Pith Number

pith:TZ2WUIMH

pith:2012:TZ2WUIMHB7N32WQKQ7FRC4C6AP

not attested not anchored not stored refs pending

Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus

F. Merlev\`ede, F. P\`ene, J. Dedecker

arxiv:1205.7022 v1 · 2012-05-31 · 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{TZ2WUIMHB7N32WQKQ7FRC4C6AP}

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	2026-05-18T03:54:36.349453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e756a21870fdbbd5a0a87cb11705e03f600f4b0051798454ce114b6fbdea052

Aliases

arxiv: 1205.7022 · arxiv_version: 1205.7022v1 · doi: 10.48550/arxiv.1205.7022 · pith_short_12: TZ2WUIMHB7N3 · pith_short_16: TZ2WUIMHB7N32WQK · pith_short_8: TZ2WUIMH

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/TZ2WUIMHB7N32WQKQ7FRC4C6AP \
  | 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: 9e756a21870fdbbd5a0a87cb11705e03f600f4b0051798454ce114b6fbdea052

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c17597281313f1e6c38b52549eb2f5e4e08e55d12e3c4dad9a27ed934b527bda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-05-31T15:43:24Z",
    "title_canon_sha256": "3dd17c52c756ef60c9298c2b6b8566bab2e66d48412ca8c24e0bcdd4a4ed983d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.7022",
    "kind": "arxiv",
    "version": 1
  }
}