Pith Number

pith:B5WRQCUW

pith:2014:B5WRQCUW6TRTLBMWOC55J5EELF

not attested not anchored not stored refs pending

Mathematical Validity of the f(R) Theory of Modified Gravity

Philippe G. LeFloch, Yue Ma

arxiv:1412.8151 v1 · 2014-12-28 · math.AP · 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{B5WRQCUW6TRTLBMWOC55J5EELF}

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	2026-05-18T02:30:23.954935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c

Aliases

arxiv: 1412.8151 · arxiv_version: 1412.8151v1 · doi: 10.48550/arxiv.1412.8151 · pith_short_12: B5WRQCUW6TRT · pith_short_16: B5WRQCUW6TRTLBMW · pith_short_8: B5WRQCUW

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/B5WRQCUW6TRTLBMWOC55J5EELF \
  | 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: 0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5adb0ef3832073077f3847451a4a8b80bf0eeb8bfd0d4de95d8173f247994b9",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-12-28T11:26:31Z",
    "title_canon_sha256": "3422c0eb9e80d78bb50b68017cd18393c385762da163aa1ea5e62e496c25318e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8151",
    "kind": "arxiv",
    "version": 1
  }
}