Pith Number

pith:KZOY6CMP

pith:2012:KZOY6CMPZXEUFUX5MK4DFZ5433

not attested not anchored not stored refs pending

The shifted wave equation on Damek--Ricci spaces and on homogeneous trees

Alberto G. Setti, Emmanuel Pedon (LM-Reims), Jean-Philippe Anker (MAPMO), Pierre Martinot (IECN)

arxiv:1206.1396 v3 · 2012-06-07 · math.AP · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KZOY6CMPZXEUFUX5MK4DFZ5433}

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	2026-05-18T03:50:24.995866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

565d8f098fcdc942d2fd62b832e7bcdedccb079438ea60ea4d9fa04a1fd72cde

Aliases

arxiv: 1206.1396 · arxiv_version: 1206.1396v3 · doi: 10.48550/arxiv.1206.1396 · pith_short_12: KZOY6CMPZXEU · pith_short_16: KZOY6CMPZXEUFUX5 · pith_short_8: KZOY6CMP

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/KZOY6CMPZXEUFUX5MK4DFZ5433 \
  | 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: 565d8f098fcdc942d2fd62b832e7bcdedccb079438ea60ea4d9fa04a1fd72cde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1efabcc37fc7e8279e1192c5f46ef1b9829d212da8d135c0fc3b450cfab7429f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-07T04:34:04Z",
    "title_canon_sha256": "80c3488586a25bd5d52801a89a142279d1776b8e992492d20b856ec2fdf9ddad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1396",
    "kind": "arxiv",
    "version": 3
  }
}