Pith Number

pith:J4WW3WRP

pith:2013:J4WW3WRPFNRVPH5NI6UNGNWU56

not attested not anchored not stored refs pending

A survey on geometry of warped product submanifolds

Bang-Yen Chen

arxiv:1307.0236 v1 · 2013-06-30 · 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{J4WW3WRPFNRVPH5NI6UNGNWU56}

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	2026-05-18T03:19:33.885911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f2d6dda2f2b63579fad47a8d336d4ef8e65b4200b4ab797cf7ac71cbf7446db

Aliases

arxiv: 1307.0236 · arxiv_version: 1307.0236v1 · doi: 10.48550/arxiv.1307.0236 · pith_short_12: J4WW3WRPFNRV · pith_short_16: J4WW3WRPFNRVPH5N · pith_short_8: J4WW3WRP

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/J4WW3WRPFNRVPH5NI6UNGNWU56 \
  | 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: 4f2d6dda2f2b63579fad47a8d336d4ef8e65b4200b4ab797cf7ac71cbf7446db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8195fe94e91c8dceac3d7e9dfff913e6c1d02af2db4d2bbcb70152fb5afc1c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-06-30T19:53:59Z",
    "title_canon_sha256": "4c4e08558f0014bbf210fe4f8d3a26de55831382bb924495746f227cf9fc0cc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0236",
    "kind": "arxiv",
    "version": 1
  }
}