Pith Number

pith:GLR2UKLZ

pith:2012:GLR2UKLZSH6B6DSEEDJNFR2WPT

not attested not anchored not stored refs pending

Constraints on the Hubble Parameter from galaxy clusters and the Validity of the Cosmic Distance Duality Relation

R. F. L. Holanda

arxiv:1202.2309 v1 · 2012-02-10 · 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{GLR2UKLZSH6B6DSEEDJNFR2WPT}

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	2026-05-18T03:14:08.814946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32e3aa297991fc1f0e4420d2d2c7567ce5dee9729bed29b96899c8b83a6d61b4

Aliases

arxiv: 1202.2309 · arxiv_version: 1202.2309v1 · doi: 10.48550/arxiv.1202.2309 · pith_short_12: GLR2UKLZSH6B · pith_short_16: GLR2UKLZSH6B6DSE · pith_short_8: GLR2UKLZ

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/GLR2UKLZSH6B6DSEEDJNFR2WPT \
  | 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: 32e3aa297991fc1f0e4420d2d2c7567ce5dee9729bed29b96899c8b83a6d61b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7dcfc9e000e4476b90c348e2c37cc9935e3f5053e95b45115d4bb0c85e530c1",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-02-10T17:06:20Z",
    "title_canon_sha256": "7bd0b97319fd2d2a65a91ab25871378596933bb178d13cb28e165e7721ac1cb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2309",
    "kind": "arxiv",
    "version": 1
  }
}