Pith Number

pith:HDXSL2U4

pith:2025:HDXSL2U4EOGU6XKCZ6OH2MSIZI

not attested not anchored not stored refs pending

On the Monotonicity of relative entropy: A Comparative Study of Petz's and Uhlmann's Approaches

Edoardo Provenzi, Francesco Bottacin, Santiago Matheus

arxiv:2509.11221 v1 · 2025-09-14 · 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{HDXSL2U4EOGU6XKCZ6OH2MSIZI}

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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	2026-07-05T12:11:35.545368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38ef25ea9c238d4f5d42cf9c7d3248ca29a915eb79a9d14a1cadfb3be470d7b6

Aliases

arxiv: 2509.11221 · arxiv_version: 2509.11221v1 · doi: 10.48550/arxiv.2509.11221 · pith_short_12: HDXSL2U4EOGU · pith_short_16: HDXSL2U4EOGU6XKC · pith_short_8: HDXSL2U4

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/HDXSL2U4EOGU6XKCZ6OH2MSIZI \
  | 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: 38ef25ea9c238d4f5d42cf9c7d3248ca29a915eb79a9d14a1cadfb3be470d7b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50c659c9880170143b91c8daae5828ba7f74fe0cd8699fe6aa8c20deaaa15150",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-09-14T11:47:38Z",
    "title_canon_sha256": "69f5b5e32360c1d104f6a9369c647f522341822651df6c685002bf461d421268"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.11221",
    "kind": "arxiv",
    "version": 1
  }
}