Pith Number

pith:HXPWVMGH

pith:2018:HXPWVMGHYB6HV4WCIS66VW2MYZ

not attested not anchored not stored refs pending

Gradient flow structure and exponential decay of the sandwiched R\'enyi divergence for primitive Lindblad equations with GNS-detailed balance

Jianfeng Lu, Yu Cao, Yulong Lu

arxiv:1810.00906 v2 · 2018-10-01 · math.FA · 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{HXPWVMGHYB6HV4WCIS66VW2MYZ}

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	2026-05-17T23:45:04.425645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811

Aliases

arxiv: 1810.00906 · arxiv_version: 1810.00906v2 · doi: 10.48550/arxiv.1810.00906 · pith_short_12: HXPWVMGHYB6H · pith_short_16: HXPWVMGHYB6HV4WC · pith_short_8: HXPWVMGH

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/HXPWVMGHYB6HV4WCIS66VW2MYZ \
  | 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: 3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce58f6ec8d74a7fc95fe4d074999428d49db54330f02893c3bc608ece4e631f0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-10-01T18:21:02Z",
    "title_canon_sha256": "0524c10788956ce01f856bdd679397f2afda0909776cc90ee2bd952354c36d7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.00906",
    "kind": "arxiv",
    "version": 2
  }
}