Pith Number

pith:MUJBKDU3

pith:2026:MUJBKDU32FBPHQOLHEB7T5556P

not attested not anchored not stored refs pending

Reassessing the Statistical Necessity of Stellar Velocity Anisotropy in Strong-Lensing Cosmology with Lens-by-Lens Photometric Constraints

Jian Hu, Jian-Ping Hu, Yi Liu, Zhongmu Li

arxiv:2605.19615 v1 · 2026-05-19 · 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{MUJBKDU32FBPHQOLHEB7T5556P}

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	2026-05-20T01:05:54.400134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6512150e9bd142f3c1cb3903f9f7bdf3ea04e633cb1ebca6809c79cc9dc5debf

Aliases

arxiv: 2605.19615 · arxiv_version: 2605.19615v1 · doi: 10.48550/arxiv.2605.19615 · pith_short_12: MUJBKDU32FBP · pith_short_16: MUJBKDU32FBPHQOL · pith_short_8: MUJBKDU3

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/MUJBKDU32FBPHQOLHEB7T5556P \
  | 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: 6512150e9bd142f3c1cb3903f9f7bdf3ea04e633cb1ebca6809c79cc9dc5debf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afb48f29439d9bc343c4c22d1bbafb35f4adf0b30aa47257725bddc0e9f5a845",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-05-19T09:55:42Z",
    "title_canon_sha256": "d67e8aed11de774c8f0df8f00839e2f636e12f585c842858a135006532a1bbaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19615",
    "kind": "arxiv",
    "version": 1
  }
}