Pith Number

pith:RG3LKKJT

pith:2010:RG3LKKJTF4MXFW665ACLK2FUVE

not attested not anchored not stored refs pending

The wave equation on hyperbolic spaces

Jean-Philippe Anker (MAPMO), Maria Vallarino (POLITO), Vittoria Pierfelice (MAPMO)

arxiv:1010.2372 v2 · 2010-10-12 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RG3LKKJTF4MXFW665ACLK2FUVE}

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	2026-05-18T04:07:40.640545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89b6b529332f1972dbdee804b568b4a913a2cc92289af4df40e62b08b599ecfc

Aliases

arxiv: 1010.2372 · arxiv_version: 1010.2372v2 · doi: 10.48550/arxiv.1010.2372 · pith_short_12: RG3LKKJTF4MX · pith_short_16: RG3LKKJTF4MXFW66 · pith_short_8: RG3LKKJT

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/RG3LKKJTF4MXFW665ACLK2FUVE \
  | 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: 89b6b529332f1972dbdee804b568b4a913a2cc92289af4df40e62b08b599ecfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7804147b05315d09d53464b9aebbc71e76a6ce871eee791cd47880c7383f73f4",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-10-12T12:36:37Z",
    "title_canon_sha256": "722d648d18359d876663278e911ccecf72a3c90df299fa82d67861703292a5c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2372",
    "kind": "arxiv",
    "version": 2
  }
}