Pith Number

pith:SSF223WX

pith:2001:SSF223WXMK2PCBN2FGRS54JTF6

not attested not anchored not stored refs pending

The von Neumann entropy and information rate for ideal quantum Gibbs ensembles

Oliver Johnson, Yuri Suhov

arxiv:math-ph/0109023 v2 · 2001-09-21 · math-ph · math.MP · math.ST · quant-ph · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SSF223WXMK2PCBN2FGRS54JTF6}

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	2026-05-18T04:08:43.401610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

948bad6ed762b4f105ba29a32ef1332f97500d7eca155bca169c22e406f5bbde

Aliases

arxiv: math-ph/0109023 · arxiv_version: math-ph/0109023v2 · doi: 10.48550/arxiv.math-ph/0109023 · pith_short_12: SSF223WXMK2P · pith_short_16: SSF223WXMK2PCBN2 · pith_short_8: SSF223WX

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/SSF223WXMK2PCBN2FGRS54JTF6 \
  | 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: 948bad6ed762b4f105ba29a32ef1332f97500d7eca155bca169c22e406f5bbde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40c66af235d97e3615b566453837468a377c985bc2b3e063b370bb0bda334d52",
    "cross_cats_sorted": [
      "math.MP",
      "math.ST",
      "quant-ph",
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2001-09-21T22:24:01Z",
    "title_canon_sha256": "488e67dc52306f3b2eb08cd9e07f107d7e21bb96fad726121c50a74937a9d220"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0109023",
    "kind": "arxiv",
    "version": 2
  }
}