Pith Number

pith:CXJ33PSQ

pith:2011:CXJ33PSQ2JBHIW4XMAYUJPOEEJ

not attested not anchored not stored refs pending

Lyapunov exponents, shape theorems and large deviations for the random walk in random potential

Jean-Christophe Mourrat

arxiv:1106.3995 v2 · 2011-06-20 · 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{CXJ33PSQ2JBHIW4XMAYUJPOEEJ}

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	2026-05-18T03:59:25.441458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15d3bdbe50d242745b97603144bdc4224ef415db3a012aa881959004e614d831

Aliases

arxiv: 1106.3995 · arxiv_version: 1106.3995v2 · doi: 10.48550/arxiv.1106.3995 · pith_short_12: CXJ33PSQ2JBH · pith_short_16: CXJ33PSQ2JBHIW4X · pith_short_8: CXJ33PSQ

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/CXJ33PSQ2JBHIW4XMAYUJPOEEJ \
  | 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: 15d3bdbe50d242745b97603144bdc4224ef415db3a012aa881959004e614d831

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d689c7f0f3ad7aa90bebb096140edb74b336d42acc887932996dd6bd497a76f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-06-20T19:11:07Z",
    "title_canon_sha256": "5508d5702b9e3575f35cba6f8f6868def8b8016042e6cc7428d3fd510fa3ec56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3995",
    "kind": "arxiv",
    "version": 2
  }
}