Pith Number

pith:YHRF6P3X

pith:1996:YHRF6P3XMLU2PRSVMQZK3GB6WU

not attested not anchored not stored refs pending

Age of the Universe: Influence of the Inhomogeneities on the global Expansion-Factor

G. B\"orner, H. Russ, M. H. Soffel, M. Kasai

arxiv:astro-ph/9612218 v3 · 1996-12-23 · astro-ph · 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{YHRF6P3XMLU2PRSVMQZK3GB6WU}

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	2026-07-04T16:00:21.165202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7

Aliases

arxiv: astro-ph/9612218 · arxiv_version: astro-ph/9612218v3 · doi: 10.48550/arxiv.astro-ph/9612218 · pith_short_12: YHRF6P3XMLU2 · pith_short_16: YHRF6P3XMLU2PRSV · pith_short_8: YHRF6P3X

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/YHRF6P3XMLU2PRSVMQZK3GB6WU \
  | 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: c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f239477de8b088b15caf82e7178451c2cfa9373cb7f9ad1c58ab2fe0ba551c93",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1996-12-23T09:17:34Z",
    "title_canon_sha256": "cfa5368981157869293e03e20160cf9b2a986eaa49e8c188936e0907aac1bec9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9612218",
    "kind": "arxiv",
    "version": 3
  }
}