Pith Number

pith:5FD3KE6Y

pith:2026:5FD3KE6YZ6LSFYXGJB5LJ3WYFD

not attested not anchored not stored refs pending

Defocusing dark energy: Raychaudhuri diagnostics beyond $w<-1/3$ and the phantom divide

Antonio De Felice, N. Merve Uzun, \"Ozg\"ur Akarsu

arxiv:2607.18008 v1 · 2026-07-20 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5FD3KE6YZ6LSFYXGJB5LJ3WYFD}

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	2026-07-21T02:22:11.536054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e947b513d8cf9722e2e6487ab4eed828eab2813b54b134475d6cc749ed9d0745

Aliases

arxiv: 2607.18008 · arxiv_version: 2607.18008v1 · doi: 10.48550/arxiv.2607.18008 · pith_short_12: 5FD3KE6YZ6LS · pith_short_16: 5FD3KE6YZ6LSFYXG · pith_short_8: 5FD3KE6Y

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/5FD3KE6YZ6LSFYXGJB5LJ3WYFD \
  | 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: e947b513d8cf9722e2e6487ab4eed828eab2813b54b134475d6cc749ed9d0745

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a878ce78e267c1f37a214e6cf67d89855bbf6c3c5a9928c268cb932faecd00ea",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-20T14:41:08Z",
    "title_canon_sha256": "27495f5425ade204876f1606f936b279f7eabe9e6835207387cb66d4101e853a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18008",
    "kind": "arxiv",
    "version": 1
  }
}