{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XUART3TXIDPYF4J7T6IUVJ5ZTS","short_pith_number":"pith:XUART3TX","schema_version":"1.0","canonical_sha256":"bd0119ee7740df82f13f9f914aa7b99c8a64edcc1fa65acd3f4232ed07a442d4","source":{"kind":"arxiv","id":"1605.05046","version":2},"attestation_state":"computed","paper":{"title":"Geodesics in the (anti-)de Sitter spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Nguyen Phuc Ky Tho","submitted_at":"2016-05-17T07:51:00Z","abstract_excerpt":"A class of exact solutions of the geodesic equations in (anti-)de Sitter AdS$_4$ and dS$_4$ spacetimes is presented. The geodesics for test particles in AdS$_4$ and dS$_4$ spacetimes are respectively sinusoidal and hyperbolic sine world lines. The world line for light rays is straight lines as known. In particular, the world lines of test particles are not dependent on their energy. Spontaneous symmetry breaking of AdS$_4$ spacetime provides a physical explanation for arising of the virtual particle and antiparticle pairs in vacuum. Interestingly, the energy of a pair and the time its particle"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.05046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-05-17T07:51:00Z","cross_cats_sorted":[],"title_canon_sha256":"4cc141909be328ad3fb5905bb2589683f528bd47081a91b94e1e51b3bea8f996","abstract_canon_sha256":"eadf7eeb77b8ed8e233eec29040a6e465baf0ad846713e722f07aeece782bc6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:37.564574Z","signature_b64":"5Y/MnHyO+6sLW5/nDJxS6QkkfUPr0UyHMJp9JVKfKXwVgHnaWUgCsltRLR53NUj4/QVrgS5pgn0dwC5F59+gDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd0119ee7740df82f13f9f914aa7b99c8a64edcc1fa65acd3f4232ed07a442d4","last_reissued_at":"2026-05-18T01:10:37.564026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:37.564026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geodesics in the (anti-)de Sitter spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Nguyen Phuc Ky Tho","submitted_at":"2016-05-17T07:51:00Z","abstract_excerpt":"A class of exact solutions of the geodesic equations in (anti-)de Sitter AdS$_4$ and dS$_4$ spacetimes is presented. The geodesics for test particles in AdS$_4$ and dS$_4$ spacetimes are respectively sinusoidal and hyperbolic sine world lines. The world line for light rays is straight lines as known. In particular, the world lines of test particles are not dependent on their energy. Spontaneous symmetry breaking of AdS$_4$ spacetime provides a physical explanation for arising of the virtual particle and antiparticle pairs in vacuum. Interestingly, the energy of a pair and the time its particle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05046","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.05046","created_at":"2026-05-18T01:10:37.564113+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05046v2","created_at":"2026-05-18T01:10:37.564113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05046","created_at":"2026-05-18T01:10:37.564113+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUART3TXIDPY","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUART3TXIDPYF4J7","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUART3TX","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.09501","citing_title":"Experimental observation of hyperbolic spacetime dynamics","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS","json":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS.json","graph_json":"https://pith.science/api/pith-number/XUART3TXIDPYF4J7T6IUVJ5ZTS/graph.json","events_json":"https://pith.science/api/pith-number/XUART3TXIDPYF4J7T6IUVJ5ZTS/events.json","paper":"https://pith.science/paper/XUART3TX"},"agent_actions":{"view_html":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS","download_json":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS.json","view_paper":"https://pith.science/paper/XUART3TX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05046&json=true","fetch_graph":"https://pith.science/api/pith-number/XUART3TXIDPYF4J7T6IUVJ5ZTS/graph.json","fetch_events":"https://pith.science/api/pith-number/XUART3TXIDPYF4J7T6IUVJ5ZTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS/action/storage_attestation","attest_author":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS/action/author_attestation","sign_citation":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS/action/citation_signature","submit_replication":"https://pith.science/pith/XUART3TXIDPYF4J7T6IUVJ5ZTS/action/replication_record"}},"created_at":"2026-05-18T01:10:37.564113+00:00","updated_at":"2026-05-18T01:10:37.564113+00:00"}