Pith Number

pith:OBIZ2FEF

pith:2011:OBIZ2FEFJFFBDZMLS4Q5HE5454

not attested not anchored not stored refs pending

A geometric measure-type regularity criterion for solutions to the 3D Navier-Stokes equations

Zoran Grujic

arxiv:1111.0217 v5 · 2011-11-01 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBIZ2FEFJFFBDZMLS4Q5HE5454}

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	2026-05-18T03:41:20.348000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a

Aliases

arxiv: 1111.0217 · arxiv_version: 1111.0217v5 · doi: 10.48550/arxiv.1111.0217 · pith_short_12: OBIZ2FEFJFFB · pith_short_16: OBIZ2FEFJFFBDZML · pith_short_8: OBIZ2FEF

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/OBIZ2FEFJFFBDZMLS4Q5HE5454 \
  | 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: 70519d1485494a11e58b9721d393bcef00811616001d55c502b1da4315d46c1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4be88503b5e21ebfce6709a54a89288c14a9f6c3e7bbea8724869dbc065ec427",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-01T15:15:06Z",
    "title_canon_sha256": "be826aced54fbb6ca6307143def7f3db0534c2aebcb0ca058813415265db7f88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0217",
    "kind": "arxiv",
    "version": 5
  }
}