Pith Number

pith:YSYGA2EQ

pith:2022:YSYGA2EQZ5XLO3UFEVYPBDCKHE

not attested not anchored not stored refs pending

Integral formula for quantum relative entropy implies data processing inequality

P\'eter E. Frenkel

arxiv:2208.12194 v4 · 2022-08-25 · quant-ph · math-ph · math.FA · 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{YSYGA2EQZ5XLO3UFEVYPBDCKHE}

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

Hockey stick $f$-divergences

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

Receipt and verification

First computed	2026-07-05T06:49:57.809234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4b0606890cf6eb76e852570f08c4a3927fa4bb9a88a68f15403e5ab94151bf4

Aliases

arxiv: 2208.12194 · arxiv_version: 2208.12194v4 · doi: 10.48550/arxiv.2208.12194 · pith_short_12: YSYGA2EQZ5XL · pith_short_16: YSYGA2EQZ5XLO3UF · pith_short_8: YSYGA2EQ

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/YSYGA2EQZ5XLO3UFEVYPBDCKHE \
  | 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: c4b0606890cf6eb76e852570f08c4a3927fa4bb9a88a68f15403e5ab94151bf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1783ee22dd2d0bf470f02664eedd1e4a03aceb7f4a14933d54e2e0190409097",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2022-08-25T16:32:02Z",
    "title_canon_sha256": "f975f93c689e46fdea7eb3c95f029a815c3b05afb5ca82c930444ce24fce1f0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.12194",
    "kind": "arxiv",
    "version": 4
  }
}