Pith Number

pith:23ZVYBYO

pith:2011:23ZVYBYOHD7O7UL3FCZABWWOWS

not attested not anchored not stored refs pending

A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with Vacuum

Qiao Liu, Shangbin Cui

arxiv:1111.6760 v1 · 2011-11-29 · 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{23ZVYBYOHD7O7UL3FCZABWWOWS}

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	2026-05-18T04:07:28.572790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6f35c070e38feefd17b28b200daceb482b649a440d40fa49305bbd702343291

Aliases

arxiv: 1111.6760 · arxiv_version: 1111.6760v1 · doi: 10.48550/arxiv.1111.6760 · pith_short_12: 23ZVYBYOHD7O · pith_short_16: 23ZVYBYOHD7O7UL3 · pith_short_8: 23ZVYBYO

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/23ZVYBYOHD7O7UL3FCZABWWOWS \
  | 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: d6f35c070e38feefd17b28b200daceb482b649a440d40fa49305bbd702343291

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79c46a610a0d8a4773f2d3ed994d6ed31d12012c17abde8b4d3a40936cd134ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-29T10:45:03Z",
    "title_canon_sha256": "94b8bb6a3b7c4ebcc160b4f8360080db0357244641b06fa78a599c7c687c2866"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6760",
    "kind": "arxiv",
    "version": 1
  }
}