Pith Number

pith:BBT2TYM4

pith:2016:BBT2TYM4RYKZCAEW5UFLWAIYV5

not attested not anchored not stored refs pending

Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance

Eric A. Carlen, Jan Maas

arxiv:1609.01254 v3 · 2016-09-05 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BBT2TYM4RYKZCAEW5UFLWAIYV5}

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	2026-05-18T00:45:34.637368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0867a9e19c8e15910096ed0abb0118af5eb6420f46f0dc5ad50765cf0d291ca7

Aliases

arxiv: 1609.01254 · arxiv_version: 1609.01254v3 · doi: 10.48550/arxiv.1609.01254 · pith_short_12: BBT2TYM4RYKZ · pith_short_16: BBT2TYM4RYKZCAEW · pith_short_8: BBT2TYM4

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/BBT2TYM4RYKZCAEW5UFLWAIYV5 \
  | 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: 0867a9e19c8e15910096ed0abb0118af5eb6420f46f0dc5ad50765cf0d291ca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a878c5b21592b4a23b14d5dc59b7b71529a2da61c4097f670c8014690489d39e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-09-05T18:56:46Z",
    "title_canon_sha256": "a80ddcd37ae525b83ccc88a97da1532ff74cbb03ac8772f9a719c89c7bb48c40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01254",
    "kind": "arxiv",
    "version": 3
  }
}