Pith Number

pith:PHBT7C6W

pith:2015:PHBT7C6WBZSMYZLPDD2EJ5VBGE

not attested not anchored not stored refs pending

A hierarchy of Poisson brackets in non-equilibrium thermodynamics

Michal Pavelka, Miroslav Grmela, Ogul Esen, Vaclav Klika

arxiv:1512.08010 v2 · 2015-12-25 · math-ph · math.MP · physics.flu-dyn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHBT7C6WBZSMYZLPDD2EJ5VBGE}

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	2026-05-18T01:11:21.591550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79c33f8bd60e64cc656f18f444f6a131017f2fa718e761e0439682165f15428c

Aliases

arxiv: 1512.08010 · arxiv_version: 1512.08010v2 · doi: 10.48550/arxiv.1512.08010 · pith_short_12: PHBT7C6WBZSM · pith_short_16: PHBT7C6WBZSMYZLP · pith_short_8: PHBT7C6W

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/PHBT7C6WBZSMYZLPDD2EJ5VBGE \
  | 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: 79c33f8bd60e64cc656f18f444f6a131017f2fa718e761e0439682165f15428c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4609afe5d21ab4d621b73b1fcc1237d188dcafc6955ef1b17cba957806e2831",
    "cross_cats_sorted": [
      "math.MP",
      "physics.flu-dyn"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-12-25T15:32:30Z",
    "title_canon_sha256": "bba2095cc728bc2e4f47a8530a618e2b6edea1fed7d6e7f95b5bdfbe487281a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08010",
    "kind": "arxiv",
    "version": 2
  }
}