Pith Number

pith:DJO5L2ZP

pith:2010:DJO5L2ZPS77F3HO36VPEFJHI3B

not attested not anchored not stored refs pending

Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

Alexander Bihlo, Roman O. Popovych

arxiv:1010.1542 v2 · 2010-10-07 · math-ph · math.MP · physics.ao-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DJO5L2ZPS77F3HO36VPEFJHI3B}

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	2026-05-18T04:07:41.808484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a5dd5eb2f97fe5d9ddbf55e42a4e8d87729721f7731b6afe5dbee807905b042

Aliases

arxiv: 1010.1542 · arxiv_version: 1010.1542v2 · doi: 10.48550/arxiv.1010.1542 · pith_short_12: DJO5L2ZPS77F · pith_short_16: DJO5L2ZPS77F3HO3 · pith_short_8: DJO5L2ZP

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/DJO5L2ZPS77F3HO36VPEFJHI3B \
  | 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: 1a5dd5eb2f97fe5d9ddbf55e42a4e8d87729721f7731b6afe5dbee807905b042

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "745eaf010073803c7ac7443adb6a12c7e2828c8f4db559fa705a9dc560f08fc4",
    "cross_cats_sorted": [
      "math.MP",
      "physics.ao-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-10-07T20:31:03Z",
    "title_canon_sha256": "078e6f92b792083713b70bb1235ff5cc15860b347f015282632e7b4039fa5791"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1542",
    "kind": "arxiv",
    "version": 2
  }
}