{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SEOFQ5VPWYRHAPSWIGWEXMIRFU","short_pith_number":"pith:SEOFQ5VP","canonical_record":{"source":{"id":"2412.18814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-12-25T07:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"a6743ce1b4229ccf3a3a8c4d4cc2167e14e3866f6452b05f2ebfc998d35c4401","abstract_canon_sha256":"6b8cb83e529755f7ea8bde06f688958eba8adc1fd58fd7fc16d66357d0bc1821"},"schema_version":"1.0"},"canonical_sha256":"911c5876afb622703e5641ac4bb1112d3a7575ea8512653d4b1a39ca2c8d6d3a","source":{"kind":"arxiv","id":"2412.18814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18814","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18814v1","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18814","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"SEOFQ5VPWYRH","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_16","alias_value":"SEOFQ5VPWYRHAPSW","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_8","alias_value":"SEOFQ5VP","created_at":"2026-07-05T09:54:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SEOFQ5VPWYRHAPSWIGWEXMIRFU","target":"record","payload":{"canonical_record":{"source":{"id":"2412.18814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-12-25T07:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"a6743ce1b4229ccf3a3a8c4d4cc2167e14e3866f6452b05f2ebfc998d35c4401","abstract_canon_sha256":"6b8cb83e529755f7ea8bde06f688958eba8adc1fd58fd7fc16d66357d0bc1821"},"schema_version":"1.0"},"canonical_sha256":"911c5876afb622703e5641ac4bb1112d3a7575ea8512653d4b1a39ca2c8d6d3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:11.230353Z","signature_b64":"4edHMI8sS6AjDrGwUk5BcGg92TDf73II6P3AdQUbO6m5S+MrPjrgeUHcSTllH05ZBR8BucyoT9G1ExOvHtSZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911c5876afb622703e5641ac4bb1112d3a7575ea8512653d4b1a39ca2c8d6d3a","last_reissued_at":"2026-07-05T09:54:11.229855Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:11.229855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.18814","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:54:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWoHzOlGKTxA0mvr6SsEPPEZDKYuf1PslBAiNuDshpHpRinCpJSsY76w0Ou7oL6z5ELLIMlT2/Nf/QXoaf+uBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:14:30.355053Z"},"content_sha256":"860a50db7de20bce4b210925e55a7e7dcb6d5388de1f47cdc2c182cf79ac753d","schema_version":"1.0","event_id":"sha256:860a50db7de20bce4b210925e55a7e7dcb6d5388de1f47cdc2c182cf79ac753d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SEOFQ5VPWYRHAPSWIGWEXMIRFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal cosmological solutions in Lovelock gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Aleksei Nikolaev","submitted_at":"2024-12-25T07:50:05Z","abstract_excerpt":"This paper explores the Friedmann field equations within the framework of Lovelock gravity, a natural extension of Einstein's gravity, focusing on both flat and open universes. Utilizing an approach based on independent Riemann tensor components, we derive generalized Friedmann equations for Lovelock gravity and categorize the solutions into Type I and Type II types. We identify additional vacuum solutions in a flat universe and present a comprehensive solution for a pressure-free scenario in an open universe, both unique to Lovelock gravity. These findings provide new insights into the cosmol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18814","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.18814/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:54:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ykU86fyYcMTykyBNd33Gr+ijdaUgTWk1NRJn0xJWZCO0CvoGIdBVO36Ru7/RMzNyDlBAUNtyW5RpuZZGok9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:14:30.355552Z"},"content_sha256":"1bf1cfb9dee896b2dca66a97b26e50400fa4264871f07afde273f683a67fb832","schema_version":"1.0","event_id":"sha256:1bf1cfb9dee896b2dca66a97b26e50400fa4264871f07afde273f683a67fb832"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU/bundle.json","state_url":"https://pith.science/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T06:14:30Z","links":{"resolver":"https://pith.science/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU","bundle":"https://pith.science/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU/bundle.json","state":"https://pith.science/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEOFQ5VPWYRHAPSWIGWEXMIRFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SEOFQ5VPWYRHAPSWIGWEXMIRFU","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":"6b8cb83e529755f7ea8bde06f688958eba8adc1fd58fd7fc16d66357d0bc1821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-12-25T07:50:05Z","title_canon_sha256":"a6743ce1b4229ccf3a3a8c4d4cc2167e14e3866f6452b05f2ebfc998d35c4401"},"schema_version":"1.0","source":{"id":"2412.18814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18814","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18814v1","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18814","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"SEOFQ5VPWYRH","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_16","alias_value":"SEOFQ5VPWYRHAPSW","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_8","alias_value":"SEOFQ5VP","created_at":"2026-07-05T09:54:11Z"}],"graph_snapshots":[{"event_id":"sha256:1bf1cfb9dee896b2dca66a97b26e50400fa4264871f07afde273f683a67fb832","target":"graph","created_at":"2026-07-05T09:54:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.18814/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores the Friedmann field equations within the framework of Lovelock gravity, a natural extension of Einstein's gravity, focusing on both flat and open universes. Utilizing an approach based on independent Riemann tensor components, we derive generalized Friedmann equations for Lovelock gravity and categorize the solutions into Type I and Type II types. We identify additional vacuum solutions in a flat universe and present a comprehensive solution for a pressure-free scenario in an open universe, both unique to Lovelock gravity. These findings provide new insights into the cosmol","authors_text":"Aleksei Nikolaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-12-25T07:50:05Z","title":"Universal cosmological solutions in Lovelock gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18814","kind":"arxiv","version":1},"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":"sha256:860a50db7de20bce4b210925e55a7e7dcb6d5388de1f47cdc2c182cf79ac753d","target":"record","created_at":"2026-07-05T09:54:11Z","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":"6b8cb83e529755f7ea8bde06f688958eba8adc1fd58fd7fc16d66357d0bc1821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-12-25T07:50:05Z","title_canon_sha256":"a6743ce1b4229ccf3a3a8c4d4cc2167e14e3866f6452b05f2ebfc998d35c4401"},"schema_version":"1.0","source":{"id":"2412.18814","kind":"arxiv","version":1}},"canonical_sha256":"911c5876afb622703e5641ac4bb1112d3a7575ea8512653d4b1a39ca2c8d6d3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911c5876afb622703e5641ac4bb1112d3a7575ea8512653d4b1a39ca2c8d6d3a","first_computed_at":"2026-07-05T09:54:11.229855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:11.229855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4edHMI8sS6AjDrGwUk5BcGg92TDf73II6P3AdQUbO6m5S+MrPjrgeUHcSTllH05ZBR8BucyoT9G1ExOvHtSZAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:11.230353Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.18814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:860a50db7de20bce4b210925e55a7e7dcb6d5388de1f47cdc2c182cf79ac753d","sha256:1bf1cfb9dee896b2dca66a97b26e50400fa4264871f07afde273f683a67fb832"],"state_sha256":"e37bf227cd17cf8cbbf4abd8128864d0723153104dfa2ccd5f8fbfe3759512f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lykhg7urDjauTCssVzA6m0y2u7Cc6H8Apm0Yq8tbQUZ4LVnbIq7ssP79Fzup50+ojKHFCwylrmpOH/ookNftAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T06:14:30.359959Z","bundle_sha256":"2ab66d4fd55f448ffd1b13c8da2d60840c9370391ccba6ba082072dbe17e694a"}}