Pith Number

pith:5OU6BY4A

pith:2011:5OU6BY4A4GV3STYH3ZLEAQFHMZ

not attested not anchored not stored refs pending

Burkholder inequalities for submartingales, Bessel processes and conformal martingales

Adam Os\c{e}kowsk, Rodrigo Ba\~nuelos

arxiv:1112.0551 v1 · 2011-12-02 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5OU6BY4A4GV3STYH3ZLEAQFHMZ}

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	2026-05-18T01:09:21.876908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eba9e0e380e1abb94f07de564040a766781ef5f07f0f59a50e4b78f730f887f9

Aliases

arxiv: 1112.0551 · arxiv_version: 1112.0551v1 · doi: 10.48550/arxiv.1112.0551 · pith_short_12: 5OU6BY4A4GV3 · pith_short_16: 5OU6BY4A4GV3STYH · pith_short_8: 5OU6BY4A

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/5OU6BY4A4GV3STYH3ZLEAQFHMZ \
  | 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: eba9e0e380e1abb94f07de564040a766781ef5f07f0f59a50e4b78f730f887f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1726e2d53513b3891c0b5024cc7f5de6bb151b5c0fc56f2951b6f80fc14fc491",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-12-02T20:07:02Z",
    "title_canon_sha256": "b2f3b633aa514b9549ba0305d3bd4a4edff771c325e192565ff0a1b77846c116"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0551",
    "kind": "arxiv",
    "version": 1
  }
}