{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:HDCTFWIPIJY7BQXY7FAJP47GDL","short_pith_number":"pith:HDCTFWIP","canonical_record":{"source":{"id":"gr-qc/0410046","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-10-11T19:45:34Z","cross_cats_sorted":["astro-ph","hep-th"],"title_canon_sha256":"ad6e15b3e58d407e1c72f1aeed38d13bbb60e0b89995037f04b3270b42b225ba","abstract_canon_sha256":"71402328adf39a3ccb319ba74ec2916a3765bc754707956cf1f495620f28a343"},"schema_version":"1.0"},"canonical_sha256":"38c532d90f4271f0c2f8f94097f3e61ae1e2bae27dddd854b219cd561f02b49e","source":{"kind":"arxiv","id":"gr-qc/0410046","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0410046","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0410046v4","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0410046","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"HDCTFWIPIJY7","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"pith_short_16","alias_value":"HDCTFWIPIJY7BQXY","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"pith_short_8","alias_value":"HDCTFWIP","created_at":"2026-07-04T16:47:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:HDCTFWIPIJY7BQXY7FAJP47GDL","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0410046","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-10-11T19:45:34Z","cross_cats_sorted":["astro-ph","hep-th"],"title_canon_sha256":"ad6e15b3e58d407e1c72f1aeed38d13bbb60e0b89995037f04b3270b42b225ba","abstract_canon_sha256":"71402328adf39a3ccb319ba74ec2916a3765bc754707956cf1f495620f28a343"},"schema_version":"1.0"},"canonical_sha256":"38c532d90f4271f0c2f8f94097f3e61ae1e2bae27dddd854b219cd561f02b49e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:47:48.905820Z","signature_b64":"45h2ek8yaNPyHxnMSCJk7Kl1JqhA3PFyTRapGJRiLqUZF6QCb2RJwbwoxY7GnJIcrf/WMJjgyk5adwQqdEYCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38c532d90f4271f0c2f8f94097f3e61ae1e2bae27dddd854b219cd561f02b49e","last_reissued_at":"2026-07-04T16:47:48.905456Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:47:48.905456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0410046","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:47:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5zATJhn4/vyHXplTS9WRsKK5PPI4HTuyQFoelQB9MT459V/bXxzZ8v0fqjZRHsuzwDgaH5+zeN4QZ2AJBbo1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T02:58:18.876289Z"},"content_sha256":"aeefe9aa49249c6b095efe6fa026d8efb475d1b89a05323b3abec4dda06af991","schema_version":"1.0","event_id":"sha256:aeefe9aa49249c6b095efe6fa026d8efb475d1b89a05323b3abec4dda06af991"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:HDCTFWIPIJY7BQXY7FAJP47GDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosmological dynamics of R^n gravity","license":"","headline":"","cross_cats":["astro-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"A. Troisi, P. K. S. Dunsby, S. Capozziello, S. Carloni","submitted_at":"2004-10-11T19:45:34Z","abstract_excerpt":"A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0410046","kind":"arxiv","version":4},"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/gr-qc/0410046/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":"2026-07-04T16:47:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5z1pjW3d1r/BVbU1r1b4TaJIppENPzyfI8affbSz/y3/6072sJ+E8WK23vPsjdAVxAoCCiEFmIrJmtlCPnKCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T02:58:18.876825Z"},"content_sha256":"6cbd4264fc219783d5301e5609c9ea69ec1153264b84c1f1f47c41958b8bec7a","schema_version":"1.0","event_id":"sha256:6cbd4264fc219783d5301e5609c9ea69ec1153264b84c1f1f47c41958b8bec7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDCTFWIPIJY7BQXY7FAJP47GDL/bundle.json","state_url":"https://pith.science/pith/HDCTFWIPIJY7BQXY7FAJP47GDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDCTFWIPIJY7BQXY7FAJP47GDL/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":"2026-08-16T02:58:18Z","links":{"resolver":"https://pith.science/pith/HDCTFWIPIJY7BQXY7FAJP47GDL","bundle":"https://pith.science/pith/HDCTFWIPIJY7BQXY7FAJP47GDL/bundle.json","state":"https://pith.science/pith/HDCTFWIPIJY7BQXY7FAJP47GDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDCTFWIPIJY7BQXY7FAJP47GDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:HDCTFWIPIJY7BQXY7FAJP47GDL","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":"71402328adf39a3ccb319ba74ec2916a3765bc754707956cf1f495620f28a343","cross_cats_sorted":["astro-ph","hep-th"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-10-11T19:45:34Z","title_canon_sha256":"ad6e15b3e58d407e1c72f1aeed38d13bbb60e0b89995037f04b3270b42b225ba"},"schema_version":"1.0","source":{"id":"gr-qc/0410046","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0410046","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0410046v4","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0410046","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"HDCTFWIPIJY7","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"pith_short_16","alias_value":"HDCTFWIPIJY7BQXY","created_at":"2026-07-04T16:47:48Z"},{"alias_kind":"pith_short_8","alias_value":"HDCTFWIP","created_at":"2026-07-04T16:47:48Z"}],"graph_snapshots":[{"event_id":"sha256:6cbd4264fc219783d5301e5609c9ea69ec1153264b84c1f1f47c41958b8bec7a","target":"graph","created_at":"2026-07-04T16:47:48Z","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/gr-qc/0410046/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and ","authors_text":"A. Troisi, P. K. S. Dunsby, S. Capozziello, S. Carloni","cross_cats":["astro-ph","hep-th"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2004-10-11T19:45:34Z","title":"Cosmological dynamics of R^n gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0410046","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:aeefe9aa49249c6b095efe6fa026d8efb475d1b89a05323b3abec4dda06af991","target":"record","created_at":"2026-07-04T16:47:48Z","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":"71402328adf39a3ccb319ba74ec2916a3765bc754707956cf1f495620f28a343","cross_cats_sorted":["astro-ph","hep-th"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-10-11T19:45:34Z","title_canon_sha256":"ad6e15b3e58d407e1c72f1aeed38d13bbb60e0b89995037f04b3270b42b225ba"},"schema_version":"1.0","source":{"id":"gr-qc/0410046","kind":"arxiv","version":4}},"canonical_sha256":"38c532d90f4271f0c2f8f94097f3e61ae1e2bae27dddd854b219cd561f02b49e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38c532d90f4271f0c2f8f94097f3e61ae1e2bae27dddd854b219cd561f02b49e","first_computed_at":"2026-07-04T16:47:48.905456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:47:48.905456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45h2ek8yaNPyHxnMSCJk7Kl1JqhA3PFyTRapGJRiLqUZF6QCb2RJwbwoxY7GnJIcrf/WMJjgyk5adwQqdEYCCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:47:48.905820Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0410046","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeefe9aa49249c6b095efe6fa026d8efb475d1b89a05323b3abec4dda06af991","sha256:6cbd4264fc219783d5301e5609c9ea69ec1153264b84c1f1f47c41958b8bec7a"],"state_sha256":"e8572c48df1896cda21070893414fa3d2ae38f0a2ae62bb9007eba621376b6fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yhbBbD1XPnrXIO4ynsgKPohS/W5vZGc5IIvFjjCb2vX9iV0Tiydxv6rNTi4g4hCeyfF8Ny1QjR/eiKMDjzv7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T02:58:18.880221Z","bundle_sha256":"c4c73c2adef6e2f611b8a45d6c9527defb66bbbd9802a205641df5f3e6a14cf3"}}