Pith Number

pith:AKT3GOOB

pith:2018:AKT3GOOBGNKXJNSOWNCJ4XEUGP

not attested not anchored not stored refs pending

Geometry of warped product and CR-warped product submanifolds in Kaehler manifolds: modified version

Bang-Yen Chen

arxiv:1806.11102 v1 · 2018-06-27 · 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{AKT3GOOBGNKXJNSOWNCJ4XEUGP}

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	2026-05-18T00:12:03.561053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02a7b339c1335574b64eb3449e5c9433c1cb4ea9a7e8a2a8af0a5ce9fdeb1018

Aliases

arxiv: 1806.11102 · arxiv_version: 1806.11102v1 · doi: 10.48550/arxiv.1806.11102 · pith_short_12: AKT3GOOBGNKX · pith_short_16: AKT3GOOBGNKXJNSO · pith_short_8: AKT3GOOB

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/AKT3GOOBGNKXJNSOWNCJ4XEUGP \
  | 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: 02a7b339c1335574b64eb3449e5c9433c1cb4ea9a7e8a2a8af0a5ce9fdeb1018

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51e90725cc7980cbbbe6cd240ceea7a226b69387611520d1d765b63bc008e336",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-06-27T18:23:40Z",
    "title_canon_sha256": "180d5ae991c67e00afda940387b31e850a9324fc042b066efb85082e56774ddb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.11102",
    "kind": "arxiv",
    "version": 1
  }
}