Pith Number

pith:7UTQTCLD

pith:2013:7UTQTCLDZ4OY3QCT2YE4GP4LV6

not attested not anchored not stored refs pending

Intermediate homogenization of the Universe and the problem of gravitational entropy

Krzysztof Bolejko, William R. Stoeger

arxiv:1309.5695 v1 · 2013-09-23 · 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{7UTQTCLDZ4OY3QCT2YE4GP4LV6}

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	2026-05-18T03:12:11.125775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc

Aliases

arxiv: 1309.5695 · arxiv_version: 1309.5695v1 · doi: 10.48550/arxiv.1309.5695 · pith_short_12: 7UTQTCLDZ4OY · pith_short_16: 7UTQTCLDZ4OY3QCT · pith_short_8: 7UTQTCLD

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/7UTQTCLDZ4OY3QCT2YE4GP4LV6 \
  | 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: fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78f981d2caff061d91706113acae7b58b5c27e87ceb4fa01bd0d73e4ed9d1ae7",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-09-23T04:59:15Z",
    "title_canon_sha256": "1ddf4477a1f731263ea579eb4d3d57d181be488a8fafd27bab8db855193a9fb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5695",
    "kind": "arxiv",
    "version": 1
  }
}