Pith Number

pith:OYA5ZSRN

pith:2025:OYA5ZSRNYAA4GUORF325UAJCVG

not attested not anchored not stored refs pending

From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties

Gennaro Auricchio, Giovanni Brigati, Giuseppe Toscani, Paolo Giudici

arxiv:2507.11387 v1 · 2025-07-15 · math-ph · cs.AI · cs.LG · cs.MA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OYA5ZSRNYAA4GUORF325UAJCVG}

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.

Cited by

2 papers in Pith

Sharp Rates of MMD Empirical Estimation with Power Kernels

Receipt and verification

First computed	2026-07-05T11:37:38.314647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7601dcca2dc001c351d12ef5da0122a988a5e17272828e791bd7c064f2f22ed2

Aliases

arxiv: 2507.11387 · arxiv_version: 2507.11387v1 · doi: 10.48550/arxiv.2507.11387 · pith_short_12: OYA5ZSRNYAA4 · pith_short_16: OYA5ZSRNYAA4GUOR · pith_short_8: OYA5ZSRN

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/OYA5ZSRNYAA4GUORF325UAJCVG \
  | 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: 7601dcca2dc001c351d12ef5da0122a988a5e17272828e791bd7c064f2f22ed2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffac1727cb22635471f5a10fec86bf2f4d1e66e2569de95831ba55653e4ed742",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "cs.MA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-07-15T14:56:25Z",
    "title_canon_sha256": "f897fcab34714a962c05aa240b2b93f945b96b129b74cf2d499ab2ffa5121fd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.11387",
    "kind": "arxiv",
    "version": 1
  }
}