Pith Number

pith:LAN4SAUJ

pith:2009:LAN4SAUJLJZ73LYMCUDXKFSJON

not attested not anchored not stored refs pending

Singular Seifert surfaces and Smale invariants for a family of 3-sphere immersions

Masamichi Takase, Tobias Ekholm

arxiv:0903.0238 v3 · 2009-03-02 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LAN4SAUJLJZ73LYMCUDXKFSJON}

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	2026-05-18T02:16:48.335444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

581bc902895a73fdaf0c15077516497347def4cea62c374d00997ea454ffe696

Aliases

arxiv: 0903.0238 · arxiv_version: 0903.0238v3 · doi: 10.48550/arxiv.0903.0238 · pith_short_12: LAN4SAUJLJZ7 · pith_short_16: LAN4SAUJLJZ73LYM · pith_short_8: LAN4SAUJ

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/LAN4SAUJLJZ73LYMCUDXKFSJON \
  | 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: 581bc902895a73fdaf0c15077516497347def4cea62c374d00997ea454ffe696

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aad6595ffa34443f00413ffa5e5c4df9614a85286b6b3d66c60b6ae8281ce62d",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-03-02T09:04:22Z",
    "title_canon_sha256": "56922954c98c1c975221eaa7e352204366796ba4143dcceee6dab42b7883119c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.0238",
    "kind": "arxiv",
    "version": 3
  }
}