Pith Number

pith:WF2UZ6MI

pith:2021:WF2UZ6MI45UXE4KRREED6DKB3W

not attested not anchored not stored refs pending

Prescribed Weingarten curvature equations in warped product manifolds

Chenyang Liu, Jing Mao, Ya Gao

arxiv:2111.01636 v2 · 2021-11-02 · 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{WF2UZ6MI45UXE4KRREED6DKB3W}

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	2026-07-05T03:35:33.873431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1754cf988e76972715189083f0d41ddbcb67b47b07bbc99189c8343ba1ac3da

Aliases

arxiv: 2111.01636 · arxiv_version: 2111.01636v2 · doi: 10.48550/arxiv.2111.01636 · pith_short_12: WF2UZ6MI45UX · pith_short_16: WF2UZ6MI45UXE4KR · pith_short_8: WF2UZ6MI

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/WF2UZ6MI45UXE4KRREED6DKB3W \
  | 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: b1754cf988e76972715189083f0d41ddbcb67b47b07bbc99189c8343ba1ac3da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb02c6d763a8769ca9729dcb252b22777c1778ffa12941f5b0c50b203a7e2df5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-11-02T14:50:43Z",
    "title_canon_sha256": "5b86b6eac2fafd1a23febc7a901dc6050208741fb7985f41adbdf2b454f236a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.01636",
    "kind": "arxiv",
    "version": 2
  }
}