Pith Number

pith:3E5CWPVA

pith:2016:3E5CWPVANHKHG2WUOWYCPSQ2NE

not attested not anchored not stored refs pending

Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time

Etienne Takou, Fidele L. Ciake Ciake

arxiv:1609.05613 v1 · 2016-09-19 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3E5CWPVANHKHG2WUOWYCPSQ2NE}

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	2026-05-18T01:04:25.881481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d93a2b3ea069d4736ad475b027ca1a6911e9d19c67447b49dd9387328517c7a2

Aliases

arxiv: 1609.05613 · arxiv_version: 1609.05613v1 · doi: 10.48550/arxiv.1609.05613 · pith_short_12: 3E5CWPVANHKH · pith_short_16: 3E5CWPVANHKHG2WU · pith_short_8: 3E5CWPVA

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/3E5CWPVANHKHG2WUOWYCPSQ2NE \
  | 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: d93a2b3ea069d4736ad475b027ca1a6911e9d19c67447b49dd9387328517c7a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63219369b2725294faf7b6b61626eb303fa28106ddf65b12e8be7da39956b396",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-09-19T07:10:16Z",
    "title_canon_sha256": "e7738ee6e14da5da8e912ed1abbc3ae6a7074609261ad480c289cc421b11caa6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05613",
    "kind": "arxiv",
    "version": 1
  }
}