Pith Number

pith:EZXOVGP4

pith:2012:EZXOVGP4PG6B6VY6SOOK3PVEYL

not attested not anchored not stored refs pending

A Hopf-bifurcation theorem for the critically dissipative quasi-geostrophic equation

Weiping Yan, Yong Li

arxiv:1205.3851 v2 · 2012-05-17 · math.DS · 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{EZXOVGP4PG6B6VY6SOOK3PVEYL}

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	2026-05-18T02:54:28.143780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

266eea99fc79bc1f571e939cadbea4c2eda16cad5076f478c94c776d49100088

Aliases

arxiv: 1205.3851 · arxiv_version: 1205.3851v2 · doi: 10.48550/arxiv.1205.3851 · pith_short_12: EZXOVGP4PG6B · pith_short_16: EZXOVGP4PG6B6VY6 · pith_short_8: EZXOVGP4

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/EZXOVGP4PG6B6VY6SOOK3PVEYL \
  | 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: 266eea99fc79bc1f571e939cadbea4c2eda16cad5076f478c94c776d49100088

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1eb44f0fed7f835c5affea17d5b6da14e8b0345814a89f243ee0304581fe98e7",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-05-17T05:12:48Z",
    "title_canon_sha256": "abdc7a92b078b01f23ebe065ee4b1dbcb9e76c2d0dfb3f329e7ad06870cebaf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3851",
    "kind": "arxiv",
    "version": 2
  }
}