Pith Number

pith:4TSXTWEW

pith:2025:4TSXTWEWMEOQKNXYGM276EWX36

not attested not anchored not stored refs pending

The Monge optimal transport barycenter problem

Andrew D. Lipnick, Esteban G. Tabak, Giulio Trigila, Wenjun Zhao, Xuancheng Ye, Yating Wang

arxiv:2507.03669 v3 · 2025-07-04 · math.OC · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TSXTWEWMEOQKNXYGM276EWX36}

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	2026-06-25T01:17:45.317668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4e579d896611d0536f83335ff12d7dfa8092a669772b2653f6a2b39d95f2e70

Aliases

arxiv: 2507.03669 · arxiv_version: 2507.03669v3 · doi: 10.48550/arxiv.2507.03669 · pith_short_12: 4TSXTWEWMEOQ · pith_short_16: 4TSXTWEWMEOQKNXY · pith_short_8: 4TSXTWEW

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/4TSXTWEWMEOQKNXYGM276EWX36 \
  | 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: e4e579d896611d0536f83335ff12d7dfa8092a669772b2653f6a2b39d95f2e70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2bafc8ca271ba8bfb6917aeb39dc0f1ec46091239b3d5449ddc9a5840500106",
    "cross_cats_sorted": [
      "stat.ME"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-04T15:43:33Z",
    "title_canon_sha256": "44e2e7841b5026615e05cdf75c7e11606ac885069d8be4830b9ef3eab6cf2b04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.03669",
    "kind": "arxiv",
    "version": 3
  }
}