/suitability contract that prevents “hidden assumption” disputes at the Gate–B endpoint layer. # Label-first convention (robust under renumbering) To reduce version-fragility, both notes use a **label-first convention**:package components are cited by their **names** first (e.g., Gate A, CT3 persistence, Route–T extraction, Gate B),with theorem numbers only as secondary parenthetical metadata. # Scope & non-claims - These notes do **not** claim to resolve turbulence phenomenology.- They do **not** replace the main package proof.- They are “referee/verification notes” that reorganize consequences and contracts once global regularity is accepted. # How to cite - For the **main Clay-level claim and core proofs**, cite the main package: - “SAPZ Singularity Principle for Navier–Stokes (v5.6r1)”, Zenodo DOI \(10.5281/zenodo.18835992\). - For the **corollary ledger / suitability contract exposition**, cite this supplementary record. # Author Lee Byoungwoo