Pith Number

pith:ZDTHQIIG

pith:2026:ZDTHQIIGTMQIJ3QNEPF4674DEW

not attested not anchored not stored refs pending

Optimal Transport under Group Fairness Constraints

Aur\'elien Bellet, Francisco Andrade, Linus Bleistein, Mathieu Dagr\'eou, Thomas Boudou

arxiv:2601.07144 v3 · 2026-01-12 · stat.ML · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZDTHQIIGTMQIJ3QNEPF4674DEW}

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	2026-06-04T01:08:39.647011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf

Aliases

arxiv: 2601.07144 · arxiv_version: 2601.07144v3 · doi: 10.48550/arxiv.2601.07144 · pith_short_12: ZDTHQIIGTMQI · pith_short_16: ZDTHQIIGTMQIJ3QN · pith_short_8: ZDTHQIIG

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/ZDTHQIIGTMQIJ3QNEPF4674DEW \
  | 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: c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "270f66d95c9e440361529b2702ef95aad7e387803b3c0564727de2871e5bfe26",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-01-12T02:26:32Z",
    "title_canon_sha256": "f70be8eba644a359b9514c2b89bdd224f6c7f352611737eea15b225b88840a81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.07144",
    "kind": "arxiv",
    "version": 3
  }
}