Pith Number

pith:UGPP2ZLH

pith:2011:UGPP2ZLH354N76EPJPVMF42QVH

not attested not anchored not stored refs pending

A probabilistic view on the general relativistic Boltzmann equation

Frabrice Debbasch, Ismael Bailleul

arxiv:1107.0567 v1 · 2011-07-04 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UGPP2ZLH354N76EPJPVMF42QVH}

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	2026-05-18T04:18:53.747863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a19efd6567df78dff88f4beac2f350a9ed64d88ab47385d7e60e070eb23cf9bf

Aliases

arxiv: 1107.0567 · arxiv_version: 1107.0567v1 · doi: 10.48550/arxiv.1107.0567 · pith_short_12: UGPP2ZLH354N · pith_short_16: UGPP2ZLH354N76EP · pith_short_8: UGPP2ZLH

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/UGPP2ZLH354N76EPJPVMF42QVH \
  | 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: a19efd6567df78dff88f4beac2f350a9ed64d88ab47385d7e60e070eb23cf9bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f543157076e6af0c988d18863757066bf150a3dffb8aa47474cbfe6da29fe46",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-07-04T09:14:10Z",
    "title_canon_sha256": "80c14abca71cca4c760542cf964ceff340a5870a20846b0302e275687ba93227"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0567",
    "kind": "arxiv",
    "version": 1
  }
}