{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IGUKQZSHOLX3643AL4QJA77ZHJ","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":"83410a384f5e0e0b7ea8088f32f3c91df4eaa4474b27d158ebae71f686acf261","cross_cats_sorted":["gr-qc","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-10T15:52:09Z","title_canon_sha256":"3ea98670d971c1ca270809f3a9910547a2e1700bad80f71c523d25977f07673b"},"schema_version":"1.0","source":{"id":"1310.2862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2862","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2862v1","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2862","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"IGUKQZSHOLX3","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IGUKQZSHOLX3643A","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IGUKQZSH","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:f84cdf4d78ec0288b6bf857813744ec7339b98083b9867da599bb8294f461a32","target":"graph","created_at":"2026-05-18T03:10:46Z","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":"Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of time machines which can travel forward and backward in time and which differ from models based on closed timelike curves (CTCs). In the continuum limit, we explore the interaction between such time reversing machines and quantum mechanical objects, employing a recent description of quantum-classical hybrids.","authors_text":"Hans-Thomas Elze","cross_cats":["gr-qc","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-10T15:52:09Z","title":"Discrete mechanics, time machines and hybrid systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2862","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:d1e6228e34f4f647366e3c2b911b5421769a25fd55102e115ddc88eb049b6516","target":"record","created_at":"2026-05-18T03:10:46Z","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":"83410a384f5e0e0b7ea8088f32f3c91df4eaa4474b27d158ebae71f686acf261","cross_cats_sorted":["gr-qc","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-10T15:52:09Z","title_canon_sha256":"3ea98670d971c1ca270809f3a9910547a2e1700bad80f71c523d25977f07673b"},"schema_version":"1.0","source":{"id":"1310.2862","kind":"arxiv","version":1}},"canonical_sha256":"41a8a8664772efbf73605f20907ff93a697244a8008a1c22b7a5d76a4bf9ae01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41a8a8664772efbf73605f20907ff93a697244a8008a1c22b7a5d76a4bf9ae01","first_computed_at":"2026-05-18T03:10:46.437907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:46.437907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MrdFOphtt7WXAQ/KMN8z83dCcUasXkNFItY5oOIgOZP2u164rAtZOSp1+O9rrjj2G1wgSjG0LLmOW32WdXCbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:46.438521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1e6228e34f4f647366e3c2b911b5421769a25fd55102e115ddc88eb049b6516","sha256:f84cdf4d78ec0288b6bf857813744ec7339b98083b9867da599bb8294f461a32"],"state_sha256":"8fa8bdf7605c105fb411e62ae586da4d4b49c6e2736d6eee1739ca74cd4bd6dc"}