Pith Number

pith:XJ7YZWFX

pith:2010:XJ7YZWFX4ALS2PMZHWXRV4NHH2

not attested not anchored not stored refs pending

Lie algebra automorphisms as Lie point symmetries and the solution space for Bianchi Type I, II, IV, V vacuum geometries

Petros A. Terzis, T. Christodoulakis

arxiv:1007.1561 v2 · 2010-07-09 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XJ7YZWFX4ALS2PMZHWXRV4NHH2}

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	2026-05-18T03:06:52.155429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba7f8cd8b7e0172d3d993daf1af1a73eb4b8ca95ca260810f2b90ac3e38ac8bd

Aliases

arxiv: 1007.1561 · arxiv_version: 1007.1561v2 · doi: 10.48550/arxiv.1007.1561 · pith_short_12: XJ7YZWFX4ALS · pith_short_16: XJ7YZWFX4ALS2PMZ · pith_short_8: XJ7YZWFX

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/XJ7YZWFX4ALS2PMZHWXRV4NHH2 \
  | 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: ba7f8cd8b7e0172d3d993daf1af1a73eb4b8ca95ca260810f2b90ac3e38ac8bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f7151d47991afd9e4c83c8d21539e93c3e426a0e9c202f95620c74b2d0ca993",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-07-09T11:21:31Z",
    "title_canon_sha256": "312b1423ffe23d38f59cdddf2037c529e8d933bcf7a43a791e46e33d3cd04d8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1561",
    "kind": "arxiv",
    "version": 2
  }
}