Pith Number

pith:PPMMY3UI

pith:2006:PPMMY3UIDEYM4JX2OUNRSF22DX

not attested not anchored not stored refs pending

Constraining f(R) Gravity as a Scalar Tensor Theory

Emory F. Bunn (Richmond), Max Tegmark (MIT), Thomas Faulkner (MIT), Yi Mao (MIT)

arxiv:astro-ph/0612569 v1 · 2006-12-20 · astro-ph · 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{PPMMY3UIDEYM4JX2OUNRSF22DX}

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

ACT Data and Positive Running of the Spectral Index for Scalar Theory and Modified Gravity

Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model

Receipt and verification

First computed	2026-07-04T15:21:50.913304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bd8cc6e881930ce26fa751b19175a1dfb5dae335f81df7bfb61db4194e1343d

Aliases

arxiv: astro-ph/0612569 · arxiv_version: astro-ph/0612569v1 · doi: 10.48550/arxiv.astro-ph/0612569 · pith_short_12: PPMMY3UIDEYM · pith_short_16: PPMMY3UIDEYM4JX2 · pith_short_8: PPMMY3UI

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/PPMMY3UIDEYM4JX2OUNRSF22DX \
  | 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: 7bd8cc6e881930ce26fa751b19175a1dfb5dae335f81df7bfb61db4194e1343d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a42504808243db262224d7923ba40cdabedc223fef5ea6e8d2bc9b751e6e162",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-12-20T20:50:13Z",
    "title_canon_sha256": "ea9ac57bf13eba1cef7fe4d454dfcb352bfa3f1cdaaa5d6fd1b70c03a00be62c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0612569",
    "kind": "arxiv",
    "version": 1
  }
}