Pith Number

pith:JXFLUONS

pith:2010:JXFLUONSFEGM46RC6UA6JBT3PM

not attested not anchored not stored refs pending

From the Schr\"odinger problem to the Monge-Kantorovich problem

Christian L\'eonard (MODAL'X)

arxiv:1011.2564 v1 · 2010-11-11 · math.OC · 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{JXFLUONSFEGM46RC6UA6JBT3PM}

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	2026-05-18T03:17:00.511624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dcaba39b2290cce7a22f501e4867b7b10cee55ed1d4303af08a187af882b249

Aliases

arxiv: 1011.2564 · arxiv_version: 1011.2564v1 · doi: 10.48550/arxiv.1011.2564 · pith_short_12: JXFLUONSFEGM · pith_short_16: JXFLUONSFEGM46RC · pith_short_8: JXFLUONS

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/JXFLUONSFEGM46RC6UA6JBT3PM \
  | 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: 4dcaba39b2290cce7a22f501e4867b7b10cee55ed1d4303af08a187af882b249

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41b00dc77493f96dc0fb11ce1474bac6327b2aa929cf4a8738199ea1d3fcba7c",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-11-11T05:50:55Z",
    "title_canon_sha256": "69de5fc30d3b1187ccf26c59902c4f8622a004371d34f6b0ef96ec7fb70719cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2564",
    "kind": "arxiv",
    "version": 1
  }
}