Pith Number

pith:4ZJBBUA4

pith:2018:4ZJBBUA44AQZKHJTEM4R54SGTN

not attested not anchored not stored refs pending

On the Relation between Very Weak and Leray-Hopf Solutions to Navier-Stokes Equations

Giovanni P. Galdi

arxiv:1809.03991 v1 · 2018-09-11 · 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{4ZJBBUA44AQZKHJTEM4R54SGTN}

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	2026-05-18T00:05:57.613872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e65210d01ce021951d3323391ef2469b5b9a189df188d91a94f624b371a117da

Aliases

arxiv: 1809.03991 · arxiv_version: 1809.03991v1 · doi: 10.48550/arxiv.1809.03991 · pith_short_12: 4ZJBBUA44AQZ · pith_short_16: 4ZJBBUA44AQZKHJT · pith_short_8: 4ZJBBUA4

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/4ZJBBUA44AQZKHJTEM4R54SGTN \
  | 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: e65210d01ce021951d3323391ef2469b5b9a189df188d91a94f624b371a117da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b03467f1806f93436ff249a9a57b7f87ad98d4741b294271fd210d5e7ce3e525",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-09-11T15:52:43Z",
    "title_canon_sha256": "8b6930d24effe8ba1b692aba66e1a3fc5d17880a542f7be6c7d6e43a2241e2ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.03991",
    "kind": "arxiv",
    "version": 1
  }
}