{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZKPMH37P7R26ZWRFQ2AB5Y3LIP","short_pith_number":"pith:ZKPMH37P","canonical_record":{"source":{"id":"0909.1183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-07T09:22:45Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"5c02f7892d66ae956b460c45dd755312e2f1f254a62037d61d2c0eab1b3d0ede","abstract_canon_sha256":"be4d7547740bb53bddda5081acb7e4d1049ae713a0b803b0c6e9ab40523b6473"},"schema_version":"1.0"},"canonical_sha256":"ca9ec3efeffc75ecda2586801ee36b43f5666b7b5e55540676274bd470b7751c","source":{"kind":"arxiv","id":"0909.1183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1183","created_at":"2026-05-18T02:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1183v1","created_at":"2026-05-18T02:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1183","created_at":"2026-05-18T02:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZKPMH37P7R26","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZKPMH37P7R26ZWRF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZKPMH37P","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZKPMH37P7R26ZWRFQ2AB5Y3LIP","target":"record","payload":{"canonical_record":{"source":{"id":"0909.1183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-07T09:22:45Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"5c02f7892d66ae956b460c45dd755312e2f1f254a62037d61d2c0eab1b3d0ede","abstract_canon_sha256":"be4d7547740bb53bddda5081acb7e4d1049ae713a0b803b0c6e9ab40523b6473"},"schema_version":"1.0"},"canonical_sha256":"ca9ec3efeffc75ecda2586801ee36b43f5666b7b5e55540676274bd470b7751c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:59.198626Z","signature_b64":"YtO90BPOok6PkXi8lacX76L4YsOC9AC5xmuEkPlYsMXV6G2YYkt6Df9ztL6nfXwMwMJqYGHvWmnAs+7qXDLzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca9ec3efeffc75ecda2586801ee36b43f5666b7b5e55540676274bd470b7751c","last_reissued_at":"2026-05-18T02:11:59.198039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:59.198039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.1183","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":"2026-05-18T02:11:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9VA3T6jInAhf6+b2JCcbAQOz3c2UL0LYWFg8K86yfs3B5G94n3ZS6ha2jeH6vLKOCl3ktIelxs25R4pGHpLTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:55:13.758704Z"},"content_sha256":"81ab5a48b365cae67920aee5bd9291103be914b5a9c294756cb669abd9dada3f","schema_version":"1.0","event_id":"sha256:81ab5a48b365cae67920aee5bd9291103be914b5a9c294756cb669abd9dada3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZKPMH37P7R26ZWRFQ2AB5Y3LIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On fractional time quantum dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander Iomin","submitted_at":"2009-09-07T09:22:45Z","abstract_excerpt":"Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schr\\\"odinger equation (SE), which differs from the standard SE by the fractional time derivative: $\\frac{\\prt}{\\prt t}\\to \\frac{\\prt^{\\alpha}}{\\prt t^{\\alpha}}$. It is shown that for $\\alpha =1/2$ the fractional SE is isospectral to a comb model. An analytical expression for the Green functions of the systems are obtained. The semiclassical limit is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1183","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":"2026-05-18T02:11:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsZ+YTM7Vkbnts1Me6FHbJiIqCM3V5l/TfmtZLQ4pzK4ZFKN0Pc05ZHaexz+JlKFAoQNWXgo7OFGuYpdM8i0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:55:13.759374Z"},"content_sha256":"6eef93cf8af0a0d9259547d287de1c90335c319252c421692fb1104ffd278e4f","schema_version":"1.0","event_id":"sha256:6eef93cf8af0a0d9259547d287de1c90335c319252c421692fb1104ffd278e4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP/bundle.json","state_url":"https://pith.science/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP/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":"2026-06-09T16:55:13Z","links":{"resolver":"https://pith.science/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP","bundle":"https://pith.science/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP/bundle.json","state":"https://pith.science/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKPMH37P7R26ZWRFQ2AB5Y3LIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZKPMH37P7R26ZWRFQ2AB5Y3LIP","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":"be4d7547740bb53bddda5081acb7e4d1049ae713a0b803b0c6e9ab40523b6473","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-07T09:22:45Z","title_canon_sha256":"5c02f7892d66ae956b460c45dd755312e2f1f254a62037d61d2c0eab1b3d0ede"},"schema_version":"1.0","source":{"id":"0909.1183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1183","created_at":"2026-05-18T02:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1183v1","created_at":"2026-05-18T02:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1183","created_at":"2026-05-18T02:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZKPMH37P7R26","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZKPMH37P7R26ZWRF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZKPMH37P","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:6eef93cf8af0a0d9259547d287de1c90335c319252c421692fb1104ffd278e4f","target":"graph","created_at":"2026-05-18T02:11:59Z","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":"Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schr\\\"odinger equation (SE), which differs from the standard SE by the fractional time derivative: $\\frac{\\prt}{\\prt t}\\to \\frac{\\prt^{\\alpha}}{\\prt t^{\\alpha}}$. It is shown that for $\\alpha =1/2$ the fractional SE is isospectral to a comb model. An analytical expression for the Green functions of the systems are obtained. The semiclassical limit is discussed.","authors_text":"Alexander Iomin","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-07T09:22:45Z","title":"On fractional time quantum dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1183","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":"sha256:81ab5a48b365cae67920aee5bd9291103be914b5a9c294756cb669abd9dada3f","target":"record","created_at":"2026-05-18T02:11:59Z","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":"be4d7547740bb53bddda5081acb7e4d1049ae713a0b803b0c6e9ab40523b6473","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-07T09:22:45Z","title_canon_sha256":"5c02f7892d66ae956b460c45dd755312e2f1f254a62037d61d2c0eab1b3d0ede"},"schema_version":"1.0","source":{"id":"0909.1183","kind":"arxiv","version":1}},"canonical_sha256":"ca9ec3efeffc75ecda2586801ee36b43f5666b7b5e55540676274bd470b7751c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca9ec3efeffc75ecda2586801ee36b43f5666b7b5e55540676274bd470b7751c","first_computed_at":"2026-05-18T02:11:59.198039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:59.198039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YtO90BPOok6PkXi8lacX76L4YsOC9AC5xmuEkPlYsMXV6G2YYkt6Df9ztL6nfXwMwMJqYGHvWmnAs+7qXDLzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:59.198626Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81ab5a48b365cae67920aee5bd9291103be914b5a9c294756cb669abd9dada3f","sha256:6eef93cf8af0a0d9259547d287de1c90335c319252c421692fb1104ffd278e4f"],"state_sha256":"03106aed998119999442af99863a494177b4755046e0aac7c431f159e8974f1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9N+BPylULTV5txDjZFxd+3b2G0F7uu9tncyo/ooTEtkeGCdVR9j9juh9YDmTGwRoDOpd4uVLzljtQraQWNGvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:55:13.763846Z","bundle_sha256":"9a57065f8838d14646aa903be8dc78556b511e3a96a13513492b9b7f2fe0e9a1"}}