Pith Number

pith:TVBOFHIS

pith:2021:TVBOFHISTQDK33A5K7LOX4JWWK

not attested not anchored not stored refs pending

The $\alpha \to 1$ Limit of the Sharp Quantum R\'enyi Divergence

Bjarne Bergh, Nilanjana Datta, Robert Salzmann

arxiv:2102.06576 v3 · 2021-02-12 · quant-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TVBOFHISTQDK33A5K7LOX4JWWK}

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

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

Receipt and verification

First computed	2026-07-05T03:21:08.451273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d42e29d129c06adec1d57d6ebf136b289f8caebea924a0a231706d731daabb7

Aliases

arxiv: 2102.06576 · arxiv_version: 2102.06576v3 · doi: 10.48550/arxiv.2102.06576 · pith_short_12: TVBOFHISTQDK · pith_short_16: TVBOFHISTQDK33A5 · pith_short_8: TVBOFHIS

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/TVBOFHISTQDK33A5K7LOX4JWWK \
  | 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: 9d42e29d129c06adec1d57d6ebf136b289f8caebea924a0a231706d731daabb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3d86cd83bb1c2092eea20764ca943fcb5f7315fcf26317796fa114120b49272",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2021-02-12T15:35:14Z",
    "title_canon_sha256": "54497360549c4fc86e6b73baa693269f0842a6c3dd3332f93321793864575aef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.06576",
    "kind": "arxiv",
    "version": 3
  }
}