Pith Number

pith:TILSPHYA

pith:2021:TILSPHYA3SBHDUJKG7AJBZELFA

not attested not anchored not stored refs pending

Gagliardo-Nirenberg inequalities in Lorentz type spaces and energy equality for the Navier-Stokes system

Wei Wei, Yanqing Wang, Yulin Ye

arxiv:2106.11212 v1 · 2021-06-21 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TILSPHYA3SBHDUJKG7AJBZELFA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T02:50:57.888514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a17279f00dc8271d12a37c090e48b280fa01739943f9e7484fe859ede8b01a1

Aliases

arxiv: 2106.11212 · arxiv_version: 2106.11212v1 · doi: 10.48550/arxiv.2106.11212 · pith_short_12: TILSPHYA3SBH · pith_short_16: TILSPHYA3SBHDUJK · pith_short_8: TILSPHYA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TILSPHYA3SBHDUJKG7AJBZELFA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9a17279f00dc8271d12a37c090e48b280fa01739943f9e7484fe859ede8b01a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28719aca343f1d11abfb0e41fdfb3a8ce98aa78a50cf10890fef9b2ddbddc28a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-06-21T15:54:24Z",
    "title_canon_sha256": "e2cfce985c776783788af27bacef08b311082bcab97004956a44e4cddb225ab1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.11212",
    "kind": "arxiv",
    "version": 1
  }
}