Pith Number

pith:OPN5MDJE

pith:2009:OPN5MDJEK75UHWD6XAZRIB2BH4

not attested not anchored not stored refs pending

Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties

Chun Liu, Hao Wu, Xiang Xu

arxiv:0901.1751 v2 · 2009-01-13 · 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{OPN5MDJEK75UHWD6XAZRIB2BH4}

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	2026-05-18T03:42:34.219887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73dbd60d2457fb43d87eb8331407413f2b02ca8241723a390509b56d0b255b4c

Aliases

arxiv: 0901.1751 · arxiv_version: 0901.1751v2 · doi: 10.48550/arxiv.0901.1751 · pith_short_12: OPN5MDJEK75U · pith_short_16: OPN5MDJEK75UHWD6 · pith_short_8: OPN5MDJE

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/OPN5MDJEK75UHWD6XAZRIB2BH4 \
  | 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: 73dbd60d2457fb43d87eb8331407413f2b02ca8241723a390509b56d0b255b4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efabd4983dec16dd4b79d103c16a92415816db3e6afd7b371819bfe6f8f40a58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-01-13T10:30:07Z",
    "title_canon_sha256": "7a3ce9529e0261425a3ef94787217237b51c61947a78e129744b472b7880cfa6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.1751",
    "kind": "arxiv",
    "version": 2
  }
}