Pith Number

pith:UGI5TRCV

pith:2026:UGI5TRCVPE3SZHRICEJ5KTKMNB

not attested not anchored not stored refs pending

$L^2$ over Wasserstein: Statistical Analysis for Optimal Transport

Pengcheng Ye, Riccardo Passeggeri, Rohan M. Shenoy

arxiv:2605.21365 v1 · 2026-05-20 · math.ST · stat.ML · 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{UGI5TRCVPE3SZHRICEJ5KTKMNB}

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	2026-05-21T02:05:31.191625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a191d9c45579372c9e281113d54d4c6854c051c831f8732b04c01011db3de5a6

Aliases

arxiv: 2605.21365 · arxiv_version: 2605.21365v1 · doi: 10.48550/arxiv.2605.21365 · pith_short_12: UGI5TRCVPE3S · pith_short_16: UGI5TRCVPE3SZHRI · pith_short_8: UGI5TRCV

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/UGI5TRCVPE3SZHRICEJ5KTKMNB \
  | 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: a191d9c45579372c9e281113d54d4c6854c051c831f8732b04c01011db3de5a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaf84a1c15e0b5105834bd0f59b541ec54fb44ded4c333e56650803ac45c2603",
    "cross_cats_sorted": [
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-20T16:29:01Z",
    "title_canon_sha256": "a80c10f81229351355c0a6e2b06425cc3d3e7a7c89600a99d5bf868a5b50729a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21365",
    "kind": "arxiv",
    "version": 1
  }
}