Pith Number

pith:MO3PJE2R

pith:2014:MO3PJE2RWA7XKZ4B6HSVRLFWHF

not attested not anchored not stored refs pending

R\'enyi entropy and Tsallis entropy associated with positive linear operators

Ioan Ra\c{s}a

arxiv:1412.4971 v1 · 2014-12-16 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MO3PJE2RWA7XKZ4B6HSVRLFWHF}

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	2026-05-18T02:31:09.990588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63b6f49351b03f756781f1e558acb6394baae9ab89c661fb53b8b664a5153baf

Aliases

arxiv: 1412.4971 · arxiv_version: 1412.4971v1 · doi: 10.48550/arxiv.1412.4971 · pith_short_12: MO3PJE2RWA7X · pith_short_16: MO3PJE2RWA7XKZ4B · pith_short_8: MO3PJE2R

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/MO3PJE2RWA7XKZ4B6HSVRLFWHF \
  | 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: 63b6f49351b03f756781f1e558acb6394baae9ab89c661fb53b8b664a5153baf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ee103c1abb0a5629ae808e08b2b9999804ded333222a1f5582f3c7f9d91b34a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-12-16T12:16:27Z",
    "title_canon_sha256": "1a3966e50c1f42b7610a47c53f299153e8b79a2a012797d91076129c1c53cf50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.4971",
    "kind": "arxiv",
    "version": 1
  }
}