Pith Number

pith:KQAAHZ7B

pith:2004:KQAAHZ7BQJVTUU7MV2XNP6DCQS

not attested not anchored not stored refs pending

Strong Lensing Probabilities in a Cosmological Model with a Running Primordial Power Spectrum

Beijing Normal University), Tong-Jie Zhang, Xiang-Tao He (Department of Astronomy, Zhi-Liang Yang

arxiv:astro-ph/0410431 v3 · 2004-10-19 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KQAAHZ7BQJVTUU7MV2XNP6DCQS}

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	2026-05-18T04:37:01.632634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

540003e7e1826b3a53ecaeaed7f86284954dfdde765476f458fe0c89171ec5f8

Aliases

arxiv: astro-ph/0410431 · arxiv_version: astro-ph/0410431v3 · doi: 10.48550/arxiv.astro-ph/0410431 · pith_short_12: KQAAHZ7BQJVT · pith_short_16: KQAAHZ7BQJVTUU7M · pith_short_8: KQAAHZ7B

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/KQAAHZ7BQJVTUU7MV2XNP6DCQS \
  | 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: 540003e7e1826b3a53ecaeaed7f86284954dfdde765476f458fe0c89171ec5f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54ac080f73b4b38448babca75632227b3e3fc0d2e5f55d88f853b3ef748e9ded",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-10-19T10:26:05Z",
    "title_canon_sha256": "f364e99f68a6562fce71d98d503dfb4f2b4adf0b90cbde26e4e4f5f484888e16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0410431",
    "kind": "arxiv",
    "version": 3
  }
}