{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:BO3KMBPUORCCXIMRJOGZA2JDTF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e270313122d329ad10b9c9deedbe6b6704c2986bbcb8afed4e957fe5d1cb0805","cross_cats_sorted":["astro-ph","hep-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2001-05-05T15:51:58Z","title_canon_sha256":"5c126ccc91b40ead3a68ab731b71c9154b8278b73716ae10f716f13466b7819c"},"schema_version":"1.0","source":{"id":"gr-qc/0105022","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0105022","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0105022v4","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0105022","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"BO3KMBPUORCC","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"BO3KMBPUORCCXIMR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"BO3KMBPU","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:4b679506600437cf5714bcceab50e11bb31b781a3da5381f7918eb70955058e3","target":"graph","created_at":"2026-05-18T04:17:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron family of space-time line element with a nonzero Cosmological Constant. The resulting solution connects, in an intrinsic way, General Relativity with the theory of modular forms and elliptic curves. The homogeneous FLRW limit of the above space-time elements is recovered and we solve exactly the resulting Friedmann Robertson field equation with the appropri","authors_text":"G.V. Kraniotis, S.B. Whitehouse","cross_cats":["astro-ph","hep-ph"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2001-05-05T15:51:58Z","title":"General Relativity, the Cosmological Constant and Modular Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0105022","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2c7409d8a2bfcc978882817f15013c7d44c33825cfe702fe31eebe3f8a32f6a7","target":"record","created_at":"2026-05-18T04:17:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e270313122d329ad10b9c9deedbe6b6704c2986bbcb8afed4e957fe5d1cb0805","cross_cats_sorted":["astro-ph","hep-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2001-05-05T15:51:58Z","title_canon_sha256":"5c126ccc91b40ead3a68ab731b71c9154b8278b73716ae10f716f13466b7819c"},"schema_version":"1.0","source":{"id":"gr-qc/0105022","kind":"arxiv","version":4}},"canonical_sha256":"0bb6a605f474442ba1914b8d906923995eb019e4a19a7271a76d407157ddcba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bb6a605f474442ba1914b8d906923995eb019e4a19a7271a76d407157ddcba2","first_computed_at":"2026-05-18T04:17:53.157878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:53.157878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rSzYI4yO8VEPVmL8jbx6mTTDuxM9+T2gjkI/iW/hvGGPCEfrYqPBPLL/CzMmSWuoT5gbLRxwEP4klBEUMCB7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:53.158429Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0105022","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c7409d8a2bfcc978882817f15013c7d44c33825cfe702fe31eebe3f8a32f6a7","sha256:4b679506600437cf5714bcceab50e11bb31b781a3da5381f7918eb70955058e3"],"state_sha256":"316f60fbf0b45766b5e8bde81213190587b5b4fd37bb3ca165257078a37ac5b1"}