Pith Number

pith:DWSIWECR

pith:2013:DWSIWECROS5ZXIZOP7P5IIIUJE

not attested not anchored not stored refs pending

An Explicit Martingale Version of Brenier's Theorem

Nizar Touzi (CMAP), Pierre Henry-Labordere (SOCIETE Generale)

arxiv:1302.4854 v3 · 2013-02-20 · q-fin.CP · 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{DWSIWECROS5ZXIZOP7P5IIIUJE}

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	2026-05-18T03:28:32.868505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1da48b105174bb9ba32e7fdfd42114490b54c547c59e6e764d08702938f4ff77

Aliases

arxiv: 1302.4854 · arxiv_version: 1302.4854v3 · doi: 10.48550/arxiv.1302.4854 · pith_short_12: DWSIWECROS5Z · pith_short_16: DWSIWECROS5ZXIZO · pith_short_8: DWSIWECR

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/DWSIWECROS5ZXIZOP7P5IIIUJE \
  | 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: 1da48b105174bb9ba32e7fdfd42114490b54c547c59e6e764d08702938f4ff77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9de04542c53616d4d3bbe511905d455b2b93aba49e50bf7cdc75569316a8a924",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.CP",
    "submitted_at": "2013-02-20T09:50:06Z",
    "title_canon_sha256": "ff72fca2fcfc93131be6fda027a77a9f754e51035529e1692ea318c203a07510"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4854",
    "kind": "arxiv",
    "version": 3
  }
}