Pith Number

pith:UQXEVBEH

pith:2026:UQXEVBEHAOB2JMWH4UPQVXX2WV

not attested not anchored not stored refs pending

Gravitational Lensing of Gravitational Waves from Astrophysical Sources: Theory, Detection, and Applications

Youjun Lu, Zhiwei Chen

Lensed gravitational waves from merging black holes and other compact objects produce multiple images or frequency-modulated waveforms that can constrain dark matter and the Hubble constant.

arxiv:2605.06321 v2 · 2026-05-07 · astro-ph.HE · 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{UQXEVBEHAOB2JMWH4UPQVXX2WV}

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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.

Claims

C1strongest claim

Once confirmed, lensed GWs will be powerful probes of fundamental physics and cosmology: they can constrain dark matter, lensing structures, the Hubble constant, and other cosmological parameters.

C2weakest assumption

Detection rates depend on the redshift and mass distributions of sources and lenses, with promising prospects for future observatories; this assumes current population models and instrument sensitivities will yield sufficient events without major revisions.

C3one line summary

A review of gravitational lensing of astrophysical gravitational waves, outlining theory in geometric and wave optics, identification methods, predicted rates, and applications to dark matter and cosmology.

Receipt and verification

First computed	2026-05-20T00:03:14.436731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a42e4a84870383a4b2c7e51f0adefab57b7cc2f783cfa9e670dc45516996b135

Aliases

arxiv: 2605.06321 · arxiv_version: 2605.06321v2 · doi: 10.48550/arxiv.2605.06321 · pith_short_12: UQXEVBEHAOB2 · pith_short_16: UQXEVBEHAOB2JMWH · pith_short_8: UQXEVBEH

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/UQXEVBEHAOB2JMWH4UPQVXX2WV \
  | 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: a42e4a84870383a4b2c7e51f0adefab57b7cc2f783cfa9e670dc45516996b135

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "256a01f0f58e6aaed6fdfd3b0c7b476f82f847b832cf7d09f1dc683608efa2b1",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.HE",
    "submitted_at": "2026-05-07T14:20:17Z",
    "title_canon_sha256": "53f57a4d6cc6eb4eabb96a7ff8692b8b2d901f24ce81c7b9fa9b0a423cb2feb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06321",
    "kind": "arxiv",
    "version": 2
  }
}