Pith Number

pith:HBOZVU2W

pith:2011:HBOZVU2WS7YNS6IPMCLHJYJMKI

not attested not anchored not stored refs pending

Strong approximation of partial sums under dependence conditions with application to dynamical systems

Emmanuel Rio, Florence Merlev\`ede

arxiv:1103.3241 v1 · 2011-03-16 · 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{HBOZVU2WS7YNS6IPMCLHJYJMKI}

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	2026-05-18T04:26:44.522407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

385d9ad35697f0d9790f609674e12c523d9ab9620fd61b88e33f30c46f415892

Aliases

arxiv: 1103.3241 · arxiv_version: 1103.3241v1 · doi: 10.48550/arxiv.1103.3241 · pith_short_12: HBOZVU2WS7YN · pith_short_16: HBOZVU2WS7YNS6IP · pith_short_8: HBOZVU2W

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/HBOZVU2WS7YNS6IPMCLHJYJMKI \
  | 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: 385d9ad35697f0d9790f609674e12c523d9ab9620fd61b88e33f30c46f415892

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "109bfe919f288dfc3dca8ebfe846a1a3f426f15c408c1f8681084a0347cbc0dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-16T17:35:08Z",
    "title_canon_sha256": "73868b151cf86aa094dd335a1f19fc1a894dbb8ed579486e91617e5ce183b98d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3241",
    "kind": "arxiv",
    "version": 1
  }
}