Pith Number

pith:7UBYE325

pith:2011:7UBYE3256HZWQQWK24RDJV4ZMN

not attested not anchored not stored refs pending

An integral representation for Folland's fundamental solution of the sub-Laplacian on Heisenberg groups $\Bbb{H}^{n}$

Allal Ghanmi, Zouha\"ir Mouayn

arxiv:1103.0705 v2 · 2011-03-03 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7UBYE3256HZWQQWK24RDJV4ZMN}

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	2026-05-18T04:26:55.434448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd03826f5df1f36842cad72234d7996356e21d7f4a1be1635da9b8390c09674c

Aliases

arxiv: 1103.0705 · arxiv_version: 1103.0705v2 · doi: 10.48550/arxiv.1103.0705 · pith_short_12: 7UBYE3256HZW · pith_short_16: 7UBYE3256HZWQQWK · pith_short_8: 7UBYE325

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/7UBYE3256HZWQQWK24RDJV4ZMN \
  | 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: fd03826f5df1f36842cad72234d7996356e21d7f4a1be1635da9b8390c09674c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78172cac76530da38397a3f152b47b134531c61708db3888a61ca10a36116638",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-03-03T14:48:23Z",
    "title_canon_sha256": "0e33f2f1ffb0fcfb99f13618a42563e021dea163d9248e7f3b590e5235bb7ae7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0705",
    "kind": "arxiv",
    "version": 2
  }
}