Pith Number

pith:VVFSVQZC

pith:2012:VVFSVQZCDDHKH6BBSGOELPWCIE

not attested not anchored not stored refs pending

Disk and elliptical galaxies within renormalization group improved gravity

Davi C. Rodrigues, Ilya L. Shapiro, Julio C. Fabris, Paulo L. C. de Oliveira

arxiv:1209.0504 v1 · 2012-09-03 · astro-ph.CO · astro-ph.GA · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVFSVQZCDDHKH6BBSGOELPWCIE}

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	2026-05-18T01:54:47.749514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad4b2ac32218cea3f821919c45bec24102b26a97a3452274133fea602a976cf7

Aliases

arxiv: 1209.0504 · arxiv_version: 1209.0504v1 · doi: 10.48550/arxiv.1209.0504 · pith_short_12: VVFSVQZCDDHK · pith_short_16: VVFSVQZCDDHKH6BB · pith_short_8: VVFSVQZC

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/VVFSVQZCDDHKH6BBSGOELPWCIE \
  | 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: ad4b2ac32218cea3f821919c45bec24102b26a97a3452274133fea602a976cf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "876a4aa31ff027c8637edabc179d418816250ab7b21e1b5509ac7802d9d2ca07",
    "cross_cats_sorted": [
      "astro-ph.GA",
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-09-03T23:44:33Z",
    "title_canon_sha256": "73aa8483bd6fe2303251510e46eb6ed41b8a734e9a0f8b309495285d5e1248a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0504",
    "kind": "arxiv",
    "version": 1
  }
}