{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T7D7FH4BKXYAE3HKBQBFTDLJYV","short_pith_number":"pith:T7D7FH4B","canonical_record":{"source":{"id":"1905.01904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-06T09:52:01Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"2c9833b641614fa73aa62ae49930ccd9db43466ef885bee70ab8f67d858a6c87","abstract_canon_sha256":"5bfba05ffe641db6389af66a8a6f347facbd2cb6bc7c3177d49b8860a08f942e"},"schema_version":"1.0"},"canonical_sha256":"9fc7f29f8155f0026cea0c02598d69c554604ca23e4d27e460f29a2e59957b5f","source":{"kind":"arxiv","id":"1905.01904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01904","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01904v1","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01904","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"T7D7FH4BKXYA","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"pith_short_16","alias_value":"T7D7FH4BKXYAE3HK","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"pith_short_8","alias_value":"T7D7FH4B","created_at":"2026-07-05T01:03:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T7D7FH4BKXYAE3HKBQBFTDLJYV","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-06T09:52:01Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"2c9833b641614fa73aa62ae49930ccd9db43466ef885bee70ab8f67d858a6c87","abstract_canon_sha256":"5bfba05ffe641db6389af66a8a6f347facbd2cb6bc7c3177d49b8860a08f942e"},"schema_version":"1.0"},"canonical_sha256":"9fc7f29f8155f0026cea0c02598d69c554604ca23e4d27e460f29a2e59957b5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:03:59.013368Z","signature_b64":"fOBZLKsAomK0s7oiV29BtQ8GhWJVULiPYjj8eEJPIpWBBUnqO0YxDy+WBdqOv5JDA1TBmf+XpIFfMwr0f8bJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fc7f29f8155f0026cea0c02598d69c554604ca23e4d27e460f29a2e59957b5f","last_reissued_at":"2026-07-05T01:03:59.012928Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:03:59.012928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01904","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":"2026-07-05T01:03:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YN0iVgTZPQKlS/gEqSgi4RDh5jAZIBI9eyr72YobI6psjC91yLnSQvA42LlMY/kPEtNDZ4GvwvJfAyIBFoMoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:28:03.326939Z"},"content_sha256":"6dd706a2def2d0ff8674783188ba1f902d9bb3c928c97a310fc66d5d27718d88","schema_version":"1.0","event_id":"sha256:6dd706a2def2d0ff8674783188ba1f902d9bb3c928c97a310fc66d5d27718d88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T7D7FH4BKXYAE3HKBQBFTDLJYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Phase Space of $k$-Essence $f(R)$ Gravity Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"N. Chatzarakis, V.K. Oikonomou","submitted_at":"2019-05-06T09:52:01Z","abstract_excerpt":"Among the remaining viable theories that can successfully describe the late-time era is the $k$-Essence theory and in this work we study in detail the phase space of $k$-Essence $f(R)$ gravity in vacuum. This theory can describe in a viable way the inflationary era too, so we shall study the phase space in detail, since this investigation may reveal general properties regarding the inflationary attractors. By appropriately choosing the dimensionless variables corresponding to the cosmological system, we shall construct an autonomous dynamical system, and we find the fixed points of the system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01904","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/1905.01904/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":"2026-07-05T01:03:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNiHA2Y/NjJ0E9ml6S3pTIjqeIuc5U51ZWtZneNIal5jfNDdaDCrhzlMJ7FFmAflGf+eF4K7AbryHYu8/63hAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:28:03.327983Z"},"content_sha256":"616ab8de18134186910d35cdea7eb04c34de62c9e0a6108e032e449aa435e274","schema_version":"1.0","event_id":"sha256:616ab8de18134186910d35cdea7eb04c34de62c9e0a6108e032e449aa435e274"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV/bundle.json","state_url":"https://pith.science/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV/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":"2026-08-19T14:28:03Z","links":{"resolver":"https://pith.science/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV","bundle":"https://pith.science/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV/bundle.json","state":"https://pith.science/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7D7FH4BKXYAE3HKBQBFTDLJYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T7D7FH4BKXYAE3HKBQBFTDLJYV","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":"5bfba05ffe641db6389af66a8a6f347facbd2cb6bc7c3177d49b8860a08f942e","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-06T09:52:01Z","title_canon_sha256":"2c9833b641614fa73aa62ae49930ccd9db43466ef885bee70ab8f67d858a6c87"},"schema_version":"1.0","source":{"id":"1905.01904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01904","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01904v1","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01904","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"T7D7FH4BKXYA","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"pith_short_16","alias_value":"T7D7FH4BKXYAE3HK","created_at":"2026-07-05T01:03:59Z"},{"alias_kind":"pith_short_8","alias_value":"T7D7FH4B","created_at":"2026-07-05T01:03:59Z"}],"graph_snapshots":[{"event_id":"sha256:616ab8de18134186910d35cdea7eb04c34de62c9e0a6108e032e449aa435e274","target":"graph","created_at":"2026-07-05T01:03:59Z","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/1905.01904/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Among the remaining viable theories that can successfully describe the late-time era is the $k$-Essence theory and in this work we study in detail the phase space of $k$-Essence $f(R)$ gravity in vacuum. This theory can describe in a viable way the inflationary era too, so we shall study the phase space in detail, since this investigation may reveal general properties regarding the inflationary attractors. By appropriately choosing the dimensionless variables corresponding to the cosmological system, we shall construct an autonomous dynamical system, and we find the fixed points of the system.","authors_text":"N. Chatzarakis, 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":"2019-05-06T09:52:01Z","title":"The Phase Space of $k$-Essence $f(R)$ Gravity Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01904","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":"sha256:6dd706a2def2d0ff8674783188ba1f902d9bb3c928c97a310fc66d5d27718d88","target":"record","created_at":"2026-07-05T01:03:59Z","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":"5bfba05ffe641db6389af66a8a6f347facbd2cb6bc7c3177d49b8860a08f942e","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-06T09:52:01Z","title_canon_sha256":"2c9833b641614fa73aa62ae49930ccd9db43466ef885bee70ab8f67d858a6c87"},"schema_version":"1.0","source":{"id":"1905.01904","kind":"arxiv","version":1}},"canonical_sha256":"9fc7f29f8155f0026cea0c02598d69c554604ca23e4d27e460f29a2e59957b5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fc7f29f8155f0026cea0c02598d69c554604ca23e4d27e460f29a2e59957b5f","first_computed_at":"2026-07-05T01:03:59.012928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:03:59.012928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fOBZLKsAomK0s7oiV29BtQ8GhWJVULiPYjj8eEJPIpWBBUnqO0YxDy+WBdqOv5JDA1TBmf+XpIFfMwr0f8bJAw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:03:59.013368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dd706a2def2d0ff8674783188ba1f902d9bb3c928c97a310fc66d5d27718d88","sha256:616ab8de18134186910d35cdea7eb04c34de62c9e0a6108e032e449aa435e274"],"state_sha256":"bb59f84c697bdbca1da975050fa9099ba579b4334193866bc427b7981d5ee71c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pKftdDOkOlcO2uEFjSNaEE06JXLktUl/EmsT8tZ6bGL26CChosOZWsANYEyU/q7+QJQPiJF4fTo3irS6JwWiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T14:28:03.334093Z","bundle_sha256":"0746f5d91fefda0a891d6e6359ca168ab3b0d4239fc708730f755c2a5b4a6be8"}}