Pith Number

pith:GGF2SZXK

pith:2011:GGF2SZXKDDFYO7CDCNUEESFE3I

not attested not anchored not stored refs pending

Continuity bounds on the quantum relative entropy - II

Jens Eisert, Koenraad M.R. Audenaert

arxiv:1105.2656 v3 · 2011-05-13 · math-ph · math.MP · 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{GGF2SZXKDDFYO7CDCNUEESFE3I}

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	2026-05-18T02:01:58.672947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

318ba966ea18cb877c4313684248a4da191bb80bc265ac2df5cc244899c07351

Aliases

arxiv: 1105.2656 · arxiv_version: 1105.2656v3 · doi: 10.48550/arxiv.1105.2656 · pith_short_12: GGF2SZXKDDFY · pith_short_16: GGF2SZXKDDFYO7CD · pith_short_8: GGF2SZXK

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/GGF2SZXKDDFYO7CDCNUEESFE3I \
  | 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: 318ba966ea18cb877c4313684248a4da191bb80bc265ac2df5cc244899c07351

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b965b4970f2f0bb4329e9e70b6dad7ce86da7df3830ab3ce859818cef64a611f",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-05-13T08:37:07Z",
    "title_canon_sha256": "33695293c7ee08666a363225ad37c6b78fa29100176144452ae7e14c1a4a3b71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2656",
    "kind": "arxiv",
    "version": 3
  }
}