Pith Number

pith:ECNPQ4Z7

pith:2015:ECNPQ4Z723XL54RLQEKS3AWNON

not attested not anchored not stored refs pending

Central limit theorems for mapping class groups and $\text{Out}(F_N)$

Camille Horbez

arxiv:1506.07244 v2 · 2015-06-24 · math.GR · math.GT · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ECNPQ4Z723XL54RLQEKS3AWNON}

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	2026-05-18T00:21:00.375962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

209af8733fd6eebef22b81152d82cd737a52c3f8357a71fda228cce44c4fa1d0

Aliases

arxiv: 1506.07244 · arxiv_version: 1506.07244v2 · doi: 10.48550/arxiv.1506.07244 · pith_short_12: ECNPQ4Z723XL · pith_short_16: ECNPQ4Z723XL54RL · pith_short_8: ECNPQ4Z7

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/ECNPQ4Z723XL54RLQEKS3AWNON \
  | 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: 209af8733fd6eebef22b81152d82cd737a52c3f8357a71fda228cce44c4fa1d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a4e19fc7c08e9deac71101b22ebf1e10c9e249d6a1a4d2c218e72df1ffdad5f",
    "cross_cats_sorted": [
      "math.GT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-24T05:08:19Z",
    "title_canon_sha256": "d841afcbdf43e7b5afef1eba30c431912c68634355429591021f7f4833f9c84c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07244",
    "kind": "arxiv",
    "version": 2
  }
}