Pith Number

pith:GIFYCP4Y

pith:2010:GIFYCP4YMAIFTDGHYVM2JC6RMP

not attested not anchored not stored refs pending

Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type

Jeremy Tyson, Nicola Garofalo

arxiv:1005.4090 v1 · 2010-05-21 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIFYCP4YMAIFTDGHYVM2JC6RMP}

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	2026-05-18T02:58:02.141128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

320b813f986010598cc7c559a48bd163e40a099fd5c72788cba462037e25fa24

Aliases

arxiv: 1005.4090 · arxiv_version: 1005.4090v1 · doi: 10.48550/arxiv.1005.4090 · pith_short_12: GIFYCP4YMAIF · pith_short_16: GIFYCP4YMAIFTDGH · pith_short_8: GIFYCP4Y

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/GIFYCP4YMAIFTDGHYVM2JC6RMP \
  | 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: 320b813f986010598cc7c559a48bd163e40a099fd5c72788cba462037e25fa24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dadcf88c6271d220459d7ea3b4a123558fd2575d5e8613235ac07df903f0c9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-05-21T22:08:11Z",
    "title_canon_sha256": "3a6e30d610a56e61f63c262b5a39eb00c1c9b84359a5ea90fb64f11bc65ef42d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4090",
    "kind": "arxiv",
    "version": 1
  }
}