Pith Number

pith:VKWRP2XG

pith:2007:VKWRP2XGVOL7Z5XLIRE7MTRBO7

not attested not anchored not stored refs pending

Probability Density of the Multipole Vectors for a Gaussian Cosmic Microwave Background

Kate Land, Mark R. Dennis

arxiv:0704.3657 v2 · 2007-04-27 · astro-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKWRP2XGVOL7Z5XLIRE7MTRBO7}

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

Multipolar structure of the local expansion rate from incomplete sky data

Receipt and verification

First computed	2026-07-04T17:03:25.004454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaad17eae6ab97fcf6eb4449f64e2177e1fb2ac3cafa8d2ae4e8380c69274aca

Aliases

arxiv: 0704.3657 · arxiv_version: 0704.3657v2 · doi: 10.48550/arxiv.0704.3657 · pith_short_12: VKWRP2XGVOL7 · pith_short_16: VKWRP2XGVOL7Z5XL · pith_short_8: VKWRP2XG

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/VKWRP2XGVOL7Z5XLIRE7MTRBO7 \
  | 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: aaad17eae6ab97fcf6eb4449f64e2177e1fb2ac3cafa8d2ae4e8380c69274aca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff3653d385842997b37ceb18d2bc297439fc905a9ebbe130ba057bbb7987c90a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2007-04-27T18:48:17Z",
    "title_canon_sha256": "a00a564daf86aa9407b06958c36acd641fa2069cbe306450092f247ed0406770"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.3657",
    "kind": "arxiv",
    "version": 2
  }
}