Pith Number

pith:6NL5ZV4U

pith:2009:6NL5ZV4UHHDOC6TFYYD4EFKLUE

not attested not anchored not stored refs pending

Galaxy rotation curves from General Relativity with Renormalization Group corrections

Davi C. Rodrigues, Ilya L. Shapiro, Patricio S. Letelier

arxiv:0911.4967 v4 · 2009-11-26 · astro-ph.CO · astro-ph.GA · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6NL5ZV4UHHDOC6TFYYD4EFKLUE}

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	2026-05-18T02:34:03.473012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f357dcd79439c6e17a65c607c2154ba115379bfaadd3d2b3fe6969ac5b6cc7a5

Aliases

arxiv: 0911.4967 · arxiv_version: 0911.4967v4 · doi: 10.48550/arxiv.0911.4967 · pith_short_12: 6NL5ZV4UHHDO · pith_short_16: 6NL5ZV4UHHDOC6TF · pith_short_8: 6NL5ZV4U

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/6NL5ZV4UHHDOC6TFYYD4EFKLUE \
  | 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: f357dcd79439c6e17a65c607c2154ba115379bfaadd3d2b3fe6969ac5b6cc7a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed74b6137a3ebaf09428f90bd1be014fc59aa3a16ca5288265275ec79939b0ee",
    "cross_cats_sorted": [
      "astro-ph.GA",
      "gr-qc",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2009-11-26T18:10:28Z",
    "title_canon_sha256": "50c5b0115f5099b32a66444dbdd61dd2e1674427afee042b0a1c0ca22f98bcaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4967",
    "kind": "arxiv",
    "version": 4
  }
}