Pith Number

pith:BQQSXHET

pith:2008:BQQSXHET4DEJCZ7C3JUNWXKOU6

not attested not anchored not stored refs pending

Stable commutator length is rational in free groups

Danny Calegari

arxiv:0802.1352 v3 · 2008-02-10 · math.GR · 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{BQQSXHET4DEJCZ7C3JUNWXKOU6}

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	2026-05-18T02:16:01.179953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c212b9c93e0c89167e2da68db5d4ea79b947b90d8babb37b2dad09ed521d341

Aliases

arxiv: 0802.1352 · arxiv_version: 0802.1352v3 · doi: 10.48550/arxiv.0802.1352 · pith_short_12: BQQSXHET4DEJ · pith_short_16: BQQSXHET4DEJCZ7C · pith_short_8: BQQSXHET

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/BQQSXHET4DEJCZ7C3JUNWXKOU6 \
  | 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: 0c212b9c93e0c89167e2da68db5d4ea79b947b90d8babb37b2dad09ed521d341

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7f041d24f45988fa89ca924fb71289843db61862b8c6b246527824b145e8d90",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-02-10T21:04:53Z",
    "title_canon_sha256": "1db23eb5ef2df8a8dab0b68afa7517a5ffc3f801764d1cbffd4b08fe40476151"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.1352",
    "kind": "arxiv",
    "version": 3
  }
}