{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7CO536PHDTJFERDUNFNXY6TUTW","short_pith_number":"pith:7CO536PH","canonical_record":{"source":{"id":"1407.4313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-16T13:55:47Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"4471307996ffbfd63678e5f503e2a78d02c80105dce3faccb58376f18849e370","abstract_canon_sha256":"6c94a54e4987c44af7c81644d00253cc98c9b8765e8e8ac6b8da61bf02aede82"},"schema_version":"1.0"},"canonical_sha256":"f89dddf9e71cd2524474695b7c7a749daced05fe86c6a431f01d3624e80b5a50","source":{"kind":"arxiv","id":"1407.4313","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4313","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4313v1","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4313","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"7CO536PHDTJF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7CO536PHDTJFERDU","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7CO536PH","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7CO536PHDTJFERDUNFNXY6TUTW","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-16T13:55:47Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"4471307996ffbfd63678e5f503e2a78d02c80105dce3faccb58376f18849e370","abstract_canon_sha256":"6c94a54e4987c44af7c81644d00253cc98c9b8765e8e8ac6b8da61bf02aede82"},"schema_version":"1.0"},"canonical_sha256":"f89dddf9e71cd2524474695b7c7a749daced05fe86c6a431f01d3624e80b5a50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:31.509110Z","signature_b64":"oPo3C6rCvZn1Nqho9432lk/hCEnqPhUbUNlQNVsOQ61ZLsRPQ4GhMKbMwLFHMsf3vH098lYRsv3230pCL/r0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f89dddf9e71cd2524474695b7c7a749daced05fe86c6a431f01d3624e80b5a50","last_reissued_at":"2026-05-18T02:28:31.508398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:31.508398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4313","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":"2026-05-18T02:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OXiO3V+CuTAXo44P7xC7WCRgITYVPqWAt3pF7vCc85+4pW7S/X5F7yBLiZJTDDwxlIjtwEvXrlB5okiRFfmkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:47:26.007168Z"},"content_sha256":"b7bb09efcaa516c0a44e17be9a746398dd49ee91e04a6e13a0d64e95b8c4889d","schema_version":"1.0","event_id":"sha256:b7bb09efcaa516c0a44e17be9a746398dd49ee91e04a6e13a0d64e95b8c4889d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7CO536PHDTJFERDUNFNXY6TUTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant solutions and Noether symmetries in Hybrid Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Andronikos Paliathanasis, Andrzej Borowiec, Aneta Wojnar, Francisco S.N. Lobo, Mariacristina Paolella, Mariafelicia De Laurentis, Salvatore Capozziello","submitted_at":"2014-07-16T13:55:47Z","abstract_excerpt":"Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific Lagrangians. In this work, we consider the application of point symmetries in the recently proposed metric-Palatini Hybrid Gravity in order to select the $f({\\cal R})$ functional form and to find analytical solutions for the field equations and for the related Wheeler-DeWitt (WDW) equation. We show that, in order to find out integrable $f({\\cal R})$ models, conformal transformations in the Lagrang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4313","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":"2026-05-18T02:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4tnvt7pTPYzPPIJpTFbXEtooUIRkBBtqwPtOK9/vYOdZMHEmuELoKNvwoipEBmA7mNGD99+pnt/0axsBOEpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T20:47:26.007543Z"},"content_sha256":"15a0b053f246c2c5d6c84db2acf911f7dcb96c9164ebb829bbf2dd8810518173","schema_version":"1.0","event_id":"sha256:15a0b053f246c2c5d6c84db2acf911f7dcb96c9164ebb829bbf2dd8810518173"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CO536PHDTJFERDUNFNXY6TUTW/bundle.json","state_url":"https://pith.science/pith/7CO536PHDTJFERDUNFNXY6TUTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CO536PHDTJFERDUNFNXY6TUTW/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":"2026-05-24T20:47:26Z","links":{"resolver":"https://pith.science/pith/7CO536PHDTJFERDUNFNXY6TUTW","bundle":"https://pith.science/pith/7CO536PHDTJFERDUNFNXY6TUTW/bundle.json","state":"https://pith.science/pith/7CO536PHDTJFERDUNFNXY6TUTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CO536PHDTJFERDUNFNXY6TUTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7CO536PHDTJFERDUNFNXY6TUTW","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":"6c94a54e4987c44af7c81644d00253cc98c9b8765e8e8ac6b8da61bf02aede82","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-16T13:55:47Z","title_canon_sha256":"4471307996ffbfd63678e5f503e2a78d02c80105dce3faccb58376f18849e370"},"schema_version":"1.0","source":{"id":"1407.4313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4313","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4313v1","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4313","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"7CO536PHDTJF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7CO536PHDTJFERDU","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7CO536PH","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:15a0b053f246c2c5d6c84db2acf911f7dcb96c9164ebb829bbf2dd8810518173","target":"graph","created_at":"2026-05-18T02:28:31Z","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":"Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific Lagrangians. In this work, we consider the application of point symmetries in the recently proposed metric-Palatini Hybrid Gravity in order to select the $f({\\cal R})$ functional form and to find analytical solutions for the field equations and for the related Wheeler-DeWitt (WDW) equation. We show that, in order to find out integrable $f({\\cal R})$ models, conformal transformations in the Lagrang","authors_text":"Andronikos Paliathanasis, Andrzej Borowiec, Aneta Wojnar, Francisco S.N. Lobo, Mariacristina Paolella, Mariafelicia De Laurentis, Salvatore Capozziello","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-16T13:55:47Z","title":"Invariant solutions and Noether symmetries in Hybrid Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4313","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:b7bb09efcaa516c0a44e17be9a746398dd49ee91e04a6e13a0d64e95b8c4889d","target":"record","created_at":"2026-05-18T02:28:31Z","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":"6c94a54e4987c44af7c81644d00253cc98c9b8765e8e8ac6b8da61bf02aede82","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-16T13:55:47Z","title_canon_sha256":"4471307996ffbfd63678e5f503e2a78d02c80105dce3faccb58376f18849e370"},"schema_version":"1.0","source":{"id":"1407.4313","kind":"arxiv","version":1}},"canonical_sha256":"f89dddf9e71cd2524474695b7c7a749daced05fe86c6a431f01d3624e80b5a50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f89dddf9e71cd2524474695b7c7a749daced05fe86c6a431f01d3624e80b5a50","first_computed_at":"2026-05-18T02:28:31.508398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:31.508398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oPo3C6rCvZn1Nqho9432lk/hCEnqPhUbUNlQNVsOQ61ZLsRPQ4GhMKbMwLFHMsf3vH098lYRsv3230pCL/r0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:31.509110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7bb09efcaa516c0a44e17be9a746398dd49ee91e04a6e13a0d64e95b8c4889d","sha256:15a0b053f246c2c5d6c84db2acf911f7dcb96c9164ebb829bbf2dd8810518173"],"state_sha256":"b2bc64c35a3d187b4d4e382b866b7792eeaaf2b5b29eed09c0e345fa2753f60e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pWO/JPKp7xAApCFWygIFbJQhLuTStI9ppotF/YXiuvOz1JZshMy9+Ce/rOkzpn+APHqusWGskIIkqzmWTlxBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T20:47:26.009629Z","bundle_sha256":"c914a69fb09f6c957723c44b0c89c8c85a4c4acd2326ceec232188a7452b5f59"}}