Pith Number

pith:BQZZKZSK

pith:2007:BQZZKZSKOTBPU5C7BUOY3EIYZP

not attested not anchored not stored refs pending

A Simple Proof of the Entropy-Power Inequality via Properties of Mutual Information

Olivier Rioul

arxiv:cs/0701050 v2 · 2007-01-08 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BQZZKZSKOTBPU5C7BUOY3EIYZP}

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	2026-05-18T00:58:26.563416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c3395664a74c2fa745f0d1d8d9118cbf94c0d29c3d2bdebda67c774aff4d97c

Aliases

arxiv: cs/0701050 · arxiv_version: cs/0701050v2 · doi: 10.48550/arxiv.cs/0701050 · pith_short_12: BQZZKZSKOTBP · pith_short_16: BQZZKZSKOTBPU5C7 · pith_short_8: BQZZKZSK

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/BQZZKZSKOTBPU5C7BUOY3EIYZP \
  | 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: 0c3395664a74c2fa745f0d1d8d9118cbf94c0d29c3d2bdebda67c774aff4d97c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f0bad68e956e37205d89f18ac82bf16e35c7c8d35433d03bf0e4b13062211e2",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "",
    "primary_cat": "cs.IT",
    "submitted_at": "2007-01-08T16:35:58Z",
    "title_canon_sha256": "71a1f07d6007eabb614be74f00cc73bc76c5407f7ad14684666f88ad92fe1d64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0701050",
    "kind": "arxiv",
    "version": 2
  }
}