Pith Number

pith:JZN2UJBD

pith:2011:JZN2UJBD6FDIY4J7DVCLWFFMJI

not attested not anchored not stored refs pending

On closed leaves of foliations, multisections and stable commutator lengths

Jonathan Bowden

arxiv:1105.4444 v1 · 2011-05-23 · math.GT · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JZN2UJBD6FDIY4J7DVCLWFFMJI}

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	2026-05-18T04:03:32.353045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e5baa2423f1468c713f1d44bb14ac4a0dc64217272fae503d285578088eaf9c

Aliases

arxiv: 1105.4444 · arxiv_version: 1105.4444v1 · doi: 10.48550/arxiv.1105.4444 · pith_short_12: JZN2UJBD6FDI · pith_short_16: JZN2UJBD6FDIY4J7 · pith_short_8: JZN2UJBD

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/JZN2UJBD6FDIY4J7DVCLWFFMJI \
  | 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: 4e5baa2423f1468c713f1d44bb14ac4a0dc64217272fae503d285578088eaf9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0039cd46ca779d9877d45fae3ef60e6b3f56e172b9af0bd06ce1858ea58c95e4",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-05-23T09:35:42Z",
    "title_canon_sha256": "dc0c0c93e8e0219e1f4b70f356d6e3edef15f8c06e66c34021147fd1fdeba8d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4444",
    "kind": "arxiv",
    "version": 1
  }
}