Pith Number

pith:YCZTUPOB

pith:2001:YCZTUPOB5CVDFBP6Z2DJ3QV6SH

not attested not anchored not stored refs pending

Sachs-Wolfe effect in some anisotropic models

Paulo Aguiar, Paulo Crawford

arxiv:astro-ph/0110412 v2 · 2001-10-18 · 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{YCZTUPOB5CVDFBP6Z2DJ3QV6SH}

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	2026-05-18T03:43:19.181681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0b33a3dc1e8aa3285fece869dc2be91e01f1e5a2f1e6d946b6c246f70ef8511

Aliases

arxiv: astro-ph/0110412 · arxiv_version: astro-ph/0110412v2 · doi: 10.48550/arxiv.astro-ph/0110412 · pith_short_12: YCZTUPOB5CVD · pith_short_16: YCZTUPOB5CVDFBP6 · pith_short_8: YCZTUPOB

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/YCZTUPOB5CVDFBP6Z2DJ3QV6SH \
  | 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: c0b33a3dc1e8aa3285fece869dc2be91e01f1e5a2f1e6d946b6c246f70ef8511

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95eafdbc0cf826abb3cbb037e19744c4e37c595a82c6c203ac3a21a4c1f04cef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph",
    "submitted_at": "2001-10-18T01:57:16Z",
    "title_canon_sha256": "4ce04625b40a5cdf34b28c4a03ffab789810b526bfe8faa6492800c05bafef34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0110412",
    "kind": "arxiv",
    "version": 2
  }
}