Pith Number

pith:7ZDPBOJZ

pith:2008:7ZDPBOJZINICHW3O3ID7WRHXJ6

not attested not anchored not stored refs pending

Analytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming

T.Y. Xia, Y. Zhang

arxiv:0811.4008 v1 · 2008-11-25 · 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{7ZDPBOJZINICHW3O3ID7WRHXJ6}

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	2026-07-04T17:26:23.234975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe46f0b939435023db6eda07fb44f74f8b6c30dc557516e4dfcd5757b6f16922

Aliases

arxiv: 0811.4008 · arxiv_version: 0811.4008v1 · doi: 10.48550/arxiv.0811.4008 · pith_short_12: 7ZDPBOJZINIC · pith_short_16: 7ZDPBOJZINICHW3O · pith_short_8: 7ZDPBOJZ

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/7ZDPBOJZINICHW3O3ID7WRHXJ6 \
  | 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: fe46f0b939435023db6eda07fb44f74f8b6c30dc557516e4dfcd5757b6f16922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afe46fb05103e310bd9a912b358cf701cdd7a3b9c76e0a1d2ee762f43579e324",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph",
    "submitted_at": "2008-11-25T04:12:42Z",
    "title_canon_sha256": "f810028d2cf7c35bf7ccf4c430340d0a60dd43963761faf5ccade1a17afcbd0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.4008",
    "kind": "arxiv",
    "version": 1
  }
}