Pith Number

pith:CXV35KBN

pith:2009:CXV35KBNCEBCK2MF7SFTKILBHR

not attested not anchored not stored refs pending

Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2

Andrzej Grudka, {\L}ukasz Pankowski, Micha{\l} Horodecki

arxiv:0911.2515 v2 · 2009-11-13 · 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{CXV35KBNCEBCK2MF7SFTKILBHR}

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	2026-05-18T04:39:49.345198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15ebbea82d1102256985fc8b3521613c47a49e33e966e7d31a1015c3987a28b0

Aliases

arxiv: 0911.2515 · arxiv_version: 0911.2515v2 · doi: 10.48550/arxiv.0911.2515 · pith_short_12: CXV35KBNCEBC · pith_short_16: CXV35KBNCEBCK2MF · pith_short_8: CXV35KBN

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/CXV35KBNCEBCK2MF7SFTKILBHR \
  | 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: 15ebbea82d1102256985fc8b3521613c47a49e33e966e7d31a1015c3987a28b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0a8b5802516e41770420317075be00fc58d54ccfda200bc9b53381931076aaf",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2009-11-13T00:17:09Z",
    "title_canon_sha256": "61f850bfb8f16445586d590e07b839f45b1e08b461b1a6452d817f1c849c8ed9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2515",
    "kind": "arxiv",
    "version": 2
  }
}