Pith Number

pith:GFTXAUFE

pith:2003:GFTXAUFEIGLC6TOLDRIFAFVP23

not attested not anchored not stored refs pending

Every mapping class group is generated by 6 involutions

Benson Farb, Tara E. Brendle

arxiv:math/0307039 v3 · 2003-07-02 · math.GT · 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{GFTXAUFEIGLC6TOLDRIFAFVP23}

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	2026-07-04T14:37:34.281666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31677050a441962f4dcb1c505016afd6ce00d444eef21d8ee9e2d4178568a7fa

Aliases

arxiv: math/0307039 · arxiv_version: math/0307039v3 · doi: 10.48550/arxiv.math/0307039 · pith_short_12: GFTXAUFEIGLC · pith_short_16: GFTXAUFEIGLC6TOL · pith_short_8: GFTXAUFE

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/GFTXAUFEIGLC6TOLDRIFAFVP23 \
  | 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: 31677050a441962f4dcb1c505016afd6ce00d444eef21d8ee9e2d4178568a7fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bac6ce50394e93fa3772ef823dda31054b02843248f3f37755f4a492d11d79d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2003-07-02T22:39:27Z",
    "title_canon_sha256": "5d60d3c5b280e16256c8c60b340324fb97309b6e51bdf81edbfae610ea707ece"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307039",
    "kind": "arxiv",
    "version": 3
  }
}