Pith Number

pith:W6W7KI6Z

pith:2026:W6W7KI6ZNWVWBYI6J3K2I35LEM

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Geometry of R\'enyi Entropy on the Majorization Lattice

Anuj Kumar Yadav, Yanina Y. Shkel

Rényi entropy is subadditive on the majorization lattice for every order α and supermodular for α equal to 0 or at least 1.

arxiv:2605.09655 v2 · 2026-05-10 · cs.IT · math.CO · math.IT · math.PR

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4 Citations open

5 Replications open

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Claims

C1strongest claim

for every order α ∈ [0,∞], the Rényi entropy is subadditive on the majorization lattice. We further characterize the supermodular regime, showing that Rényi entropy is supermodular on the majorization lattice for α ∈ {0} ∪ [1,∞].

C2weakest assumption

The majorization partial order forms a complete lattice on the set of ordered probability distributions, and the fundamental relation between comonotone coupling and independent coupling holds for collections of marginal distributions.

C3one line summary

Rényi entropy is subadditive on the majorization lattice for all alpha in [0, infinity] and supermodular for alpha in {0} union [1, infinity].

Formal links

2 machine-checked theorem links

Cited by

2 papers in Pith

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

Receipt and verification

First computed	2026-05-25T02:02:16.564575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7adf523d96dab60e11e4ed5a46fab233310417e17dd9aa0c553b8a88e3fc31d

Aliases

arxiv: 2605.09655 · arxiv_version: 2605.09655v2 · doi: 10.48550/arxiv.2605.09655 · pith_short_12: W6W7KI6ZNWVW · pith_short_16: W6W7KI6ZNWVWBYI6 · pith_short_8: W6W7KI6Z

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W6W7KI6ZNWVWBYI6J3K2I35LEM \
  | 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: b7adf523d96dab60e11e4ed5a46fab233310417e17dd9aa0c553b8a88e3fc31d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0376718796394f60e80a72e220b93a7aafde3bfd58840de73b56041467fc0ea1",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-10T16:58:44Z",
    "title_canon_sha256": "95240bc8f9bde406bb076acb6c19faa479c2fa081cddd1d0c3d4fb97a2195401"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09655",
    "kind": "arxiv",
    "version": 2
  }
}