{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5X4MH3IY2OIB6TY27A4CPL4BQG","short_pith_number":"pith:5X4MH3IY","canonical_record":{"source":{"id":"1806.07295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-19T14:55:59Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"43760fb510082de14c910acca94bc6afb0d77307a415a08d0b5568b43ebee7b7","abstract_canon_sha256":"d06b3689ec20422ed6148cc89eae4be600bb57ffc2c36e006de10b5b89a48839"},"schema_version":"1.0"},"canonical_sha256":"edf8c3ed18d3901f4f1af83827af81818df8d9c246786953841797bfb8ca0b4b","source":{"kind":"arxiv","id":"1806.07295","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07295","created_at":"2026-05-18T00:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07295v1","created_at":"2026-05-18T00:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07295","created_at":"2026-05-18T00:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"5X4MH3IY2OIB","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5X4MH3IY2OIB6TY2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5X4MH3IY","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5X4MH3IY2OIB6TY27A4CPL4BQG","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-19T14:55:59Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"43760fb510082de14c910acca94bc6afb0d77307a415a08d0b5568b43ebee7b7","abstract_canon_sha256":"d06b3689ec20422ed6148cc89eae4be600bb57ffc2c36e006de10b5b89a48839"},"schema_version":"1.0"},"canonical_sha256":"edf8c3ed18d3901f4f1af83827af81818df8d9c246786953841797bfb8ca0b4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:24.382795Z","signature_b64":"Wzj3In1j/UoIeDsyA0dY3m5/OGrcKQdjSwpxak5vgCHZp7cKHUqSNvL81up/0sPVx+QIkPd1V+NwLp4AYxamAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf8c3ed18d3901f4f1af83827af81818df8d9c246786953841797bfb8ca0b4b","last_reissued_at":"2026-05-18T00:09:24.382093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:24.382093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07295","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":"2026-05-18T00:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7k7uemYycjfpdmBVYI9zDS/PYkfUhB2TCXMgHTYDJsfBGq/7UAU+n/hsRhs3T90463Z08kIn6/I/FI3TF55BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T08:53:35.428648Z"},"content_sha256":"b889c464ce1e85d5b142953f92472dd9e6d7db33428c6519589442cf2b1ffd2d","schema_version":"1.0","event_id":"sha256:b889c464ce1e85d5b142953f92472dd9e6d7db33428c6519589442cf2b1ffd2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5X4MH3IY2OIB6TY27A4CPL4BQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"S.D. Odintsov, V.K. Oikonomou","submitted_at":"2018-06-19T14:55:59Z","abstract_excerpt":"In this work we shall investigate the occurrence of future cosmological finite-time singularities in the dynamical system corresponding to two cosmological theories, namely that of vacuum $f(R)$ gravity and that of three fluids. The vacuum $f(R)$ gravity is an example for which the variables we will choose to quantify the phase space dynamics, do not necessarily blow-up near a cosmological singularity. After appropriately choosing the variables, we shall investigate the behavior of the corresponding dynamical system near some types of cosmological finite-time singularities, for some limiting c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07295","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":""},"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":"2026-05-18T00:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lU/J2NdhoIroEJ+UqiLUebvWYY0kZ0NEOQoFwlTZG1vkuVFWDyQwoRITBaFFNogTfS6B6VgHEtCFxJmHeKrcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T08:53:35.429405Z"},"content_sha256":"4a254b3846e054e9e32f5f7d0423afcf1b2602e74c91e1844589a88f1b325fbd","schema_version":"1.0","event_id":"sha256:4a254b3846e054e9e32f5f7d0423afcf1b2602e74c91e1844589a88f1b325fbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5X4MH3IY2OIB6TY27A4CPL4BQG/bundle.json","state_url":"https://pith.science/pith/5X4MH3IY2OIB6TY27A4CPL4BQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5X4MH3IY2OIB6TY27A4CPL4BQG/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":"2026-05-23T08:53:35Z","links":{"resolver":"https://pith.science/pith/5X4MH3IY2OIB6TY27A4CPL4BQG","bundle":"https://pith.science/pith/5X4MH3IY2OIB6TY27A4CPL4BQG/bundle.json","state":"https://pith.science/pith/5X4MH3IY2OIB6TY27A4CPL4BQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5X4MH3IY2OIB6TY27A4CPL4BQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5X4MH3IY2OIB6TY27A4CPL4BQG","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":"d06b3689ec20422ed6148cc89eae4be600bb57ffc2c36e006de10b5b89a48839","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-19T14:55:59Z","title_canon_sha256":"43760fb510082de14c910acca94bc6afb0d77307a415a08d0b5568b43ebee7b7"},"schema_version":"1.0","source":{"id":"1806.07295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07295","created_at":"2026-05-18T00:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07295v1","created_at":"2026-05-18T00:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07295","created_at":"2026-05-18T00:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"5X4MH3IY2OIB","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5X4MH3IY2OIB6TY2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5X4MH3IY","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:4a254b3846e054e9e32f5f7d0423afcf1b2602e74c91e1844589a88f1b325fbd","target":"graph","created_at":"2026-05-18T00:09:24Z","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":"In this work we shall investigate the occurrence of future cosmological finite-time singularities in the dynamical system corresponding to two cosmological theories, namely that of vacuum $f(R)$ gravity and that of three fluids. The vacuum $f(R)$ gravity is an example for which the variables we will choose to quantify the phase space dynamics, do not necessarily blow-up near a cosmological singularity. After appropriately choosing the variables, we shall investigate the behavior of the corresponding dynamical system near some types of cosmological finite-time singularities, for some limiting c","authors_text":"S.D. Odintsov, V.K. Oikonomou","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-19T14:55:59Z","title":"Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07295","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:b889c464ce1e85d5b142953f92472dd9e6d7db33428c6519589442cf2b1ffd2d","target":"record","created_at":"2026-05-18T00:09:24Z","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":"d06b3689ec20422ed6148cc89eae4be600bb57ffc2c36e006de10b5b89a48839","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-19T14:55:59Z","title_canon_sha256":"43760fb510082de14c910acca94bc6afb0d77307a415a08d0b5568b43ebee7b7"},"schema_version":"1.0","source":{"id":"1806.07295","kind":"arxiv","version":1}},"canonical_sha256":"edf8c3ed18d3901f4f1af83827af81818df8d9c246786953841797bfb8ca0b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf8c3ed18d3901f4f1af83827af81818df8d9c246786953841797bfb8ca0b4b","first_computed_at":"2026-05-18T00:09:24.382093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:24.382093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wzj3In1j/UoIeDsyA0dY3m5/OGrcKQdjSwpxak5vgCHZp7cKHUqSNvL81up/0sPVx+QIkPd1V+NwLp4AYxamAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:24.382795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b889c464ce1e85d5b142953f92472dd9e6d7db33428c6519589442cf2b1ffd2d","sha256:4a254b3846e054e9e32f5f7d0423afcf1b2602e74c91e1844589a88f1b325fbd"],"state_sha256":"83aa93e0a6521aab3876cf6ed2db2d450dec22fc1cc01d1316f2e04b01f3c854"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6BrY4lH5ounle2USW7ZgUcPPg7Lc1cpwFZ99Dh5Dqm1R/wUjAJgFF6/55j+vOuxa3Bt6WB09oCP/OaezI7SBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T08:53:35.433155Z","bundle_sha256":"b2040aa33b311bc15be40096e6a25ab86f2144eeadb8bde9b9b3ec77c84d1cda"}}