Pith Number

pith:JK4Q5BDI

pith:2013:JK4Q5BDI7257BSKJ5UUQEEV7PH

not attested not anchored not stored refs pending

Spectral expansions of cosmological fields

Anatoliy Malyarenko

arxiv:1304.5645 v1 · 2013-04-20 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JK4Q5BDI7257BSKJ5UUQEEV7PH}

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	2026-05-18T01:19:39.124882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ab90e8468febbf0c949ed290212bf79ce5970447fbe3f37f12bd5264880eede

Aliases

arxiv: 1304.5645 · arxiv_version: 1304.5645v1 · doi: 10.48550/arxiv.1304.5645 · pith_short_12: JK4Q5BDI7257 · pith_short_16: JK4Q5BDI7257BSKJ · pith_short_8: JK4Q5BDI

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/JK4Q5BDI7257BSKJ5UUQEEV7PH \
  | 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: 4ab90e8468febbf0c949ed290212bf79ce5970447fbe3f37f12bd5264880eede

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee3e266e070afc13d40a32bc959e0ba4d4544558f26424870d9ce66d211c224f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-20T16:21:13Z",
    "title_canon_sha256": "316c1669fda01bdf1b78fe67ae900b63050bdbc3a938ececa93f738f32fb5419"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.5645",
    "kind": "arxiv",
    "version": 1
  }
}