Pith Number

pith:MXJOHXLX

pith:2001:MXJOHXLXHSRN54EYW64YRULPWC

not attested not anchored not stored refs pending

Godbillon-Vey invariants for families of foliations

D. Kotschick

arxiv:math/0111137 v1 · 2001-11-12 · 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{MXJOHXLXHSRN54EYW64YRULPWC}

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	2026-05-18T03:35:00.444121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65d2e3dd773ca2def098b7b988d16fb0b9f00113b83a4c661e1d231dcb6b8ee1

Aliases

arxiv: math/0111137 · arxiv_version: math/0111137v1 · doi: 10.48550/arxiv.math/0111137 · pith_short_12: MXJOHXLXHSRN · pith_short_16: MXJOHXLXHSRN54EY · pith_short_8: MXJOHXLX

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/MXJOHXLXHSRN54EYW64YRULPWC \
  | 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: 65d2e3dd773ca2def098b7b988d16fb0b9f00113b83a4c661e1d231dcb6b8ee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf33bb182c1e3a1d09dd67d365964ad92dc465861c931b901af5e0f68636948b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-11-12T17:56:53Z",
    "title_canon_sha256": "79efe8567b420a86984e3a5df829891d3af2c797d334eeb9d9a1ab8018ea5fea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0111137",
    "kind": "arxiv",
    "version": 1
  }
}