Pith Number

pith:B2XATG3R

pith:2025:B2XATG3R4VGPG767P7TQVXWR4E

not attested not anchored not stored refs pending

The Fluctuation Theory, Critical Phenomena and Gravitational Clustering of Galaxies

Azmat Khan, Farooq Owais, M. H. Abdullah, M. S. Khan, Shah Zahir

arxiv:2508.04237 v1 · 2025-08-06 · 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{B2XATG3R4VGPG767P7TQVXWR4E}

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	2026-07-05T11:49:23.372738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0eae099b71e54cf37fdf7fe70aded1e10830d180622a521edd5c06544d9e4dec

Aliases

arxiv: 2508.04237 · arxiv_version: 2508.04237v1 · doi: 10.48550/arxiv.2508.04237 · pith_short_12: B2XATG3R4VGP · pith_short_16: B2XATG3R4VGPG767 · pith_short_8: B2XATG3R

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/B2XATG3R4VGPG767P7TQVXWR4E \
  | 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: 0eae099b71e54cf37fdf7fe70aded1e10830d180622a521edd5c06544d9e4dec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "977cddf89a2cfef48a76460aa603fd01b8b03d4813431cee5c11eb3fa1d5efa2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2025-08-06T09:20:25Z",
    "title_canon_sha256": "5e36cb881bfe5941b9936d0a50cd8e21ed70cedb6049ba3a6ff8c37e7ad1ec31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04237",
    "kind": "arxiv",
    "version": 1
  }
}