{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:343SYDZYJFSITNIZ6VQQ73CUL3","short_pith_number":"pith:343SYDZY","schema_version":"1.0","canonical_sha256":"df372c0f38496489b519f5610fec545ed2633c05a72fd668137ac5db0bd94558","source":{"kind":"arxiv","id":"1302.7185","version":4},"attestation_state":"computed","paper":{"title":"A Generalization of Fermat's Principle for Classical and Quantum Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Tarek A. Elsayed","submitted_at":"2013-02-28T13:09:41Z","abstract_excerpt":"The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat's principle will hold. We substa"},"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":"1302.7185","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-28T13:09:41Z","cross_cats_sorted":[],"title_canon_sha256":"5a1ac9f8048b28e28f4bb0eb8d525a18d034a124c0a0288b4da28cf51834537b","abstract_canon_sha256":"e840f918daee93d7dcd4c4d3605c7479533633b5fa219884252d2bc1bca56ed9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:18.825626Z","signature_b64":"0D0t2lDa5dCp+LSNE6GrN+GEi7ZVnPIuAIos3j+a9K9Z3YNzxIqnTPh4G7JiIUraZS3L1jxHwo1TxF766k4gBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df372c0f38496489b519f5610fec545ed2633c05a72fd668137ac5db0bd94558","last_reissued_at":"2026-05-18T02:40:18.825189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:18.825189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Generalization of Fermat's Principle for Classical and Quantum Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Tarek A. Elsayed","submitted_at":"2013-02-28T13:09:41Z","abstract_excerpt":"The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat's principle will hold. We substa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7185","kind":"arxiv","version":4},"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":"1302.7185","created_at":"2026-05-18T02:40:18.825246+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.7185v4","created_at":"2026-05-18T02:40:18.825246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7185","created_at":"2026-05-18T02:40:18.825246+00:00"},{"alias_kind":"pith_short_12","alias_value":"343SYDZYJFSI","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"343SYDZYJFSITNIZ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"343SYDZY","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3","json":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3.json","graph_json":"https://pith.science/api/pith-number/343SYDZYJFSITNIZ6VQQ73CUL3/graph.json","events_json":"https://pith.science/api/pith-number/343SYDZYJFSITNIZ6VQQ73CUL3/events.json","paper":"https://pith.science/paper/343SYDZY"},"agent_actions":{"view_html":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3","download_json":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3.json","view_paper":"https://pith.science/paper/343SYDZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.7185&json=true","fetch_graph":"https://pith.science/api/pith-number/343SYDZYJFSITNIZ6VQQ73CUL3/graph.json","fetch_events":"https://pith.science/api/pith-number/343SYDZYJFSITNIZ6VQQ73CUL3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3/action/storage_attestation","attest_author":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3/action/author_attestation","sign_citation":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3/action/citation_signature","submit_replication":"https://pith.science/pith/343SYDZYJFSITNIZ6VQQ73CUL3/action/replication_record"}},"created_at":"2026-05-18T02:40:18.825246+00:00","updated_at":"2026-05-18T02:40:18.825246+00:00"}