Pith Number

pith:OJOJL3AB

pith:2016:OJOJL3ABONP7TCFKS54LNCQED6

not attested not anchored not stored refs pending

An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models

Alexander Mielke, Markus Mittnenzweig

arxiv:1609.05765 v3 · 2016-09-19 · 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{OJOJL3ABONP7TCFKS54LNCQED6}

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	2026-05-18T00:03:25.308014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

725c95ec01735ff988aa9778b68a041f8cd99ee09e4d124b47886952455f51eb

Aliases

arxiv: 1609.05765 · arxiv_version: 1609.05765v3 · doi: 10.48550/arxiv.1609.05765 · pith_short_12: OJOJL3ABONP7 · pith_short_16: OJOJL3ABONP7TCFK · pith_short_8: OJOJL3AB

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/OJOJL3ABONP7TCFKS54LNCQED6 \
  | 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: 725c95ec01735ff988aa9778b68a041f8cd99ee09e4d124b47886952455f51eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11539fc6964a4f544910f67245b29fd5b30cb8a3b6c8f431dd9f0d1930fd162c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-09-19T15:05:29Z",
    "title_canon_sha256": "098a43429ccae3240e52c5e0e6af46da84511cf83d278959882c354279c0c6ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05765",
    "kind": "arxiv",
    "version": 3
  }
}