Pith Number

pith:X7LELPM5

pith:2015:X7LELPM5ZTMOYMMKZN5WYD4OYQ

not attested not anchored not stored refs pending

About the analogy between optimal transport and minimal entropy

Christian L\'eonard (MODAL'X), Ivan Gentil (ICJ), Luigia Ripani (ICJ)

arxiv:1510.08230 v2 · 2015-10-28 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X7LELPM5ZTMOYMMKZN5WYD4OYQ}

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	2026-05-18T01:14:25.771990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfd645bd9dccd8ec318acb7b6c0f8ec42da47e3f065ef09f873aa6ec020dee1f

Aliases

arxiv: 1510.08230 · arxiv_version: 1510.08230v2 · doi: 10.48550/arxiv.1510.08230 · pith_short_12: X7LELPM5ZTMO · pith_short_16: X7LELPM5ZTMOYMMK · pith_short_8: X7LELPM5

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/X7LELPM5ZTMOYMMKZN5WYD4OYQ \
  | 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: bfd645bd9dccd8ec318acb7b6c0f8ec42da47e3f065ef09f873aa6ec020dee1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0da6e28ddd0d067e895c7b0f44083264db77a033491026b909d427f229a54fac",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-28T09:17:31Z",
    "title_canon_sha256": "a2745f75f8441852df4fd4b76f7f1b5970ed038ad604c955b542d54812f1202c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08230",
    "kind": "arxiv",
    "version": 2
  }
}