Pith Number

pith:PH2YYBKI

pith:2021:PH2YYBKI7245XAHWMP32K4VA5R

not attested not anchored not stored refs pending

Fast Calculation of Gravitational Lensing Properties of Elliptical Navarro-Frenk-White and Hernquist Density Profiles

Masamune Oguri

arxiv:2106.11464 v2 · 2021-06-22 · astro-ph.IM · astro-ph.GA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PH2YYBKI7245XAHWMP32K4VA5R}

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.

Cited by

2 papers in Pith

Lambda as a Probe of Lensing Consistency

Probing Dark Matter Substructure with Image Number Anomaly in Strong Lensing Systems

Receipt and verification

First computed	2026-07-05T03:02:55.984472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79f58c0548feb9db80f663f7a572a0ec6c71a5529497f3ddabaa4f6c5bf7fbd3

Aliases

arxiv: 2106.11464 · arxiv_version: 2106.11464v2 · doi: 10.48550/arxiv.2106.11464 · pith_short_12: PH2YYBKI7245 · pith_short_16: PH2YYBKI7245XAHW · pith_short_8: PH2YYBKI

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/PH2YYBKI7245XAHWMP32K4VA5R \
  | 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: 79f58c0548feb9db80f663f7a572a0ec6c71a5529497f3ddabaa4f6c5bf7fbd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a662259ffb5cfdef2909c3628a4800c29bc4ea6f4a24a871a7572646109a910",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.IM",
    "submitted_at": "2021-06-22T00:58:03Z",
    "title_canon_sha256": "6f196a1292bb23c2dc353ebe9f46c7bd3e87867e3f8275045704464d0347bca8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.11464",
    "kind": "arxiv",
    "version": 2
  }
}