Pith Number

pith:QEL3AUAS

pith:2018:QEL3AUASDNEUFLUFKLPTKQT3UW

not attested not anchored not stored refs pending

The distributional hyper-Jacobian determinants in fractional Sobolev spaces

Chuanxi Wu, Qiang Tu, Xueting Qiu

arxiv:1808.07190 v1 · 2018-08-22 · 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{QEL3AUASDNEUFLUFKLPTKQT3UW}

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	2026-05-18T00:07:29.649434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8117b050121b4942ae8552df35427ba59c85ba8fe7f9818f164e5e2cba910257

Aliases

arxiv: 1808.07190 · arxiv_version: 1808.07190v1 · doi: 10.48550/arxiv.1808.07190 · pith_short_12: QEL3AUASDNEU · pith_short_16: QEL3AUASDNEUFLUF · pith_short_8: QEL3AUAS

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/QEL3AUASDNEUFLUFKLPTKQT3UW \
  | 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: 8117b050121b4942ae8552df35427ba59c85ba8fe7f9818f164e5e2cba910257

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c7cf0af30afeac0ef322d128bf5b7584a637f0ff6a89596be792abc1a288d74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-08-22T02:29:53Z",
    "title_canon_sha256": "690ad1ef7036c0b289d4d6c3b3947dc5f85011c6ca61b4ed2372e8e6ee9ab22d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.07190",
    "kind": "arxiv",
    "version": 1
  }
}