Pith Number

pith:3E3ABJ3M

pith:2015:3E3ABJ3MQFUXRWSW4LYQBXUPLO

not attested not anchored not stored refs pending

Unimodular $F(R)$ Gravity

S.D. Odintsov, S. Nojiri, V.K. Oikonomou

arxiv:1512.07223 v2 · 2015-12-22 · gr-qc · astro-ph.CO · 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{3E3ABJ3MQFUXRWSW4LYQBXUPLO}

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	2026-05-18T01:13:15.907312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d93600a76c816978da56e2f100de8f5b82196592a934b67f74b2682dc1de40bd

Aliases

arxiv: 1512.07223 · arxiv_version: 1512.07223v2 · doi: 10.48550/arxiv.1512.07223 · pith_short_12: 3E3ABJ3MQFUX · pith_short_16: 3E3ABJ3MQFUXRWSW · pith_short_8: 3E3ABJ3M

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/3E3ABJ3MQFUXRWSW4LYQBXUPLO \
  | 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: d93600a76c816978da56e2f100de8f5b82196592a934b67f74b2682dc1de40bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17c65fdb210ab3067a5c7fc0bc06206004758c1ef78048bbc8073070888f31f4",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-12-22T20:02:51Z",
    "title_canon_sha256": "4bbd5b78acee5fbe43735c3db9d919edd381598b82ec7ecc4af4c89bed50ba2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07223",
    "kind": "arxiv",
    "version": 2
  }
}