Pith Number

pith:M7MFXDPD

pith:2025:M7MFXDPD4SYJJ34ZHZLR7LNXOR

not attested not anchored not stored refs pending

Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization

Changbo Zhu, Kaheon Kim, Rentian Yao, Xiaohui Chen

arxiv:2501.14635 v2 · 2025-01-24 · stat.ML · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M7MFXDPD4SYJJ34ZHZLR7LNXOR}

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	2026-07-05T11:09:07.030059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67d85b8de3e4b094ef993e571fadb77452d4c848595990d3ab36395f02a4bbab

Aliases

arxiv: 2501.14635 · arxiv_version: 2501.14635v2 · doi: 10.48550/arxiv.2501.14635 · pith_short_12: M7MFXDPD4SYJ · pith_short_16: M7MFXDPD4SYJJ34Z · pith_short_8: M7MFXDPD

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/M7MFXDPD4SYJJ34ZHZLR7LNXOR \
  | 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: 67d85b8de3e4b094ef993e571fadb77452d4c848595990d3ab36395f02a4bbab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "691344dc6cf6d4a3c185da83255b3c39e75af616daadf2111a7fc41890a31958",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-01-24T16:55:21Z",
    "title_canon_sha256": "81f4d17660c3955720c1f54394e3857bac3c5ba1c3b2d13d7fd0df4050781296"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.14635",
    "kind": "arxiv",
    "version": 2
  }
}