Pith Number

pith:MUM5L6X5

pith:2011:MUM5L6X56DILZ2RWFNLPRTG4DZ

not attested not anchored not stored refs pending

Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications

M. E. Shirokov

arxiv:1106.3297 v6 · 2011-06-16 · 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{MUM5L6X56DILZ2RWFNLPRTG4DZ}

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	2026-05-18T03:07:41.485693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6519d5fafdf0d0bcea362b56f8ccdc1e70658bf3b4745c0e1cc32bbde2842fe9

Aliases

arxiv: 1106.3297 · arxiv_version: 1106.3297v6 · doi: 10.48550/arxiv.1106.3297 · pith_short_12: MUM5L6X56DIL · pith_short_16: MUM5L6X56DILZ2RW · pith_short_8: MUM5L6X5

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/MUM5L6X56DILZ2RWFNLPRTG4DZ \
  | 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: 6519d5fafdf0d0bcea362b56f8ccdc1e70658bf3b4745c0e1cc32bbde2842fe9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22300f9b70236057492ecb6de6efc8f689e25ed71c81dac291bca437e4275c44",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-06-16T18:19:28Z",
    "title_canon_sha256": "02ded2125cd010c3c9d0b6f49cb19ec0c7698bababcef93ac7e88fe8355811fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3297",
    "kind": "arxiv",
    "version": 6
  }
}