Pith Number

pith:VIRGJOAQ

pith:2013:VIRGJOAQEZEONQFQVGHD3K6GRG

not attested not anchored not stored refs pending

Squared-Norm Empirical Process in Banach Space

Jing Lei, Vincent Q. Vu

arxiv:1312.1005 v1 · 2013-12-04 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VIRGJOAQEZEONQFQVGHD3K6GRG}

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	2026-05-18T03:05:35.183045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa2264b8102648e6c0b0a98e3dabc689ae3c08e1c1af474c5a501a68af4ec56b

Aliases

arxiv: 1312.1005 · arxiv_version: 1312.1005v1 · doi: 10.48550/arxiv.1312.1005 · pith_short_12: VIRGJOAQEZEO · pith_short_16: VIRGJOAQEZEONQFQ · pith_short_8: VIRGJOAQ

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/VIRGJOAQEZEONQFQVGHD3K6GRG \
  | 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: aa2264b8102648e6c0b0a98e3dabc689ae3c08e1c1af474c5a501a68af4ec56b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b89c13eb6f0cd3d8b332ad7f6db8b19ec6bb47e142ab1e2bf50f1fc04885339",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-04T02:13:27Z",
    "title_canon_sha256": "c61e7eb55211f92753406bf25ab45d3ad96c7f964e0ede1a075f16643c675f0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1005",
    "kind": "arxiv",
    "version": 1
  }
}