Pith Number

pith:DOJ4HIW3

pith:2012:DOJ4HIW3H2UW7URDERKTPHZ6VR

not attested not anchored not stored refs pending

Optimal computation of brightness integrals parametrized on the unit sphere

Anssi-Ville V\"anttinen, Mikko Kaasalainen, Xiaoping Lu

arxiv:1201.2822 v1 · 2012-01-13 · astro-ph.EP · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DOJ4HIW3H2UW7URDERKTPHZ6VR}

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	2026-05-18T04:01:01.465201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b93c3a2db3ea96fd2232455379f3eac489016ddf906e96cf21edd045bc9bd5b

Aliases

arxiv: 1201.2822 · arxiv_version: 1201.2822v1 · doi: 10.48550/arxiv.1201.2822 · pith_short_12: DOJ4HIW3H2UW · pith_short_16: DOJ4HIW3H2UW7URD · pith_short_8: DOJ4HIW3

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/DOJ4HIW3H2UW7URDERKTPHZ6VR \
  | 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: 1b93c3a2db3ea96fd2232455379f3eac489016ddf906e96cf21edd045bc9bd5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e35ec3035f5c5f71780b952d7dec349a3b28b324f7545130993bc7c3af5b82f",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.EP",
    "submitted_at": "2012-01-13T12:22:52Z",
    "title_canon_sha256": "fc9a2db113e8f4e8f608249ae00bab0122af081ac07fb3b2e4364e919e6f2ff3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2822",
    "kind": "arxiv",
    "version": 1
  }
}