Pith Number

pith:GLRAFNT7

pith:2008:GLRAFNT7UF3NM7P6WNPJMBWSUU

not attested not anchored not stored refs pending

The $C^{\a}$ regularity of a class hypoelliptic ultraparabolic equations

Liqun Zhang, Wendong Wang

arxiv:0804.4358 v2 · 2008-04-28 · 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{GLRAFNT7UF3NM7P6WNPJMBWSUU}

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	2026-05-18T02:15:53.332620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32e202b67fa176d67dfeb35e9606d2a51be72a7756a1ad85698be535ecad9a82

Aliases

arxiv: 0804.4358 · arxiv_version: 0804.4358v2 · doi: 10.48550/arxiv.0804.4358 · pith_short_12: GLRAFNT7UF3N · pith_short_16: GLRAFNT7UF3NM7P6 · pith_short_8: GLRAFNT7

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/GLRAFNT7UF3NM7P6WNPJMBWSUU \
  | 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: 32e202b67fa176d67dfeb35e9606d2a51be72a7756a1ad85698be535ecad9a82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "689cf1f1c7f37095ce34fd3e7434284ea9492abd163fd504627802e2123907f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-04-28T09:45:03Z",
    "title_canon_sha256": "bccc5dcf92b1e724f24e769fc8b6cdebd6c94347b287e5b66c81631032b3d262"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.4358",
    "kind": "arxiv",
    "version": 2
  }
}