Pith Number

pith:WLNBRZRU

pith:2013:WLNBRZRU67PQOEVWDJMTHYB5JX

not attested not anchored not stored refs pending

Stable commutator length on mapping class groups

Ken Bromberg, Koji Fujiwara, Mladen Bestvina

arxiv:1306.2394 v1 · 2013-06-11 · 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{WLNBRZRU67PQOEVWDJMTHYB5JX}

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	2026-05-18T03:21:21.117638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2da18e634f7df0712b61a5933e03d4dcf3ce0898a358c690be15401e08b2e35

Aliases

arxiv: 1306.2394 · arxiv_version: 1306.2394v1 · doi: 10.48550/arxiv.1306.2394 · pith_short_12: WLNBRZRU67PQ · pith_short_16: WLNBRZRU67PQOEVW · pith_short_8: WLNBRZRU

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/WLNBRZRU67PQOEVWDJMTHYB5JX \
  | 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: b2da18e634f7df0712b61a5933e03d4dcf3ce0898a358c690be15401e08b2e35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76a2a8b4357240524e521a1c1072fc182e9a7bd9d01aff96839998ffd45ccf4e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-11T01:00:18Z",
    "title_canon_sha256": "690e9aeb56c42a0d10d7e39ebdab80912865fc80a1cef5bf04e791ca93778eff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2394",
    "kind": "arxiv",
    "version": 1
  }
}