Pith Number

pith:MZBP3HNM

pith:2015:MZBP3HNMYKDCJVJNLOVPFHE643

not attested not anchored not stored refs pending

Clusters of galaxies in a Weyl geometric approach to gravity

Erhard Scholz

arxiv:1506.09138 v5 · 2015-06-30 · astro-ph.CO · 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{MZBP3HNMYKDCJVJNLOVPFHE643}

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	2026-05-18T00:56:46.770677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6642fd9dacc28624d52d5baaf29c9ee6daaa499c21a0b53542cdbf9de59002f7

Aliases

arxiv: 1506.09138 · arxiv_version: 1506.09138v5 · doi: 10.48550/arxiv.1506.09138 · pith_short_12: MZBP3HNMYKDC · pith_short_16: MZBP3HNMYKDCJVJN · pith_short_8: MZBP3HNM

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/MZBP3HNMYKDCJVJNLOVPFHE643 \
  | 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: 6642fd9dacc28624d52d5baaf29c9ee6daaa499c21a0b53542cdbf9de59002f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d80507f3122ba3336cede3614163769a2a4db053ccd1dc3ec76505b70059e78",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2015-06-30T16:11:04Z",
    "title_canon_sha256": "6a181d0959e3d61b00925a448b149d4f67a5e34130a81bc6922cd9b5d6d83cd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.09138",
    "kind": "arxiv",
    "version": 5
  }
}