Pith Number

pith:T4ISW5H2

pith:2012:T4ISW5H2UGH5ZFDB2BTRZOYSTQ

not attested not anchored not stored refs pending

Volume-preserving normal forms of Hopf-zero singularity

Fahimeh Mokhtari, Majid Gazor

arxiv:1203.1807 v7 · 2012-03-08 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T4ISW5H2UGH5ZFDB2BTRZOYSTQ}

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	2026-05-18T02:21:17.187501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f112b74faa18fdc9461d0671cbb129c3449c4042f81b13ac4ee2ed6f9e345db

Aliases

arxiv: 1203.1807 · arxiv_version: 1203.1807v7 · doi: 10.48550/arxiv.1203.1807 · pith_short_12: T4ISW5H2UGH5 · pith_short_16: T4ISW5H2UGH5ZFDB · pith_short_8: T4ISW5H2

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/T4ISW5H2UGH5ZFDB2BTRZOYSTQ \
  | 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: 9f112b74faa18fdc9461d0671cbb129c3449c4042f81b13ac4ee2ed6f9e345db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35bc395b07d0759fcf78d7ef53d1385e7460222d645e678ddd86f1d7eb050903",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-08T14:16:13Z",
    "title_canon_sha256": "266eabf1af8881e1eb7b5bb0511796b2aa5ff6150429c8d286e7abb6e5f8e697"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1807",
    "kind": "arxiv",
    "version": 7
  }
}