Pith Number

pith:J36XWGQO

pith:2003:J36XWGQOOKZRYBN4HBKMAQAZUW

not attested not anchored not stored refs pending

Cut vertices in commutative graphs

Ferenc Gerlits, James Conant, Karen Vogtmann

arxiv:math/0307364 v3 · 2003-07-28 · math.QA · 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{J36XWGQOOKZRYBN4HBKMAQAZUW}

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	2026-05-18T04:41:54.055741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4efd7b1a0e72b31c05bc3854c04019a5856afc3c31f0ac3bba526f6365689ffc

Aliases

arxiv: math/0307364 · arxiv_version: math/0307364v3 · doi: 10.48550/arxiv.math/0307364 · pith_short_12: J36XWGQOOKZR · pith_short_16: J36XWGQOOKZRYBN4 · pith_short_8: J36XWGQO

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/J36XWGQOOKZRYBN4HBKMAQAZUW \
  | 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: 4efd7b1a0e72b31c05bc3854c04019a5856afc3c31f0ac3bba526f6365689ffc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "860e12bfac602f29034fbc9643d1b176ac734bbe2704c5f6093368732abdd7e7",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2003-07-28T15:59:32Z",
    "title_canon_sha256": "ab4e5f1b6a417d688f27299353b463e7971927fa02855c23fe5147ace38d30e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307364",
    "kind": "arxiv",
    "version": 3
  }
}