Supplementary Notes to "SAPZ Singularity Principle for Navier–Stokes (v5.6r1)": Corollaries and LEI Contract
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901439731728384 |
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| author | Lee, Byoungwoo |
| author_facet | Lee, Byoungwoo |
| contents | <p>## What is new in v0.4</p> <p>- **Referee snapshot table added:** the Corollary Ledger now includes a **one-page table** (Claim → Inputs → 3-line proof map) to make downstream implications auditable at a glance.<br>- **Label-first convention strengthened:** both notes explicitly state that **theorem numbers are secondary**, included only parenthetically; the primary references are by **package module names** (A, P, T3, B, CRIT, GR).<br>- **Pressure gauge clarified (bounded domains):** the Suitability/LEI Contract note now records standard **gauge options** (e.g., mean-zero normalization) and the corresponding bounded-domain pressure reconstruction; the \(\mathbb{R}^3\) Riesz-transform form is also noted.</p> <p># Overview</p> <p>This record releases two **supplementary notes** to the main package:</p> <p>- **Main package (v5.6r1):** “SAPZ Singularity Principle for Navier–Stokes” (Main + Companion + Verification Note), Zenodo DOI: \(10.5281/zenodo.18835992\).</p> <p>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.</p> <p># What is included</p> <p>1) **Corollary ledger + proof maps (v0.3)**<br>- File: `SAPZ_Corollary_Ledger_v5.6r1_v0.3.tex` (and PDF if included)<br>- Content: a list of downstream consequences that become available once the package-level global regularity theorem is accepted<br> (e.g., emptiness of the singular set, instant smoothing for \(t>0\), higher-regularity propagation, uniqueness in the package class,<br> bounded-domain qualitative dynamics), each with a short “proof map” referencing package checkpoints.</p> <p>2) **Suitability / LEI contract note (v0.3)**<br>- File: `SAPZ_Suitability_Contract_v5.6r1_v0.3.tex` (and PDF if included)<br>- Content: an explicit, checklist-style sealing of the **local energy inequality (LEI)** contract used at the endpoint continuation (Gate B),<br> restricted to the **solution class covered by the package** (Leray–Hopf limits produced by standard approximation schemes).</p> <p># Relation to the main package (v5.6r1)</p> <p>These notes are intended to be linked in Zenodo as **“isSupplementTo”** the main package record (DOI \(10.5281/zenodo.18835992\)).</p> <p>- The **main package** contains the proof architecture and the trusted core base (TCB).<br>- The **supplementary notes** provide:<br> - a corollary ledger that answers “what automatically follows if the proof is validated,” and<br> - a standalone LEI/suitability contract that prevents “hidden assumption” disputes at the Gate–B endpoint layer.</p> <p># Label-first convention (robust under renumbering)</p> <p>To reduce version-fragility, both notes use a **label-first convention**:<br>package components are cited by their **names** first (e.g., Gate A, CT3 persistence, Route–T extraction, Gate B),<br>with theorem numbers only as secondary parenthetical metadata.</p> <p># Scope & non-claims</p> <p>- These notes do **not** claim to resolve turbulence phenomenology.<br>- They do **not** replace the main package proof.<br>- They are “referee/verification notes” that reorganize consequences and contracts once global regularity is accepted.</p> <p># How to cite</p> <p>- For the **main Clay-level claim and core proofs**, cite the main package:<br> - “SAPZ Singularity Principle for Navier–Stokes (v5.6r1)”, Zenodo DOI \(10.5281/zenodo.18835992\).</p> <p>- For the **corollary ledger / suitability contract exposition**, cite this supplementary record.</p> <p># Author</p> <p>Lee Byoungwoo</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18845268 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Supplementary Notes to "SAPZ Singularity Principle for Navier–Stokes (v5.6r1)": Corollaries and LEI Contract Lee, Byoungwoo Navier–Stokes equations global regularity Clay Millennium Problem partial regularity suitable weak solutions local energy inequality (LEI) Leray–Hopf solutions Caffarelli–Kohn–Nirenberg (CKN) SAPZ threshold Route–T corollary ledger proof map verification protocol transport defect extraction nonlinear PDE <p>## What is new in v0.4</p> <p>- **Referee snapshot table added:** the Corollary Ledger now includes a **one-page table** (Claim → Inputs → 3-line proof map) to make downstream implications auditable at a glance.<br>- **Label-first convention strengthened:** both notes explicitly state that **theorem numbers are secondary**, included only parenthetically; the primary references are by **package module names** (A, P, T3, B, CRIT, GR).<br>- **Pressure gauge clarified (bounded domains):** the Suitability/LEI Contract note now records standard **gauge options** (e.g., mean-zero normalization) and the corresponding bounded-domain pressure reconstruction; the \(\mathbb{R}^3\) Riesz-transform form is also noted.</p> <p># Overview</p> <p>This record releases two **supplementary notes** to the main package:</p> <p>- **Main package (v5.6r1):** “SAPZ Singularity Principle for Navier–Stokes” (Main + Companion + Verification Note), Zenodo DOI: \(10.5281/zenodo.18835992\).</p> <p>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.</p> <p># What is included</p> <p>1) **Corollary ledger + proof maps (v0.3)**<br>- File: `SAPZ_Corollary_Ledger_v5.6r1_v0.3.tex` (and PDF if included)<br>- Content: a list of downstream consequences that become available once the package-level global regularity theorem is accepted<br> (e.g., emptiness of the singular set, instant smoothing for \(t>0\), higher-regularity propagation, uniqueness in the package class,<br> bounded-domain qualitative dynamics), each with a short “proof map” referencing package checkpoints.</p> <p>2) **Suitability / LEI contract note (v0.3)**<br>- File: `SAPZ_Suitability_Contract_v5.6r1_v0.3.tex` (and PDF if included)<br>- Content: an explicit, checklist-style sealing of the **local energy inequality (LEI)** contract used at the endpoint continuation (Gate B),<br> restricted to the **solution class covered by the package** (Leray–Hopf limits produced by standard approximation schemes).</p> <p># Relation to the main package (v5.6r1)</p> <p>These notes are intended to be linked in Zenodo as **“isSupplementTo”** the main package record (DOI \(10.5281/zenodo.18835992\)).</p> <p>- The **main package** contains the proof architecture and the trusted core base (TCB).<br>- The **supplementary notes** provide:<br> - a corollary ledger that answers “what automatically follows if the proof is validated,” and<br> - a standalone LEI/suitability contract that prevents “hidden assumption” disputes at the Gate–B endpoint layer.</p> <p># Label-first convention (robust under renumbering)</p> <p>To reduce version-fragility, both notes use a **label-first convention**:<br>package components are cited by their **names** first (e.g., Gate A, CT3 persistence, Route–T extraction, Gate B),<br>with theorem numbers only as secondary parenthetical metadata.</p> <p># Scope & non-claims</p> <p>- These notes do **not** claim to resolve turbulence phenomenology.<br>- They do **not** replace the main package proof.<br>- They are “referee/verification notes” that reorganize consequences and contracts once global regularity is accepted.</p> <p># How to cite</p> <p>- For the **main Clay-level claim and core proofs**, cite the main package:<br> - “SAPZ Singularity Principle for Navier–Stokes (v5.6r1)”, Zenodo DOI \(10.5281/zenodo.18835992\).</p> <p>- For the **corollary ledger / suitability contract exposition**, cite this supplementary record.</p> <p># Author</p> <p>Lee Byoungwoo</p> |
| title | Supplementary Notes to "SAPZ Singularity Principle for Navier–Stokes (v5.6r1)": Corollaries and LEI Contract |
| topic | Navier–Stokes equations global regularity Clay Millennium Problem partial regularity suitable weak solutions local energy inequality (LEI) Leray–Hopf solutions Caffarelli–Kohn–Nirenberg (CKN) SAPZ threshold Route–T corollary ledger proof map verification protocol transport defect extraction nonlinear PDE |
| url | https://doi.org/10.5281/zenodo.18845268 |