Pith Number

pith:I27JBAKH

pith:2004:I27JBAKH5H2IM4IKCEFL3BCXN4

not attested not anchored not stored refs pending

Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach

Jonathan R. Pritchard, Marc Kamionkowski (Caltech)

arxiv:astro-ph/0412581 v1 · 2004-12-21 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I27JBAKH5H2IM4IKCEFL3BCXN4}

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

Rapid and accurate numerical evolution of linear cosmological perturbations with non-cold relics

Receipt and verification

First computed	2026-07-04T16:45:28.406379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46be908147e9f486710a110abd84576f289a74dd3b56c512d7c1a1e455f1e694

Aliases

arxiv: astro-ph/0412581 · arxiv_version: astro-ph/0412581v1 · doi: 10.48550/arxiv.astro-ph/0412581 · pith_short_12: I27JBAKH5H2I · pith_short_16: I27JBAKH5H2IM4IK · pith_short_8: I27JBAKH

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/I27JBAKH5H2IM4IKCEFL3BCXN4 \
  | 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: 46be908147e9f486710a110abd84576f289a74dd3b56c512d7c1a1e455f1e694

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5c2a8407accf9e4f73ad558cf543c494713ec9977070a0568f01bc012822d05",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-12-21T23:05:11Z",
    "title_canon_sha256": "c9104b558696c4575508f82b951571e05e3846f3b61513a887d066a94de0649e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0412581",
    "kind": "arxiv",
    "version": 1
  }
}