Pith Number

pith:ZI5DVUFC

pith:2012:ZI5DVUFCXGLQLEU43ZFFRPSZ66

not attested not anchored not stored refs pending

Least area Spherical Catenoids in Hyperbolic Three-Dimensional Space

Biao Wang

arxiv:1204.4943 v2 · 2012-04-22 · math.DG · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZI5DVUFCXGLQLEU43ZFFRPSZ66}

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	2026-05-18T02:26:59.174302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca3a3ad0a2b99705929cde4a58be59f7a6fa4caf1c54f7fa010e3f1b56f22e85

Aliases

arxiv: 1204.4943 · arxiv_version: 1204.4943v2 · doi: 10.48550/arxiv.1204.4943 · pith_short_12: ZI5DVUFCXGLQ · pith_short_16: ZI5DVUFCXGLQLEU4 · pith_short_8: ZI5DVUFC

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/ZI5DVUFCXGLQLEU43ZFFRPSZ66 \
  | 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: ca3a3ad0a2b99705929cde4a58be59f7a6fa4caf1c54f7fa010e3f1b56f22e85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0fe14c3c4e00f7dfe086d8800aaaa8b4048d137d92dfaf8bb960b1d75ca0a04",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-04-22T22:03:48Z",
    "title_canon_sha256": "f89472704f93c69c3d46ccd19595962b336f82765f00e544a30434dd9195c806"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4943",
    "kind": "arxiv",
    "version": 2
  }
}