Pith Number

pith:CPPK4XCH

pith:2017:CPPK4XCH35NKEXG4NHCC3RWGSL

not attested not anchored not stored refs pending

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

Anna Jen\v{c}ov\'a

arxiv:1707.00047 v2 · 2017-06-30 · 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{CPPK4XCH35NKEXG4NHCC3RWGSL}

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

Hockey stick $f$-divergences

A general proof of integer R\'enyi QNEC

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

Receipt and verification

First computed	2026-07-05T03:29:12.289587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13deae5c47df5aa25cdc69c42dc6c692d56031f83800d92742bf8f64c58b8dcc

Aliases

arxiv: 1707.00047 · arxiv_version: 1707.00047v2 · doi: 10.48550/arxiv.1707.00047 · pith_short_12: CPPK4XCH35NK · pith_short_16: CPPK4XCH35NKEXG4 · pith_short_8: CPPK4XCH

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/CPPK4XCH35NKEXG4NHCC3RWGSL \
  | 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: 13deae5c47df5aa25cdc69c42dc6c692d56031f83800d92742bf8f64c58b8dcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59a1f04c4aa25f9507e4a3d9fa4ebb4a7739c74478c6af400d3a671bdca9cc32",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2017-06-30T21:27:17Z",
    "title_canon_sha256": "37def7cc8f11ea131fd5a4b50e9c1fc67cacf322f2f6138bb181d096edc4473b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.00047",
    "kind": "arxiv",
    "version": 2
  }
}