Pith Number

pith:PZF22GWD

pith:2012:PZF22GWD3SSK6N6IR35Q6K672C

not attested not anchored not stored refs pending

Explicit harmonic and spectral analysis in Bianchi I-VII type cosmologies

Rainer Verch, Zhirayr Avetisyan

arxiv:1212.6180 v3 · 2012-12-26 · math-ph · gr-qc · 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{PZF22GWD3SSK6N6IR35Q6K672C}

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	2026-05-18T03:19:45.842814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e4bad1ac3dca4af37c88efb0f2bdfd0aeb5808b8faef3f3ed9a836fc3126a98

Aliases

arxiv: 1212.6180 · arxiv_version: 1212.6180v3 · doi: 10.48550/arxiv.1212.6180 · pith_short_12: PZF22GWD3SSK · pith_short_16: PZF22GWD3SSK6N6I · pith_short_8: PZF22GWD

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/PZF22GWD3SSK6N6IR35Q6K672C \
  | 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: 7e4bad1ac3dca4af37c88efb0f2bdfd0aeb5808b8faef3f3ed9a836fc3126a98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07057afcf15af4176f0f2e0353049a4ab44e374ab514f012e3330c0e0630ff53",
    "cross_cats_sorted": [
      "gr-qc",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-12-26T13:50:50Z",
    "title_canon_sha256": "d22a2277f69e25df1922670cd00420ba3934eb8ae2f7cec3303ff56da5652d2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6180",
    "kind": "arxiv",
    "version": 3
  }
}