Pith Number

pith:63FVDDL2

pith:2013:63FVDDL2GQAEMJSEQACKDB5TS2

not attested not anchored not stored refs pending

Monotonicity of a relative R\'enyi entropy

Elliott H. Lieb, Rupert L. Frank

arxiv:1306.5358 v3 · 2013-06-22 · math-ph · cs.IT · math.FA · math.IT · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{63FVDDL2GQAEMJSEQACKDB5TS2}

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.

Cited by

1 paper in Pith

Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization

Receipt and verification

First computed	2026-05-18T01:49:13.659419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6cb518d7a34004626448004a187b3968af6f76ff35e326b15289e499e95f2e4

Aliases

arxiv: 1306.5358 · arxiv_version: 1306.5358v3 · doi: 10.48550/arxiv.1306.5358 · pith_short_12: 63FVDDL2GQAE · pith_short_16: 63FVDDL2GQAEMJSE · pith_short_8: 63FVDDL2

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/63FVDDL2GQAEMJSEQACKDB5TS2 \
  | 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: f6cb518d7a34004626448004a187b3968af6f76ff35e326b15289e499e95f2e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29097a2c3080e8248adfec64cd822ef8a36d850f25a5612d3583c2600b99886e",
    "cross_cats_sorted": [
      "cs.IT",
      "math.FA",
      "math.IT",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-06-22T21:42:41Z",
    "title_canon_sha256": "529b366df04fd08f1aa57f4879a0f2659af4043c9d62992c07b7c5b77152edeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5358",
    "kind": "arxiv",
    "version": 3
  }
}