Pith Number

pith:4RJYEOXY

pith:2011:4RJYEOXYKSM3YY5KDHQJV6EN5O

not attested not anchored not stored refs pending

The general form of gamma-family of quantum relative entropies

Ryszard Pawe{\l} Kostecki

arxiv:1106.2225 v2 · 2011-06-11 · 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{4RJYEOXYKSM3YY5KDHQJV6EN5O}

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	2026-05-18T04:14:28.894591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e453823af85499bc63aa19e09af88deb85e92ee17f328f39f5c148c2d245013a

Aliases

arxiv: 1106.2225 · arxiv_version: 1106.2225v2 · doi: 10.48550/arxiv.1106.2225 · pith_short_12: 4RJYEOXYKSM3 · pith_short_16: 4RJYEOXYKSM3YY5K · pith_short_8: 4RJYEOXY

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/4RJYEOXYKSM3YY5KDHQJV6EN5O \
  | 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: e453823af85499bc63aa19e09af88deb85e92ee17f328f39f5c148c2d245013a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c78db62b43d656fdf9d4686de8b68e909ce7b2b9af66b3a394644a275b5ed669",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-06-11T10:44:13Z",
    "title_canon_sha256": "b79ad02ab6cb55fb2756c58cdf378558e8794af6e42db824f453917af0be00a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2225",
    "kind": "arxiv",
    "version": 2
  }
}