Pith Number

pith:YIZ6Z3C7

pith:2011:YIZ6Z3C7CXN7DVEUEJEAWKBHZR

not attested not anchored not stored refs pending

The almost sure invariance principle for unbounded functions of expanding maps

Florence Merlevede (LAMA), Jerome Dedecker (MAP5), S\'ebastien Gou\"ezel (IRMAR)

arxiv:1108.5292 v2 · 2011-08-26 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YIZ6Z3C7CXN7DVEUEJEAWKBHZR}

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	2026-05-18T04:03:54.394189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c233ecec5f15dbf1d49422480b2827cc4843ed450ea471df471449746a9760b0

Aliases

arxiv: 1108.5292 · arxiv_version: 1108.5292v2 · doi: 10.48550/arxiv.1108.5292 · pith_short_12: YIZ6Z3C7CXN7 · pith_short_16: YIZ6Z3C7CXN7DVEU · pith_short_8: YIZ6Z3C7

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/YIZ6Z3C7CXN7DVEUEJEAWKBHZR \
  | 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: c233ecec5f15dbf1d49422480b2827cc4843ed450ea471df471449746a9760b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ca511adeef94fcb36ee7fe6dcaa053e3b790b127437629914562adeff4d63cf",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-26T13:17:05Z",
    "title_canon_sha256": "683bc3381ddb5096b353da6f591a8b0d821531e79bf6dad5d66358f7ea326680"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5292",
    "kind": "arxiv",
    "version": 2
  }
}