Pith Number

pith:VNPMQK3Q

pith:2008:VNPMQK3Q72QFZ5ZNXR7VF3SSCK

not attested not anchored not stored refs pending

Constraints on modified gravity from the observed X-ray luminosity function of galaxy clusters

Adam Mantz, David Rapetti, Harald Ebeling, Steven W. Allen

arxiv:0812.2259 v2 · 2008-12-12 · 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{VNPMQK3Q72QFZ5ZNXR7VF3SSCK}

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	2026-05-18T02:15:10.782395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab5ec82b70fea05cf72dbc7f52ee5212898494733822424127f33a408af8fdd4

Aliases

arxiv: 0812.2259 · arxiv_version: 0812.2259v2 · doi: 10.48550/arxiv.0812.2259 · pith_short_12: VNPMQK3Q72QF · pith_short_16: VNPMQK3Q72QFZ5ZN · pith_short_8: VNPMQK3Q

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/VNPMQK3Q72QFZ5ZNXR7VF3SSCK \
  | 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: ab5ec82b70fea05cf72dbc7f52ee5212898494733822424127f33a408af8fdd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24363a8ec6a06f9c15a72edc8bc9f14d5c4ecbde2c76a2ab18e76b9a76a1464e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph",
    "submitted_at": "2008-12-12T00:32:58Z",
    "title_canon_sha256": "be0ca97a7cf34eeae0e0c4e067d8619842a63663f5755956564925e7cfecfd5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.2259",
    "kind": "arxiv",
    "version": 2
  }
}