Pith Number

pith:MKXFPE5X

pith:2000:MKXFPE5XJNQFL5GUWQ2GLITLBV

not attested not anchored not stored refs pending

The Quantum Boltzmann Equation in a Nontrivial Background

Kimmo Kainulainen, Michael Joyce, Tomislav Prokopec

arxiv:hep-ph/0002012 v1 · 2000-02-01 · hep-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MKXFPE5XJNQFL5GUWQ2GLITLBV}

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	2026-05-18T01:00:27.022944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62ae5793b74b6055f4d4b43465a26b0d68fc0a348eacf242db9fabda6cd09e66

Aliases

arxiv: hep-ph/0002012 · arxiv_version: hep-ph/0002012v1 · doi: 10.48550/arxiv.hep-ph/0002012 · pith_short_12: MKXFPE5XJNQF · pith_short_16: MKXFPE5XJNQFL5GU · pith_short_8: MKXFPE5X

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/MKXFPE5XJNQFL5GUWQ2GLITLBV \
  | 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: 62ae5793b74b6055f4d4b43465a26b0d68fc0a348eacf242db9fabda6cd09e66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b965ac64087c9a8f9722ece9345ff73f9cd7c9663b80d8da6734ccc3038f3c25",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2000-02-01T18:43:57Z",
    "title_canon_sha256": "8fe0a729c905b062aba8e89f9da92a45ec878c600e06c940b7d4ece87f824d6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0002012",
    "kind": "arxiv",
    "version": 1
  }
}