Pith Number

pith:PTKPJJAT

pith:2011:PTKPJJATL2RRM2CMAPWVYLPRV7

not attested not anchored not stored refs pending

Loop quantum $f(R)$ theories

Xiangdong Zhang, Yongge Ma

arxiv:1107.4921 v2 · 2011-07-25 · gr-qc · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTKPJJATL2RRM2CMAPWVYLPRV7}

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

1 paper in Pith

Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

Receipt and verification

First computed	2026-05-18T02:01:10.565567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cd4f4a4135ea316684c03ed5c2df1affa12ab3e1c68c6f64e5177545e325db2

Aliases

arxiv: 1107.4921 · arxiv_version: 1107.4921v2 · doi: 10.48550/arxiv.1107.4921 · pith_short_12: PTKPJJATL2RR · pith_short_16: PTKPJJATL2RRM2CM · pith_short_8: PTKPJJAT

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/PTKPJJATL2RRM2CMAPWVYLPRV7 \
  | 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: 7cd4f4a4135ea316684c03ed5c2df1affa12ab3e1c68c6f64e5177545e325db2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8347612ded50dff6f0a814710754a40f23a2f82432e41992b6273f6aaada0207",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-07-25T12:31:49Z",
    "title_canon_sha256": "b6d044886d0b33e86fe7af8a29f9b80b1ca70855ea1637f788394ace3cbf4846"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4921",
    "kind": "arxiv",
    "version": 2
  }
}