Pith Number

pith:E32TF6PF

pith:2026:E32TF6PFFY55WUYW4RPLDXQ3VB

not attested not anchored not stored refs pending

Predisposition of galaxy clusters to producing exotic hyperbolic umbilic lensing configurations

Ashish K. Meena (IIS Bengaluru), David J. Lagattuta (University of Hertfordshire, Durham University), Harald Ebeling (IfA Univ. of Hawaii), Johan Richard (CRAL), Quentin Basto (CRAL)

arxiv:2606.31583 v1 · 2026-06-30 · 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{E32TF6PFFY55WUYW4RPLDXQ3VB}

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	2026-07-01T01:18:08.351531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26f532f9e52e3bdb5316e45eb1de1ba87096043efa4e9e4baf36b5e1da67f48b

Aliases

arxiv: 2606.31583 · arxiv_version: 2606.31583v1 · doi: 10.48550/arxiv.2606.31583 · pith_short_12: E32TF6PFFY55 · pith_short_16: E32TF6PFFY55WUYW · pith_short_8: E32TF6PF

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/E32TF6PFFY55WUYW4RPLDXQ3VB \
  | 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: 26f532f9e52e3bdb5316e45eb1de1ba87096043efa4e9e4baf36b5e1da67f48b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b73a216f23f72570f29f7329ee8ee40dd4e81ab9784b53010d39288b1a0f11d4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-06-30T12:37:39Z",
    "title_canon_sha256": "eba62c99056542af871562ad00a2ee2bcc09181cc069e69d5711a08892ddc603"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31583",
    "kind": "arxiv",
    "version": 1
  }
}