Pith Number

pith:UADQK55Y

pith:2015:UADQK55YTWTO2DAFF7CNZWRRJZ

not attested not anchored not stored refs pending

An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR Manifold

Shu-Cheng Chang, Yen-Wen Fan

arxiv:1504.00786 v1 · 2015-04-03 · 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{UADQK55YTWTO2DAFF7CNZWRRJZ}

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	2026-05-18T02:19:37.064396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0070577b89da6ed0c052fc4dcda314e57796d29ca10c3f7a7c17f37cd3bd2a5

Aliases

arxiv: 1504.00786 · arxiv_version: 1504.00786v1 · doi: 10.48550/arxiv.1504.00786 · pith_short_12: UADQK55YTWTO · pith_short_16: UADQK55YTWTO2DAF · pith_short_8: UADQK55Y

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/UADQK55YTWTO2DAFF7CNZWRRJZ \
  | 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: a0070577b89da6ed0c052fc4dcda314e57796d29ca10c3f7a7c17f37cd3bd2a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "158ac8b14259e74ce6e74dd64c32e59f758d2dce54a2f17dd4e2a615db8ee70e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-04-03T09:04:33Z",
    "title_canon_sha256": "9a7bd169669d1d72c595de5bb2f003e1c089773c1af54eaadd77bfeaf92b6b32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00786",
    "kind": "arxiv",
    "version": 1
  }
}