Pith Number

pith:P6DNA4IQ

pith:2016:P6DNA4IQ44OM7BFR6XFKZ7RRJB

not attested not anchored not stored refs pending

R\'enyi divergences as weighted non-commutative vector valued $L_p$-spaces

Marco Tomamichel, Mario Berta, Volkher B. Scholz

arxiv:1608.05317 v2 · 2016-08-18 · math-ph · cs.IT · math.IT · math.MP · math.OA · 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{P6DNA4IQ44OM7BFR6XFKZ7RRJB}

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

2 papers in Pith

A general proof of integer R\'enyi QNEC

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

Receipt and verification

First computed	2026-05-17T23:58:42.636070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b

Aliases

arxiv: 1608.05317 · arxiv_version: 1608.05317v2 · doi: 10.48550/arxiv.1608.05317 · pith_short_12: P6DNA4IQ44OM · pith_short_16: P6DNA4IQ44OM7BFR · pith_short_8: P6DNA4IQ

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/P6DNA4IQ44OM7BFR6XFKZ7RRJB \
  | 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: 7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95563afaa89a211354d0c25b6b0bb547fd3c9ebf47514597037e1164ca1778a6",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-08-18T16:16:03Z",
    "title_canon_sha256": "bf171dc348e127e213cedb9dde961b42b37ff05b80caac3ce26ac4534b661132"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05317",
    "kind": "arxiv",
    "version": 2
  }
}