Pith Number

pith:5QYKH6KA

pith:2015:5QYKH6KAP4YJKUVCLEL5SOZL3I

not attested not anchored not stored refs pending

Local and global sharp gradient estimates for weighted $p$-harmonic functions

Nguyen Duy Dat, Nguyen Thac Dung

arxiv:1505.07623 v2 · 2015-05-28 · 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{5QYKH6KAP4YJKUVCLEL5SOZL3I}

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	2026-05-18T01:26:18.321815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec30a3f9407f309552a25917d93b2bda19111391e2ef8402508b78b777a60541

Aliases

arxiv: 1505.07623 · arxiv_version: 1505.07623v2 · doi: 10.48550/arxiv.1505.07623 · pith_short_12: 5QYKH6KAP4YJ · pith_short_16: 5QYKH6KAP4YJKUVC · pith_short_8: 5QYKH6KA

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/5QYKH6KAP4YJKUVCLEL5SOZL3I \
  | 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: ec30a3f9407f309552a25917d93b2bda19111391e2ef8402508b78b777a60541

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72eb939965207d0049b3a928cbdab3f8ddb0d49e55b00e882025fbe935689a31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-05-28T10:11:30Z",
    "title_canon_sha256": "ddae1226281921bd311ab0cbd3b909e3d59da84233640518fcdd02c58e6718a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.07623",
    "kind": "arxiv",
    "version": 2
  }
}