Pith Number

pith:SPB2KPPA

pith:2011:SPB2KPPAUPNNVRTWJ2PBZRGTPW

not attested not anchored not stored refs pending

Vector-valued decoupling and the Burkholder-Davis-Gundy inequality

Mark Veraar, Sonja Cox

arxiv:1107.2218 v2 · 2011-07-12 · math.FA · 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{SPB2KPPAUPNNVRTWJ2PBZRGTPW}

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	2026-05-18T03:47:01.424857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93c3a53de0a3dadac6764e9e1cc4d37da752d7401bb7f5826298912efe5a764a

Aliases

arxiv: 1107.2218 · arxiv_version: 1107.2218v2 · doi: 10.48550/arxiv.1107.2218 · pith_short_12: SPB2KPPAUPNN · pith_short_16: SPB2KPPAUPNNVRTW · pith_short_8: SPB2KPPA

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/SPB2KPPAUPNNVRTWJ2PBZRGTPW \
  | 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: 93c3a53de0a3dadac6764e9e1cc4d37da752d7401bb7f5826298912efe5a764a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e33f375b3106d71b2bf08dee4888884611fabe3a4bc71111c72e01897d2a0203",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-07-12T09:12:27Z",
    "title_canon_sha256": "2adaa054240a3c4fbbb555f47c4858b3ed6ea6bb7eed7795460c576791d72e18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2218",
    "kind": "arxiv",
    "version": 2
  }
}