Pith Number

pith:YX4K2S3S

pith:2010:YX4K2S3SC4KBGW3MHKMLSGGDRN

not attested not anchored not stored refs pending

Boltzmann hierarchy for the cosmic microwave background at second order including photon polarization

C. Fidler (RWTH Aachen), M. Beneke

arxiv:1003.1834 v1 · 2010-03-09 · astro-ph.CO · 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{YX4K2S3SC4KBGW3MHKMLSGGDRN}

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.

Cited by

1 paper in Pith

Tetrad formalism for exact cosmological observables

Receipt and verification

First computed	2026-05-18T02:33:41.326852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5f8ad4b721714135b6c3a98b918c38b4f721ec7e52305e3d5cb7a03bc03cec9

Aliases

arxiv: 1003.1834 · arxiv_version: 1003.1834v1 · doi: 10.48550/arxiv.1003.1834 · pith_short_12: YX4K2S3SC4KB · pith_short_16: YX4K2S3SC4KBGW3M · pith_short_8: YX4K2S3S

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/YX4K2S3SC4KBGW3MHKMLSGGDRN \
  | 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: c5f8ad4b721714135b6c3a98b918c38b4f721ec7e52305e3d5cb7a03bc03cec9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e032f9ae09f0da49956d7b95dbce5b4725dd442d5c9ba12643c42e0fe9bb9f9c",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2010-03-09T09:27:22Z",
    "title_canon_sha256": "a2d392c0683793896922148eccb0303de6267013f3d631256dd43a2bd435b41d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.1834",
    "kind": "arxiv",
    "version": 1
  }
}