Pith Number

pith:VIJRS2ZB

pith:2019:VIJRS2ZBNMLHTSIYKLP5AWJNJI

not attested not anchored not stored refs pending

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term

Gongbao LI, Tao Yang

arxiv:1908.02536 v2 · 2019-08-07 · 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{VIJRS2ZBNMLHTSIYKLP5AWJNJI}

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	2026-07-05T02:22:34.052020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa13196b216b1679c91852dfd0592d4a1005f960e8c1d6ee7c810819def2376f

Aliases

arxiv: 1908.02536 · arxiv_version: 1908.02536v2 · doi: 10.48550/arxiv.1908.02536 · pith_short_12: VIJRS2ZBNMLH · pith_short_16: VIJRS2ZBNMLHTSIY · pith_short_8: VIJRS2ZB

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/VIJRS2ZBNMLHTSIYKLP5AWJNJI \
  | 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: aa13196b216b1679c91852dfd0592d4a1005f960e8c1d6ee7c810819def2376f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f238e83fa56c92b4cf77ab9af2ffd4d752293d0fc53213e23460ccd429886ce6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-07T11:33:19Z",
    "title_canon_sha256": "b511a9a1797eca21ba91f5b47c29202696a1bf627f16b4ba2671f08f2f4bc31d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02536",
    "kind": "arxiv",
    "version": 2
  }
}