Pith Number

pith:5EWGI7O2

pith:2010:5EWGI7O255JDA3SOXZDJOFSUI4

not attested not anchored not stored refs pending

Local Gradient Estimate for $p$-harmonic functions on Riemannian Manifolds

Lei Zhang, Xiaodong Wang

arxiv:1010.2889 v1 · 2010-10-14 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5EWGI7O255JDA3SOXZDJOFSUI4}

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	2026-05-18T04:39:18.930120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e92c647ddaef52306e4ebe46971654471bbccdc3af930e751d3b86b7be3ef940

Aliases

arxiv: 1010.2889 · arxiv_version: 1010.2889v1 · doi: 10.48550/arxiv.1010.2889 · pith_short_12: 5EWGI7O255JD · pith_short_16: 5EWGI7O255JDA3SO · pith_short_8: 5EWGI7O2

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/5EWGI7O255JDA3SOXZDJOFSUI4 \
  | 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: e92c647ddaef52306e4ebe46971654471bbccdc3af930e751d3b86b7be3ef940

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "633ea31574195ff87d63f3c508508ddc3f7e371e35efd138e39dd9e77d20b994",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-10-14T12:39:58Z",
    "title_canon_sha256": "8928e75792ed73b6ac22708781dedc1821f6403d245ce200c09901a304c00adc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2889",
    "kind": "arxiv",
    "version": 1
  }
}