Pith Number

pith:IJ3OCI5F

pith:2012:IJ3OCI5FUTGUESNF6Y3NSJHEAB

not attested not anchored not stored refs pending

Invariance of the Gibbs measure for the Benjamin-Ono equation

Yu Deng

arxiv:1210.1542 v1 · 2012-10-04 · 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{IJ3OCI5FUTGUESNF6Y3NSJHEAB}

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	2026-05-18T00:50:30.087820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4276e123a5a4cd4249a5f636d924e40052b60648de79297214c3234a9fb2fa8d

Aliases

arxiv: 1210.1542 · arxiv_version: 1210.1542v1 · doi: 10.48550/arxiv.1210.1542 · pith_short_12: IJ3OCI5FUTGU · pith_short_16: IJ3OCI5FUTGUESNF · pith_short_8: IJ3OCI5F

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/IJ3OCI5FUTGUESNF6Y3NSJHEAB \
  | 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: 4276e123a5a4cd4249a5f636d924e40052b60648de79297214c3234a9fb2fa8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89682ae3929cb009d6fe03d556d8b69b1cd43cf7c160ea1c741a1ffadf2b2b46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-04T18:59:36Z",
    "title_canon_sha256": "d5f6352bc41a784c62fe736af1d111f8d7cec7b5feac91cf92d451a8130ac4a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1542",
    "kind": "arxiv",
    "version": 1
  }
}