Pith Number

pith:Z5KJVSRM

pith:2025:Z5KJVSRMUXZED7OUUAXOGBEQP4

not attested not anchored not stored refs pending

Entropic Isoperimetric and Cram\'er--Rao Inequalities for R\'enyi--Fisher Information

Hao Wu, Lei Yu

arxiv:2504.01837 v2 · 2025-04-02 · cs.IT · math.IT · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5KJVSRMUXZED7OUUAXOGBEQP4}

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	2026-07-05T11:19:26.251379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf549aca2ca5f241fdd4a02ee304907f3cc2d6115f0316240eb0f1d0a096dc80

Aliases

arxiv: 2504.01837 · arxiv_version: 2504.01837v2 · doi: 10.48550/arxiv.2504.01837 · pith_short_12: Z5KJVSRMUXZE · pith_short_16: Z5KJVSRMUXZED7OU · pith_short_8: Z5KJVSRM

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/Z5KJVSRMUXZED7OUUAXOGBEQP4 \
  | 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: cf549aca2ca5f241fdd4a02ee304907f3cc2d6115f0316240eb0f1d0a096dc80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "634f56ddc4849fdbf56de97de2062ded066d47a1b00d72c87e54bd73f8eb4aad",
    "cross_cats_sorted": [
      "math.IT",
      "math.PR",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2025-04-02T15:44:02Z",
    "title_canon_sha256": "bec8b4679a0cdec37a18728959a61b6204ecc1ac74dfad125ea3ef46022c71f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.01837",
    "kind": "arxiv",
    "version": 2
  }
}