Pith Number

pith:A4YVEMHW

pith:2016:A4YVEMHWF6O66A2WORP3YCKNCY

not attested not anchored not stored refs pending

An integral formula and its applications on sub-static manifolds

Chao Xia, Junfang Li

arxiv:1603.02201 v1 · 2016-03-07 · math.DG · 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{A4YVEMHWF6O66A2WORP3YCKNCY}

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	2026-05-18T01:19:31.378528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07315230f62f9def0356745fbc094d163853221469b80673d9f26270a505b7be

Aliases

arxiv: 1603.02201 · arxiv_version: 1603.02201v1 · doi: 10.48550/arxiv.1603.02201 · pith_short_12: A4YVEMHWF6O6 · pith_short_16: A4YVEMHWF6O66A2W · pith_short_8: A4YVEMHW

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/A4YVEMHWF6O66A2WORP3YCKNCY \
  | 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: 07315230f62f9def0356745fbc094d163853221469b80673d9f26270a505b7be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee90170e2b1333ebc5054a1229eb32442413a4624874816244cd6d6a494cc04f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-03-07T18:53:35Z",
    "title_canon_sha256": "c66a8d3f2f55425851015d9c5bb2f899f946cb37d99f1364989dbb0198bc0a5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.02201",
    "kind": "arxiv",
    "version": 1
  }
}