Pith Number

pith:PAWMO2R4

pith:2011:PAWMO2R4J2JD5FNX7C6D4RN7C6

not attested not anchored not stored refs pending

Stable laws and spectral gap properties for affine random walks

Emile Le Page, Yves Guivarc'h, Zhiqiang Gao

arxiv:1108.3146 v3 · 2011-08-16 · 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{PAWMO2R4J2JD5FNX7C6D4RN7C6}

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	2026-05-18T03:26:09.022259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

782cc76a3c4e923e95b7f8bc3e45bf17af0895d9362c1b7cf4dc511eb93f14bd

Aliases

arxiv: 1108.3146 · arxiv_version: 1108.3146v3 · doi: 10.48550/arxiv.1108.3146 · pith_short_12: PAWMO2R4J2JD · pith_short_16: PAWMO2R4J2JD5FNX · pith_short_8: PAWMO2R4

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/PAWMO2R4J2JD5FNX7C6D4RN7C6 \
  | 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: 782cc76a3c4e923e95b7f8bc3e45bf17af0895d9362c1b7cf4dc511eb93f14bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b13d6af00f0a95048e3219144313e4ec936db954cc22f14254d16cc07a525675",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-16T03:21:38Z",
    "title_canon_sha256": "407acc480b760669f27116ab1bd0d49026dcb086e7c333200e9b8c7dc9df3545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3146",
    "kind": "arxiv",
    "version": 3
  }
}