Pith Number

pith:D7V4HHP7

pith:2016:D7V4HHP73ECUELQKTYVWIU52VF

not attested not anchored not stored refs pending

The Einstein-Boltzmann equations revisited

Alexandre Refregier (ETH Zurich), Sharvari Nadkarni-Ghosh (IIT Kanpur)

arxiv:1612.06697 v2 · 2016-12-20 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D7V4HHP73ECUELQKTYVWIU52VF}

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	2026-05-18T00:33:52.862896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1febc39dffd905422e0a9e2b6453baa944043beee7fc158733f1e750b24229cd

Aliases

arxiv: 1612.06697 · arxiv_version: 1612.06697v2 · doi: 10.48550/arxiv.1612.06697 · pith_short_12: D7V4HHP73ECU · pith_short_16: D7V4HHP73ECUELQK · pith_short_8: D7V4HHP7

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/D7V4HHP73ECUELQKTYVWIU52VF \
  | 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: 1febc39dffd905422e0a9e2b6453baa944043beee7fc158733f1e750b24229cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b48364e2e4e5478a0b0504f27c28c4370696cbe5438de9a685cadab7be2b01b",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-12-20T17:36:45Z",
    "title_canon_sha256": "2a8d56da1cb46c81469a334535498f2ec0536ee8f587eac43b300c66c3f84d3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.06697",
    "kind": "arxiv",
    "version": 2
  }
}