Pith Number

pith:NQQ3JGO3

pith:2012:NQQ3JGO3IWYPGSSNTQPAYW64EX

not attested not anchored not stored refs pending

Blow-up criterion of classical solutions for the incompressible nematic liquid crystal flows

Zhensheng Gao, Zhong Tan

arxiv:1210.4140 v5 · 2012-10-15 · math.AP · cond-mat.soft

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NQQ3JGO3IWYPGSSNTQPAYW64EX}

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	2026-05-18T00:56:04.913352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c21b499db45b0f34a4d9c1e0c5bdc25e9931f462205a8caf263bcd10ec52ed5

Aliases

arxiv: 1210.4140 · arxiv_version: 1210.4140v5 · doi: 10.48550/arxiv.1210.4140 · pith_short_12: NQQ3JGO3IWYP · pith_short_16: NQQ3JGO3IWYPGSSN · pith_short_8: NQQ3JGO3

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/NQQ3JGO3IWYPGSSNTQPAYW64EX \
  | 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: 6c21b499db45b0f34a4d9c1e0c5bdc25e9931f462205a8caf263bcd10ec52ed5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d4f19f004f46717b557ff8783c7716a1d56a8c8f0f763e4f9df3f8d4ca4faad",
    "cross_cats_sorted": [
      "cond-mat.soft"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-15T19:20:06Z",
    "title_canon_sha256": "7ad1d99ecba22649cf8f3e322b1939c4d6e0c9fa333ccbdc4d9cb36ecc6c51b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4140",
    "kind": "arxiv",
    "version": 5
  }
}