Pith Number

pith:5CGPUEZC

pith:2012:5CGPUEZCST74MZUDE5STIRV74E

not attested not anchored not stored refs pending

Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics

Carl M. Bender, Sarben Sarkar

arxiv:1203.1822 v1 · 2012-03-08 · hep-th · astro-ph.HE · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5CGPUEZCST74MZUDE5STIRV74E}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:58:12.976446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e88cfa132294ffc6668327653446bfe138e47d525e8c23b174a0a02acc665690

Aliases

arxiv: 1203.1822 · arxiv_version: 1203.1822v1 · doi: 10.48550/arxiv.1203.1822 · pith_short_12: 5CGPUEZCST74 · pith_short_16: 5CGPUEZCST74MZUD · pith_short_8: 5CGPUEZC

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/5CGPUEZCST74MZUDE5STIRV74E \
  | 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: e88cfa132294ffc6668327653446bfe138e47d525e8c23b174a0a02acc665690

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33654a4e4ffaed21e5e4a70c5afedfda9704ca2ea1108052779140723f5a8b53",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2012-03-08T15:11:28Z",
    "title_canon_sha256": "8db4cc64a8f96f682b8df5702538044ddda107b65b8a96b36692fba00fd22ec4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1822",
    "kind": "arxiv",
    "version": 1
  }
}