Pith Number

pith:SIB67GZJ

pith:2018:SIB67GZJPFF66P7FGDPPPNDR72

not attested not anchored not stored refs pending

Gradient estimates and Liouville type theorems for Poisson equations

Nguyen Ngoc Khanh, Nguyen Thac Dung

arxiv:1803.07251 v1 · 2018-03-20 · 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{SIB67GZJPFF66P7FGDPPPNDR72}

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	2026-05-18T00:20:33.832565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9203ef9b29794bef3fe530def7b471fe9a701f568c1ddad79ee8ac70fd7355e0

Aliases

arxiv: 1803.07251 · arxiv_version: 1803.07251v1 · doi: 10.48550/arxiv.1803.07251 · pith_short_12: SIB67GZJPFF6 · pith_short_16: SIB67GZJPFF66P7F · pith_short_8: SIB67GZJ

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/SIB67GZJPFF66P7FGDPPPNDR72 \
  | 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: 9203ef9b29794bef3fe530def7b471fe9a701f568c1ddad79ee8ac70fd7355e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3b10bf7c7c1c6ac20c6a431a0202a24c661f45d34c0dccb0e9605ffa6d67f37",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-03-20T04:25:23Z",
    "title_canon_sha256": "ea1e4eeceeaaf992771c913cd739aba01e909bd96b47c5895eabc1ae21a50dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.07251",
    "kind": "arxiv",
    "version": 1
  }
}