Pith Number

pith:BO4WAKK2

pith:2014:BO4WAKK2ASR34OHG2O55XHZALW

not attested not anchored not stored refs pending

A strengthened monotonicity inequality of quantum relative entropy: A unifying approach via R\'{e}nyi relative entropy

Lin Zhang

arxiv:1403.5343 v4 · 2014-03-21 · 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{BO4WAKK2ASR34OHG2O55XHZALW}

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.

Receipt and verification

First computed	2026-05-18T01:18:54.547204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bb960295a04a3be38e6d3bbdb9f205dbfeab38aae25c9b340936451d98288da

Aliases

arxiv: 1403.5343 · arxiv_version: 1403.5343v4 · doi: 10.48550/arxiv.1403.5343 · pith_short_12: BO4WAKK2ASR3 · pith_short_16: BO4WAKK2ASR34OHG · pith_short_8: BO4WAKK2

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/BO4WAKK2ASR34OHG2O55XHZALW \
  | 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: 0bb960295a04a3be38e6d3bbdb9f205dbfeab38aae25c9b340936451d98288da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4880ca480c9743f82c3a5e6797f926d764c52800b00fcfe7ac6589658cbe72ff",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2014-03-21T02:01:52Z",
    "title_canon_sha256": "df02f973524786dbb634897f1ec554f7a47ea7c88e695e56515edff6501af8c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.5343",
    "kind": "arxiv",
    "version": 4
  }
}