Pith Number

pith:733ENHB4

pith:2012:733ENHB4QJMDUDD7757DWQDA5A

not attested not anchored not stored refs pending

The maximum maximum of a martingale with given $n$ marginals

Jan Ob{\l}\'oj, Nizar Touzi, Peter Spoida, Pierre Henry-Labord\`ere

arxiv:1203.6877 v4 · 2012-03-30 · math.PR · q-fin.CP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{733ENHB4QJMDUDD7757DWQDA5A}

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	2026-05-18T01:22:52.644573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fef6469c3c82583a0c7fff7e3b4060e838eb7259d5a0dc5d03b8c84c28f52b07

Aliases

arxiv: 1203.6877 · arxiv_version: 1203.6877v4 · doi: 10.48550/arxiv.1203.6877 · pith_short_12: 733ENHB4QJMD · pith_short_16: 733ENHB4QJMDUDD7 · pith_short_8: 733ENHB4

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/733ENHB4QJMDUDD7757DWQDA5A \
  | 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: fef6469c3c82583a0c7fff7e3b4060e838eb7259d5a0dc5d03b8c84c28f52b07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be64d5afdb0776299e25927dfe47bd45f0455379814ab944a359ba704ae7b6e9",
    "cross_cats_sorted": [
      "q-fin.CP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-30T18:12:17Z",
    "title_canon_sha256": "8a3a19dba35b6fbee555dae753357f3b0095d5eb30aac940a142e5fc35c99116"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6877",
    "kind": "arxiv",
    "version": 4
  }
}