Pith Number

pith:YYOE5OT4

pith:2016:YYOE5OT4K3AFFAAUW2VVUIYPHH

not attested not anchored not stored refs pending

R\'enyi relative entropies and noncommutative $L_p$-spaces

Anna Jencova

arxiv:1609.08462 v4 · 2016-09-27 · quant-ph · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YYOE5OT4K3AFFAAUW2VVUIYPHH}

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

4 papers in Pith

No off-diagonal quantum focusing for R\'enyi divergences

Integral representations of $f$-divergences for general von Neumann algebras

A general proof of integer R\'enyi QNEC

Bounding relative entropy for non-unitary excitations in quantum field theory

Receipt and verification

First computed	2026-07-05T01:06:44.931736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c61c4eba7c56c0528014b6ab5a230f39d26542e21f0bb4aab4623a7afc70d0cd

Aliases

arxiv: 1609.08462 · arxiv_version: 1609.08462v4 · doi: 10.48550/arxiv.1609.08462 · pith_short_12: YYOE5OT4K3AF · pith_short_16: YYOE5OT4K3AFFAAU · pith_short_8: YYOE5OT4

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/YYOE5OT4K3AFFAAUW2VVUIYPHH \
  | 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: c61c4eba7c56c0528014b6ab5a230f39d26542e21f0bb4aab4623a7afc70d0cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f1566e5d5f8eea04f123df7b38073707ab1b0825d608f9f24fb242de46ba21d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2016-09-27T14:12:56Z",
    "title_canon_sha256": "2e0d0ddc4d83a9850d266086e99335a677692cac6c4c868ff52b3b1291662e95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08462",
    "kind": "arxiv",
    "version": 4
  }
}