Pith Number

pith:XESKL5A4

pith:2012:XESKL5A46X2S3F5PKEMPZVGW4J

not attested not anchored not stored refs pending

Spectral gap properties for linear random walks and Pareto's asymptotics for affine stochastic recursions

Emile Le Page (LMAM), Yves Guivarc'H (IRMAR)

arxiv:1204.6004 v5 · 2012-04-26 · 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{XESKL5A46X2S3F5PKEMPZVGW4J}

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	2026-05-18T02:20:37.255663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b924a5f41cf5f52d97af5118fcd4d6e2567bc8b39e5b93d99dbfd49f3ae46f11

Aliases

arxiv: 1204.6004 · arxiv_version: 1204.6004v5 · doi: 10.48550/arxiv.1204.6004 · pith_short_12: XESKL5A46X2S · pith_short_16: XESKL5A46X2S3F5P · pith_short_8: XESKL5A4

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/XESKL5A46X2S3F5PKEMPZVGW4J \
  | 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: b924a5f41cf5f52d97af5118fcd4d6e2567bc8b39e5b93d99dbfd49f3ae46f11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5a51f1653231d347a163af3bd36ffe358d95912ac7a488dde7ae5aac7409850",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-26T19:00:39Z",
    "title_canon_sha256": "25eca1e59fe08d2fa6316e7b86954c709cbc3a52deeefef5c82871bedb89ec49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6004",
    "kind": "arxiv",
    "version": 5
  }
}