{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VWUPATXKJXLGT2DWRMODBRATR7","short_pith_number":"pith:VWUPATXK","canonical_record":{"source":{"id":"1108.0767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-03T07:31:24Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"913cd6b39a5cc5fbac8da1efd1c1b7d136f7c89f04d02a071073ab8621c54f6b","abstract_canon_sha256":"fbe549dd6b133054590ae6d8fb7ff02eb3040d2eba1e57320efa229dfd78b8a9"},"schema_version":"1.0"},"canonical_sha256":"ada8f04eea4dd669e8768b1c30c4138ffbd72cb2320a6fc996b25893917ca511","source":{"kind":"arxiv","id":"1108.0767","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0767","created_at":"2026-05-18T02:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0767v2","created_at":"2026-05-18T02:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0767","created_at":"2026-05-18T02:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"VWUPATXKJXLG","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VWUPATXKJXLGT2DW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VWUPATXK","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VWUPATXKJXLGT2DWRMODBRATR7","target":"record","payload":{"canonical_record":{"source":{"id":"1108.0767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-03T07:31:24Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"913cd6b39a5cc5fbac8da1efd1c1b7d136f7c89f04d02a071073ab8621c54f6b","abstract_canon_sha256":"fbe549dd6b133054590ae6d8fb7ff02eb3040d2eba1e57320efa229dfd78b8a9"},"schema_version":"1.0"},"canonical_sha256":"ada8f04eea4dd669e8768b1c30c4138ffbd72cb2320a6fc996b25893917ca511","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:03.741505Z","signature_b64":"XyE+zMIy9gpmT6/8RZM0v0OmdcpwcnrwfKqdxH56VOuRaC+VnmPlWIu8KmIxXUH8CASJhSI3M2FJnjNgQqKXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ada8f04eea4dd669e8768b1c30c4138ffbd72cb2320a6fc996b25893917ca511","last_reissued_at":"2026-05-18T02:01:03.740666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:03.740666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.0767","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:01:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9grNEE0Mk7UpbTx5rmgGA5Lul5lVMZTmoijEVTb9u2Ile8WcbdDJwMJPayekQu0oFAxfrihVKA5Tz024XEAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:24:00.173224Z"},"content_sha256":"7242d655fa4d0db3138db971f1aba609eab9b426719ba084dea42e0e884f429c","schema_version":"1.0","event_id":"sha256:7242d655fa4d0db3138db971f1aba609eab9b426719ba084dea42e0e884f429c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VWUPATXKJXLGT2DWRMODBRATR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclic, ekpyrotic and little rip universe in modified gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc"],"primary_cat":"hep-th","authors_text":"Diego Saez-Gomez, Sergei D. Odintsov, Shin'ichi Nojiri","submitted_at":"2011-08-03T07:31:24Z","abstract_excerpt":"We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present $F(R)$ gravity which provides the little rip evolution and gives the realistic gravitational alternative for $\\Lambda$CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip $F(R)$ solution becomes qualitatively different cosmolog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0767","kind":"arxiv","version":2},"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":"2026-05-18T02:01:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NiAxIHsNkLISbVZQe1Z6uHdDC0YOpZFsh1fgy8jSnkVQ4XgAk8dYIx/Rphx1EJA519yuD92xw6v4GjXs1FVLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:24:00.173884Z"},"content_sha256":"688a35a0fdb543d13a01b57a25595cce35a45c669fc1a6dfa6da1256e8d0c626","schema_version":"1.0","event_id":"sha256:688a35a0fdb543d13a01b57a25595cce35a45c669fc1a6dfa6da1256e8d0c626"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWUPATXKJXLGT2DWRMODBRATR7/bundle.json","state_url":"https://pith.science/pith/VWUPATXKJXLGT2DWRMODBRATR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWUPATXKJXLGT2DWRMODBRATR7/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":"2026-05-25T15:24:00Z","links":{"resolver":"https://pith.science/pith/VWUPATXKJXLGT2DWRMODBRATR7","bundle":"https://pith.science/pith/VWUPATXKJXLGT2DWRMODBRATR7/bundle.json","state":"https://pith.science/pith/VWUPATXKJXLGT2DWRMODBRATR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWUPATXKJXLGT2DWRMODBRATR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VWUPATXKJXLGT2DWRMODBRATR7","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":"fbe549dd6b133054590ae6d8fb7ff02eb3040d2eba1e57320efa229dfd78b8a9","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-03T07:31:24Z","title_canon_sha256":"913cd6b39a5cc5fbac8da1efd1c1b7d136f7c89f04d02a071073ab8621c54f6b"},"schema_version":"1.0","source":{"id":"1108.0767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0767","created_at":"2026-05-18T02:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0767v2","created_at":"2026-05-18T02:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0767","created_at":"2026-05-18T02:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"VWUPATXKJXLG","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VWUPATXKJXLGT2DW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VWUPATXK","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:688a35a0fdb543d13a01b57a25595cce35a45c669fc1a6dfa6da1256e8d0c626","target":"graph","created_at":"2026-05-18T02:01:03Z","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":"We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present $F(R)$ gravity which provides the little rip evolution and gives the realistic gravitational alternative for $\\Lambda$CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip $F(R)$ solution becomes qualitatively different cosmolog","authors_text":"Diego Saez-Gomez, Sergei D. Odintsov, Shin'ichi Nojiri","cross_cats":["astro-ph.CO","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-03T07:31:24Z","title":"Cyclic, ekpyrotic and little rip universe in modified gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0767","kind":"arxiv","version":2},"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":"sha256:7242d655fa4d0db3138db971f1aba609eab9b426719ba084dea42e0e884f429c","target":"record","created_at":"2026-05-18T02:01:03Z","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":"fbe549dd6b133054590ae6d8fb7ff02eb3040d2eba1e57320efa229dfd78b8a9","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-08-03T07:31:24Z","title_canon_sha256":"913cd6b39a5cc5fbac8da1efd1c1b7d136f7c89f04d02a071073ab8621c54f6b"},"schema_version":"1.0","source":{"id":"1108.0767","kind":"arxiv","version":2}},"canonical_sha256":"ada8f04eea4dd669e8768b1c30c4138ffbd72cb2320a6fc996b25893917ca511","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ada8f04eea4dd669e8768b1c30c4138ffbd72cb2320a6fc996b25893917ca511","first_computed_at":"2026-05-18T02:01:03.740666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:03.740666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XyE+zMIy9gpmT6/8RZM0v0OmdcpwcnrwfKqdxH56VOuRaC+VnmPlWIu8KmIxXUH8CASJhSI3M2FJnjNgQqKXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:03.741505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7242d655fa4d0db3138db971f1aba609eab9b426719ba084dea42e0e884f429c","sha256:688a35a0fdb543d13a01b57a25595cce35a45c669fc1a6dfa6da1256e8d0c626"],"state_sha256":"dfdb96912a9c3c4b4261f74e7e844fb55b3e22c710f4d38c57a36670acbac299"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/iWh0HI3+uDk0hfWPlznNbAO3kA/WEdlpcmOL/yg/GJX4rz4nkZ3ITgL4sZw2Oty63P6a8XWmh+cgc3DYwNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:24:00.177635Z","bundle_sha256":"16d5af3ac1cb61c17a7f520e6a244178d88419817b1b4cbab6f91c14a8d7dfb9"}}