Pith Number

pith:PQGZP4ZH

pith:2012:PQGZP4ZH53DICB2YIQSYQBVP75

not attested not anchored not stored refs pending

Embedded constant mean curvature tori in the three-sphere

Ben Andrews, Haizhong Li

arxiv:1204.5007 v3 · 2012-04-23 · 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{PQGZP4ZH53DICB2YIQSYQBVP75}

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	2026-05-18T03:52:27.865359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c0d97f327eec681075844258806afff527097cd88cb8785607734ec604f26ce

Aliases

arxiv: 1204.5007 · arxiv_version: 1204.5007v3 · doi: 10.48550/arxiv.1204.5007 · pith_short_12: PQGZP4ZH53DI · pith_short_16: PQGZP4ZH53DICB2Y · pith_short_8: PQGZP4ZH

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/PQGZP4ZH53DICB2YIQSYQBVP75 \
  | 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: 7c0d97f327eec681075844258806afff527097cd88cb8785607734ec604f26ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10b940d4f90ef49223fa61b9628dfb1f300941f9b6ac5aea1d4109194e10b1f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-04-23T09:12:25Z",
    "title_canon_sha256": "3a793f05a571f7ff24359fd7f831920c5aeab6bf8d2d0a0fcd5d01cd5230cdd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5007",
    "kind": "arxiv",
    "version": 3
  }
}