Pith Number

pith:NPHG3ZMK

pith:2011:NPHG3ZMKIU5SEVAGG2VRK4OZ53

not attested not anchored not stored refs pending

An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Marco Tusche, Olivier Durieu

arxiv:1110.0963 v2 · 2011-10-05 · 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{NPHG3ZMKIU5SEVAGG2VRK4OZ53}

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	2026-05-18T03:44:24.484530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bce6de58a453b22540636ab1571d9eec960296374dc2faf5c2a5fd2d8b81e64

Aliases

arxiv: 1110.0963 · arxiv_version: 1110.0963v2 · doi: 10.48550/arxiv.1110.0963 · pith_short_12: NPHG3ZMKIU5S · pith_short_16: NPHG3ZMKIU5SEVAG · pith_short_8: NPHG3ZMK

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/NPHG3ZMKIU5SEVAGG2VRK4OZ53 \
  | 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: 6bce6de58a453b22540636ab1571d9eec960296374dc2faf5c2a5fd2d8b81e64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26c56a91f45bb7e121c51c03c52df30a91af344c7544f44eff916eff7ed385ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-05T11:53:46Z",
    "title_canon_sha256": "db539490fa35ba0347fceb65adf436815b74d64d3021bb8b28300e2fb64a6d40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0963",
    "kind": "arxiv",
    "version": 2
  }
}