Pith Number

pith:ZGWDFO2N

pith:2013:ZGWDFO2NBMKZ7HZLMXC6XYJOXS

not attested not anchored not stored refs pending

Submanifolds of warped product manifolds $I\times_f S^{m-1}(k)$}} from a $p$-harmonic viewpoint

Bang-Yen Chen, Shihshu Walter Wei

arxiv:1307.1876 v1 · 2013-07-07 · 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{ZGWDFO2NBMKZ7HZLMXC6XYJOXS}

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	2026-05-18T03:19:03.276854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9ac32bb4d0b159f9f2b65c5ebe12ebc83deeeea73ff6eb564c77948e917c41f

Aliases

arxiv: 1307.1876 · arxiv_version: 1307.1876v1 · doi: 10.48550/arxiv.1307.1876 · pith_short_12: ZGWDFO2NBMKZ · pith_short_16: ZGWDFO2NBMKZ7HZL · pith_short_8: ZGWDFO2N

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/ZGWDFO2NBMKZ7HZLMXC6XYJOXS \
  | 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: c9ac32bb4d0b159f9f2b65c5ebe12ebc83deeeea73ff6eb564c77948e917c41f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41d77186ba4890e9c7d2792e40f63509a40f2f12c54250a161db99aa57fae715",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-07T15:22:14Z",
    "title_canon_sha256": "c1c62f6333d77331bb666b2f9773e73100be10127a8db1958c4e38c533209115"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1876",
    "kind": "arxiv",
    "version": 1
  }
}