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As a first step in our study we obtain the gravitational field equations in the $f\\left(R,L_m\\right)$ theory for a general static, cylindrically symmetric metric, and then for a Kasner-type metric, in which the metric tensor comp"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.8454","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-09-30T09:48:50Z","cross_cats_sorted":[],"title_canon_sha256":"51ca1755cde214acd3a7bf7c0815922552560bd8f9d32b28b912500b6e97f749","abstract_canon_sha256":"3957e7f8de1e27b5275f8b21b43250601d2238725f14b36e36b3706ef4998274"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:03.762672Z","signature_b64":"u6+Oilx/E+IrKTELHgjV+QBfKL0OZ2xKXXeBy44gaFa8jEjtC375X5PMz0T/pSgriIb9w7CAhJX97AA0iGrZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97b6e49ebeec830c65116382a8acccff27c04b2f6d14f5e714d56a06d0d14ec1","last_reissued_at":"2026-05-18T01:31:03.761808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:03.761808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cosmic strings in $f\\left(R,L_m\\right)$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Matthew J. 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