Pith Number

pith:573XK2TM

pith:2026:573XK2TM26IAJBHUGLF7OOSJ5U

not attested not anchored not stored refs pending

The Sharma-Mittal Entropy is Subadditive and Supermodular on the Majorization Lattice

Roberto Bruno, Ugo Vaccaro

arxiv:2605.18600 v1 · 2026-05-18 · cs.IT · math.CO · math.IT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{573XK2TM26IAJBHUGLF7OOSJ5U}

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	2026-05-20T00:06:10.210599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eff7756a6cd7900484f432cbf73a49ed2965789ba97115777c542bfe4f1fa6a6

Aliases

arxiv: 2605.18600 · arxiv_version: 2605.18600v1 · doi: 10.48550/arxiv.2605.18600 · pith_short_12: 573XK2TM26IA · pith_short_16: 573XK2TM26IAJBHU · pith_short_8: 573XK2TM

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/573XK2TM26IAJBHUGLF7OOSJ5U \
  | 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: eff7756a6cd7900484f432cbf73a49ed2965789ba97115777c542bfe4f1fa6a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b09d57786a22e30920e77d57a994586159650340f2506da017220bba07f0f2ba",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-18T16:12:06Z",
    "title_canon_sha256": "24a2677774cef4c19aaaf43f83266e48d0548d08ce1e22cee63d63763d769d88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18600",
    "kind": "arxiv",
    "version": 1
  }
}