Pith Number

pith:MUUX3RWG

pith:2013:MUUX3RWGPWBRAJI2UGRDXND5UX

not attested not anchored not stored refs pending

Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson-Walker spacetime

Ho Lee

arxiv:1307.5688 v1 · 2013-07-22 · 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{MUUX3RWGPWBRAJI2UGRDXND5UX}

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	2026-05-18T03:17:54.949768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65297dc6c67d8310251aa1a23bb47da5c2e678452fd84218313f8d76b1639249

Aliases

arxiv: 1307.5688 · arxiv_version: 1307.5688v1 · doi: 10.48550/arxiv.1307.5688 · pith_short_12: MUUX3RWGPWBR · pith_short_16: MUUX3RWGPWBRAJI2 · pith_short_8: MUUX3RWG

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/MUUX3RWGPWBRAJI2UGRDXND5UX \
  | 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: 65297dc6c67d8310251aa1a23bb47da5c2e678452fd84218313f8d76b1639249

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e80e3151e507f81425292c52e6a58342002811d9d8565d77ffe8367048d4d1b5",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-07-22T12:58:53Z",
    "title_canon_sha256": "fc6564d2b6b25bee24e592abcb31a497391f29c1bc9c6791ce85ecc5d85194e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5688",
    "kind": "arxiv",
    "version": 1
  }
}