Pith Number

pith:Z6MDLWM4

pith:2009:Z6MDLWM4CQVOPODUN3COR74EZX

not attested not anchored not stored refs pending

Statistics of mass substructure from strong gravitational lensing: quantifying the mass fraction and mass function

L.V.E. Koopmans, S. Vegetti

arxiv:0903.4752 v2 · 2009-03-27 · 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{Z6MDLWM4CQVOPODUN3COR74EZX}

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	2026-05-18T02:14:19.151626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf9835d99c142ae7b8746ec4e8ff84cdc46f7b6bdbfc06a04399eb53a501afd3

Aliases

arxiv: 0903.4752 · arxiv_version: 0903.4752v2 · doi: 10.48550/arxiv.0903.4752 · pith_short_12: Z6MDLWM4CQVO · pith_short_16: Z6MDLWM4CQVOPODU · pith_short_8: Z6MDLWM4

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/Z6MDLWM4CQVOPODUN3COR74EZX \
  | 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: cf9835d99c142ae7b8746ec4e8ff84cdc46f7b6bdbfc06a04399eb53a501afd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c84dc4ca327bb88e787b926ef2d5604e5fa05e401faa40d766282ee306ffd2b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2009-03-27T09:41:45Z",
    "title_canon_sha256": "94e5b42c4977f1a0bf41aaaccbb95b4aa50e6cc4947b71274ba5011c1bc24932"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.4752",
    "kind": "arxiv",
    "version": 2
  }
}