Pith Number

pith:PEPUAHEU

pith:2024:PEPUAHEUC2PY5OFJB6QC2SR4WI

not attested not anchored not stored refs pending

Gravitational Lensing of Dark Energy Models and $\Lambda$CDM Using Observational data in Loop Quantum Cosmology

G. Mustafa, Himanshu Chaudhary, Rownak Kundu, Ujjal Debnath

arxiv:2402.07515 v2 · 2024-02-12 · gr-qc · 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{PEPUAHEUC2PY5OFJB6QC2SR4WI}

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	2026-07-05T08:53:52.909614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

791f401c94169f8eb8a90fa02d4a3cb22080bb448bf0c67841b04acde1683556

Aliases

arxiv: 2402.07515 · arxiv_version: 2402.07515v2 · doi: 10.48550/arxiv.2402.07515 · pith_short_12: PEPUAHEUC2PY · pith_short_16: PEPUAHEUC2PY5OFJ · pith_short_8: PEPUAHEU

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/PEPUAHEUC2PY5OFJB6QC2SR4WI \
  | 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: 791f401c94169f8eb8a90fa02d4a3cb22080bb448bf0c67841b04acde1683556

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d437315cdfb90ffcb6d65f1e4d538d0f751bb13e17e88b956596fb5966a9efdd",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-02-12T09:40:08Z",
    "title_canon_sha256": "1b175e768ace859fd5086648dc2bccc1fb059e19f1c9a94356a7466ceb6df4e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.07515",
    "kind": "arxiv",
    "version": 2
  }
}