Pith Number

pith:3X2WUX6W

pith:2010:3X2WUX6WNIWOYLEIDGRFDZJTCZ

not attested not anchored not stored refs pending

The wave equation on Damek-Ricci spaces

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

arxiv:1012.0689 v1 · 2010-12-03 · 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{3X2WUX6WNIWOYLEIDGRFDZJTCZ}

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	2026-05-18T04:34:09.587069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddf56a5fd66a2cec2c8819a251e53316497874196f506561ad2ddb51c96c91fa

Aliases

arxiv: 1012.0689 · arxiv_version: 1012.0689v1 · doi: 10.48550/arxiv.1012.0689 · pith_short_12: 3X2WUX6WNIWO · pith_short_16: 3X2WUX6WNIWOYLEI · pith_short_8: 3X2WUX6W

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/3X2WUX6WNIWOYLEIDGRFDZJTCZ \
  | 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: ddf56a5fd66a2cec2c8819a251e53316497874196f506561ad2ddb51c96c91fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60d893e802936b9dc4490a0a00066871c81e61cabbf5e1a2048dfb0cf6874d93",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-03T10:23:08Z",
    "title_canon_sha256": "94433746d212d5ce234d86d9286eccd8155e8ff90abb51b1a7be99206c0dd252"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0689",
    "kind": "arxiv",
    "version": 1
  }
}