Pith Number

pith:4GFWTOXT

pith:2025:4GFWTOXTMOE7CJVNKOTE4WBQCM

not attested not anchored not stored refs pending

Barycentric model aggregation in the Wasserstein space of distributions and a variational approach to consistency

Athanasios N. Yannacopoulos, Emmanouil Androulakis, Georgios I. Papayiannis

arxiv:2507.11719 v2 · 2025-07-15 · stat.ME · stat.CO · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GFWTOXTMOE7CJVNKOTE4WBQCM}

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	2026-05-20T01:04:56.093499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e18b69baf36389f126ad53a64e583013273dee9ad24c2c515c60eb66bb0ea87c

Aliases

arxiv: 2507.11719 · arxiv_version: 2507.11719v2 · doi: 10.48550/arxiv.2507.11719 · pith_short_12: 4GFWTOXTMOE7 · pith_short_16: 4GFWTOXTMOE7CJVN · pith_short_8: 4GFWTOXT

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/4GFWTOXTMOE7CJVNKOTE4WBQCM \
  | 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: e18b69baf36389f126ad53a64e583013273dee9ad24c2c515c60eb66bb0ea87c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca717cb817806e1b8cb256bdfe643954275f93329533867e615e108b78b299ae",
    "cross_cats_sorted": [
      "stat.CO",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-07-15T20:41:57Z",
    "title_canon_sha256": "cc7959bc8cc01ceaacb4075995e5ee386248a17573063abbba9dde36fea4babc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.11719",
    "kind": "arxiv",
    "version": 2
  }
}