Pith Number

pith:ZCGYP5BH

pith:2010:ZCGYP5BHFKXB4WBJWZ26PE2R22

not attested not anchored not stored refs pending

Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence

Karol Zyczkowski, Mark Fannes, Wojciech Roga

arxiv:1004.4782 v1 · 2010-04-27 · 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{ZCGYP5BHFKXB4WBJWZ26PE2R22}

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	2026-05-18T02:07:53.305945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c88d87f4272aae1e5829b675e79351d6bf370aadf938d2ca0cc428fe4a6da424

Aliases

arxiv: 1004.4782 · arxiv_version: 1004.4782v1 · doi: 10.48550/arxiv.1004.4782 · pith_short_12: ZCGYP5BHFKXB · pith_short_16: ZCGYP5BHFKXB4WBJ · pith_short_8: ZCGYP5BH

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/ZCGYP5BHFKXB4WBJWZ26PE2R22 \
  | 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: c88d87f4272aae1e5829b675e79351d6bf370aadf938d2ca0cc428fe4a6da424

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef75b83bad16082ded9bd1c4a4df74fec0f6b57905e6ba92c9abf28ccfedde34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-04-27T12:40:02Z",
    "title_canon_sha256": "d4fd566dfb1a41b5b3081967e39fcd740e67ef3472546b656b49bf36a247cc13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4782",
    "kind": "arxiv",
    "version": 1
  }
}