Pith Number

pith:J2772AKW

pith:2018:J2772AKW4DGQHKSYFZIKF2BBD7

not attested not anchored not stored refs pending

Second order models for optimal transport and cubic splines on the Wasserstein space

Fran\c{c}ois-Xavier Vialard (MOKAPLAN), Jean-David Benamou (MOKAPLAN), Thomas Gallou\"et (MOKAPLAN)

arxiv:1801.04144 v2 · 2018-01-12 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J2772AKW4DGQHKSYFZIKF2BBD7}

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	2026-05-18T00:09:47.421559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ebffd0156e0cd03aa582e50a2e8211fd77b3c0be3596403a38b26c2cd7bf8cd

Aliases

arxiv: 1801.04144 · arxiv_version: 1801.04144v2 · doi: 10.48550/arxiv.1801.04144 · pith_short_12: J2772AKW4DGQ · pith_short_16: J2772AKW4DGQHKSY · pith_short_8: J2772AKW

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/J2772AKW4DGQHKSYFZIKF2BBD7 \
  | 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: 4ebffd0156e0cd03aa582e50a2e8211fd77b3c0be3596403a38b26c2cd7bf8cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f36b26979bc2a506c736d0650d067539200915a9e680549b1945553f2d29d53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-01-12T12:24:05Z",
    "title_canon_sha256": "fed9933462a527814a99d8961a9afc9854a10649916e768c9f72a85ad496d8db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.04144",
    "kind": "arxiv",
    "version": 2
  }
}