Pith Number

pith:HVI72EVD

pith:2010:HVI72EVD4RGJ33VCQJMLYYZ5OK

not attested not anchored not stored refs pending

Matrix trace inequalities on the Tsallis entropies

Shigeru Furuichi

arxiv:1001.1388 v1 · 2010-01-09 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HVI72EVD4RGJ33VCQJMLYYZ5OK}

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.

Cited by

1 paper in Pith

$r$-deformed $\alpha$-$z$-R\'enyi relative entropy

Receipt and verification

First computed	2026-07-04T17:19:15.332285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d51fd12a3e44c9deea28258bc633d729f763e57d056193a8fa0efa89d441ce4

Aliases

arxiv: 1001.1388 · arxiv_version: 1001.1388v1 · doi: 10.48550/arxiv.1001.1388 · pith_short_12: HVI72EVD4RGJ · pith_short_16: HVI72EVD4RGJ33VC · pith_short_8: HVI72EVD

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/HVI72EVD4RGJ33VCQJMLYYZ5OK \
  | 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: 3d51fd12a3e44c9deea28258bc633d729f763e57d056193a8fa0efa89d441ce4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90793686eb6679a309a3639ace03fb631009d3e950391ea90da95ae53e384ed2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-01-09T00:25:05Z",
    "title_canon_sha256": "49e711aaef8d1eb79e4f386ae9b99ae9d86a6db2b7f40a37bca91ab5a4198f5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1388",
    "kind": "arxiv",
    "version": 1
  }
}