{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3DHKO3CYSQ4WB2OL7VZSNIEI3M","short_pith_number":"pith:3DHKO3CY","canonical_record":{"source":{"id":"2308.00082","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-07-31T18:55:50Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"f681b432497fbb8c6e1e41bd2cd8a59ebcafec850236b1e113669579ec69a7aa","abstract_canon_sha256":"d57b86a0454f8874bc298c25a7ce1ac2942e02ca215a815a3bd2a140a4b6c9c0"},"schema_version":"1.0"},"canonical_sha256":"d8cea76c58943960e9cbfd7326a088db2b8ef8b8b3d07cdd5c9722ced03f6ce3","source":{"kind":"arxiv","id":"2308.00082","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.00082","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"arxiv_version","alias_value":"2308.00082v2","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.00082","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"pith_short_12","alias_value":"3DHKO3CYSQ4W","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"pith_short_16","alias_value":"3DHKO3CYSQ4WB2OL","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"pith_short_8","alias_value":"3DHKO3CY","created_at":"2026-07-05T06:43:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3DHKO3CYSQ4WB2OL7VZSNIEI3M","target":"record","payload":{"canonical_record":{"source":{"id":"2308.00082","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-07-31T18:55:50Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"f681b432497fbb8c6e1e41bd2cd8a59ebcafec850236b1e113669579ec69a7aa","abstract_canon_sha256":"d57b86a0454f8874bc298c25a7ce1ac2942e02ca215a815a3bd2a140a4b6c9c0"},"schema_version":"1.0"},"canonical_sha256":"d8cea76c58943960e9cbfd7326a088db2b8ef8b8b3d07cdd5c9722ced03f6ce3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:43:50.855712Z","signature_b64":"f+zfSLlHmuQP912KQqRooN3aDNfVeAk6UJ1rWdcSgm3zyD996MPoippEQmT9Q62+KZrm0pGEjLoPya/anzSQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8cea76c58943960e9cbfd7326a088db2b8ef8b8b3d07cdd5c9722ced03f6ce3","last_reissued_at":"2026-07-05T06:43:50.855155Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:43:50.855155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.00082","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":"2026-07-05T06:43:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQrCrOJBzhloV493uJWEfDlEwKoaByp663ILdsI6LpKeeYkpDTRIDh38SmEwMLuroq7mDompD4jr50plvzaZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:12:40.448690Z"},"content_sha256":"a64d566daf193b4c40b2d8be7c7e0fd252af3cc39c689185c09fc32100acff1e","schema_version":"1.0","event_id":"sha256:a64d566daf193b4c40b2d8be7c7e0fd252af3cc39c689185c09fc32100acff1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3DHKO3CYSQ4WB2OL7VZSNIEI3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Noether Symmetry Approach: Foundation and applications. The case of scalar-tensor Gauss-Bonnet gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Francesca Spinnato, Francesco Bajardi, Salvatore Capozziello, Tiziana Di Salvo","submitted_at":"2023-07-31T18:55:50Z","abstract_excerpt":"We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians to select symmetries. Furthermore, we extend the prescription to the first prolongation of the Noether vector. It is possible to show that the latter application provides a general constraint on the infinitesimal generator $\\xi$, related to the spacetime translations. This approach can be used fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.00082","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.00082/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":"2026-07-05T06:43:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2lG/uRhTUZlnUxNUw0bjFavQ35ZmlTd0SHcxezAP8Hthur6nwnKf/CpoNJinzJnl7XgpGkz9DOS/zDDSvFLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:12:40.449594Z"},"content_sha256":"e39be2c28fd6a58c58b5338b740b1855ea2693fd5a854e7a0c0b8de44e09e38f","schema_version":"1.0","event_id":"sha256:e39be2c28fd6a58c58b5338b740b1855ea2693fd5a854e7a0c0b8de44e09e38f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M/bundle.json","state_url":"https://pith.science/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M/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":"2026-08-03T21:12:40Z","links":{"resolver":"https://pith.science/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M","bundle":"https://pith.science/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M/bundle.json","state":"https://pith.science/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DHKO3CYSQ4WB2OL7VZSNIEI3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3DHKO3CYSQ4WB2OL7VZSNIEI3M","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":"d57b86a0454f8874bc298c25a7ce1ac2942e02ca215a815a3bd2a140a4b6c9c0","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-07-31T18:55:50Z","title_canon_sha256":"f681b432497fbb8c6e1e41bd2cd8a59ebcafec850236b1e113669579ec69a7aa"},"schema_version":"1.0","source":{"id":"2308.00082","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.00082","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"arxiv_version","alias_value":"2308.00082v2","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.00082","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"pith_short_12","alias_value":"3DHKO3CYSQ4W","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"pith_short_16","alias_value":"3DHKO3CYSQ4WB2OL","created_at":"2026-07-05T06:43:50Z"},{"alias_kind":"pith_short_8","alias_value":"3DHKO3CY","created_at":"2026-07-05T06:43:50Z"}],"graph_snapshots":[{"event_id":"sha256:e39be2c28fd6a58c58b5338b740b1855ea2693fd5a854e7a0c0b8de44e09e38f","target":"graph","created_at":"2026-07-05T06:43:50Z","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/2308.00082/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians to select symmetries. Furthermore, we extend the prescription to the first prolongation of the Noether vector. It is possible to show that the latter application provides a general constraint on the infinitesimal generator $\\xi$, related to the spacetime translations. This approach can be used fo","authors_text":"Francesca Spinnato, Francesco Bajardi, Salvatore Capozziello, Tiziana Di Salvo","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-07-31T18:55:50Z","title":"The Noether Symmetry Approach: Foundation and applications. The case of scalar-tensor Gauss-Bonnet gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.00082","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:a64d566daf193b4c40b2d8be7c7e0fd252af3cc39c689185c09fc32100acff1e","target":"record","created_at":"2026-07-05T06:43:50Z","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":"d57b86a0454f8874bc298c25a7ce1ac2942e02ca215a815a3bd2a140a4b6c9c0","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2023-07-31T18:55:50Z","title_canon_sha256":"f681b432497fbb8c6e1e41bd2cd8a59ebcafec850236b1e113669579ec69a7aa"},"schema_version":"1.0","source":{"id":"2308.00082","kind":"arxiv","version":2}},"canonical_sha256":"d8cea76c58943960e9cbfd7326a088db2b8ef8b8b3d07cdd5c9722ced03f6ce3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8cea76c58943960e9cbfd7326a088db2b8ef8b8b3d07cdd5c9722ced03f6ce3","first_computed_at":"2026-07-05T06:43:50.855155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:43:50.855155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f+zfSLlHmuQP912KQqRooN3aDNfVeAk6UJ1rWdcSgm3zyD996MPoippEQmT9Q62+KZrm0pGEjLoPya/anzSQAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:43:50.855712Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.00082","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a64d566daf193b4c40b2d8be7c7e0fd252af3cc39c689185c09fc32100acff1e","sha256:e39be2c28fd6a58c58b5338b740b1855ea2693fd5a854e7a0c0b8de44e09e38f"],"state_sha256":"becb62f6f18211ed13a626545b8d3e68b28a53ae681d600766335e1223012d1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Dnq30SjxCY2Dl1r4T+ftwx8iL5cS1WOoxcxeLNBkrLTsjZ4FpC9GQmuiiG96R4nfqyNWGq7pkTOT33vqaWqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:12:40.455823Z","bundle_sha256":"c47e55e92da60ab2ca2421ccf69a2abce7012fe934bb6ffe7e2a953f11270688"}}