Pith Number

pith:GGKG4OGX

pith:2013:GGKG4OGX3P5AQVHNYQCZMHPCGZ

not attested not anchored not stored refs pending

Singularity Problem in Teleparallel Dark Energy Models

Chao-Qiang Geng, Chung-Chi Lee, Je-An Gu

arxiv:1306.0333 v2 · 2013-06-03 · astro-ph.CO · 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{GGKG4OGX3P5AQVHNYQCZMHPCGZ}

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	2026-05-18T03:17:46.275766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31946e38d7dbfa0854edc405961de236788a57ddcfb0bf9cf57fa49a3361fc7d

Aliases

arxiv: 1306.0333 · arxiv_version: 1306.0333v2 · doi: 10.48550/arxiv.1306.0333 · pith_short_12: GGKG4OGX3P5A · pith_short_16: GGKG4OGX3P5AQVHN · pith_short_8: GGKG4OGX

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/GGKG4OGX3P5AQVHNYQCZMHPCGZ \
  | 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: 31946e38d7dbfa0854edc405961de236788a57ddcfb0bf9cf57fa49a3361fc7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cdedc8e8d495eb54c2aa617e8fd701b4a4806e6653f9adc9e07f9c7b41e1a5c",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-06-03T09:06:45Z",
    "title_canon_sha256": "cdfacb27102d0bb10bb37df4bcebd27f348c074cc4cd3d6b96a705c056547b8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0333",
    "kind": "arxiv",
    "version": 2
  }
}