Pith Number

pith:ZK7WP2IQ

pith:2012:ZK7WP2IQ4AIANCUGTDHGSDBEHE

not attested not anchored not stored refs pending

Logarithmical Blow-up Criteria for the Nematic Liquid Crystal Flows

Jihong Zhao, Qiao Liu

arxiv:1209.5623 v2 · 2012-09-25 · 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{ZK7WP2IQ4AIANCUGTDHGSDBEHE}

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	2026-05-18T03:29:27.175349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cabf67e910e010068a8698ce690c243938b1d9630a17d181c61bc7ee25fc5539

Aliases

arxiv: 1209.5623 · arxiv_version: 1209.5623v2 · doi: 10.48550/arxiv.1209.5623 · pith_short_12: ZK7WP2IQ4AIA · pith_short_16: ZK7WP2IQ4AIANCUG · pith_short_8: ZK7WP2IQ

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/ZK7WP2IQ4AIANCUGTDHGSDBEHE \
  | 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: cabf67e910e010068a8698ce690c243938b1d9630a17d181c61bc7ee25fc5539

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1a26786717da267e2db623873dd905b862ae29089464076295e99062ef2dab8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-25T14:36:32Z",
    "title_canon_sha256": "ccb428411ba0df68d63f11ee1fe8a20285471f39721572a0a8b19150a52a270a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5623",
    "kind": "arxiv",
    "version": 2
  }
}