Pith Number

pith:GGIZUADC

pith:2023:GGIZUADC4EHFUJ6W3U63NTKQLE

not attested not anchored not stored refs pending

Distribution-on-Distribution Regression with Wasserstein Metric: Multivariate Gaussian Case

Masaaki Imaizumi, Ryo Okano

arxiv:2307.06137 v3 · 2023-07-12 · stat.ME · 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{GGIZUADC4EHFUJ6W3U63NTKQLE}

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	2026-07-05T07:42:40.838672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31919a0062e10e5a27d6dd3db6cd50592663039601a53649a4db7f4a14179593

Aliases

arxiv: 2307.06137 · arxiv_version: 2307.06137v3 · doi: 10.48550/arxiv.2307.06137 · pith_short_12: GGIZUADC4EHF · pith_short_16: GGIZUADC4EHFUJ6W · pith_short_8: GGIZUADC

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/GGIZUADC4EHFUJ6W3U63NTKQLE \
  | 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: 31919a0062e10e5a27d6dd3db6cd50592663039601a53649a4db7f4a14179593

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7c52bfd77621ce79e6f3b455a07a2f2f050cb9fa8ee034fe7d984d7f9912000",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2023-07-12T12:40:16Z",
    "title_canon_sha256": "4c079ce0d58f6b90ceb3422296550420076d962158d9527cf5743aa3952cb173"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.06137",
    "kind": "arxiv",
    "version": 3
  }
}