{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:E4UON6MHCEH5LO7FAEUBSL62TN","short_pith_number":"pith:E4UON6MH","canonical_record":{"source":{"id":"1306.5301","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-22T09:04:22Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"4f643f9fd9dc865270d4512b06d5d3feb04a5b2117fb9ee23e856678aea9917a","abstract_canon_sha256":"7531e82ce44e5cef7641774a1144d3e0c33c9f78efa7a0f897004cfce7a8afe8"},"schema_version":"1.0"},"canonical_sha256":"2728e6f987110fd5bbe50128192fda9b470cc51b38a81d9fed45045645865c0d","source":{"kind":"arxiv","id":"1306.5301","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5301","created_at":"2026-05-18T01:49:13Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5301v3","created_at":"2026-05-18T01:49:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5301","created_at":"2026-05-18T01:49:13Z"},{"alias_kind":"pith_short_12","alias_value":"E4UON6MHCEH5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E4UON6MHCEH5LO7F","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E4UON6MH","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:E4UON6MHCEH5LO7FAEUBSL62TN","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5301","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-22T09:04:22Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"4f643f9fd9dc865270d4512b06d5d3feb04a5b2117fb9ee23e856678aea9917a","abstract_canon_sha256":"7531e82ce44e5cef7641774a1144d3e0c33c9f78efa7a0f897004cfce7a8afe8"},"schema_version":"1.0"},"canonical_sha256":"2728e6f987110fd5bbe50128192fda9b470cc51b38a81d9fed45045645865c0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:13.710426Z","signature_b64":"CIi/MluxKACWII9yO75SDUdOUw+EYMyDFZTqjj1s+9GIOmxRUh411o1tJ+lyVCdAWwVe65vzEXq+SphAFjtBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2728e6f987110fd5bbe50128192fda9b470cc51b38a81d9fed45045645865c0d","last_reissued_at":"2026-05-18T01:49:13.709805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:13.709805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5301","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:49:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJGOc+eZOkocrq0d0RK/8JuutJJns6SojSs/RHVCso0SbRT/neWh08AdbkK2vSB8S9fpIlx/Se1sS5NZJ1UuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:11:03.816666Z"},"content_sha256":"5966d4b943fcb3f4aa9a27a45c2deef6ed968f6091617435fd6b4b0be292a6a6","schema_version":"1.0","event_id":"sha256:5966d4b943fcb3f4aa9a27a45c2deef6ed968f6091617435fd6b4b0be292a6a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:E4UON6MHCEH5LO7FAEUBSL62TN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Metaplectic Operators and the Schr\\\"odinger Equation with a Potential in the Sj\\\"ostrand Class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.AP","authors_text":"Elena Cordero, Fabio Nicola, Karlheinz Gr\\\"ochenig, Luigi Rodino","submitted_at":"2013-06-22T09:04:22Z","abstract_excerpt":"It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra generated by metaplectic operators and by pseudodifferential opertators in a Sj\\\"ostrand class enjoys the same decay properties. We study the behavior of these generalized metaplectic operators and represent them by Fourier integral operators. Our main result shows that the one-parameter group generated by a Hamiltonian operator with a potential in the Sj\\\"ostrand class consists of generalized metaplectic operators. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5301","kind":"arxiv","version":3},"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":"2026-05-18T01:49:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHqhAu3NIhN2FEFmvbaBxVM0NNvlCxS8UMnOHkauJcfjGc0XCBFiPVGIHIheKDBfsTLXzvLOG+1OlO3l9nZ/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:11:03.817370Z"},"content_sha256":"6dfb4290c2558eee3b2cf4a78f0a9eb8834108abeb65a752aafb5e6d1c0b2d17","schema_version":"1.0","event_id":"sha256:6dfb4290c2558eee3b2cf4a78f0a9eb8834108abeb65a752aafb5e6d1c0b2d17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4UON6MHCEH5LO7FAEUBSL62TN/bundle.json","state_url":"https://pith.science/pith/E4UON6MHCEH5LO7FAEUBSL62TN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4UON6MHCEH5LO7FAEUBSL62TN/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":"2026-05-31T06:11:03Z","links":{"resolver":"https://pith.science/pith/E4UON6MHCEH5LO7FAEUBSL62TN","bundle":"https://pith.science/pith/E4UON6MHCEH5LO7FAEUBSL62TN/bundle.json","state":"https://pith.science/pith/E4UON6MHCEH5LO7FAEUBSL62TN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4UON6MHCEH5LO7FAEUBSL62TN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E4UON6MHCEH5LO7FAEUBSL62TN","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":"7531e82ce44e5cef7641774a1144d3e0c33c9f78efa7a0f897004cfce7a8afe8","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-22T09:04:22Z","title_canon_sha256":"4f643f9fd9dc865270d4512b06d5d3feb04a5b2117fb9ee23e856678aea9917a"},"schema_version":"1.0","source":{"id":"1306.5301","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5301","created_at":"2026-05-18T01:49:13Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5301v3","created_at":"2026-05-18T01:49:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5301","created_at":"2026-05-18T01:49:13Z"},{"alias_kind":"pith_short_12","alias_value":"E4UON6MHCEH5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E4UON6MHCEH5LO7F","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E4UON6MH","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:6dfb4290c2558eee3b2cf4a78f0a9eb8834108abeb65a752aafb5e6d1c0b2d17","target":"graph","created_at":"2026-05-18T01:49:13Z","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":"It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra generated by metaplectic operators and by pseudodifferential opertators in a Sj\\\"ostrand class enjoys the same decay properties. We study the behavior of these generalized metaplectic operators and represent them by Fourier integral operators. Our main result shows that the one-parameter group generated by a Hamiltonian operator with a potential in the Sj\\\"ostrand class consists of generalized metaplectic operators. A","authors_text":"Elena Cordero, Fabio Nicola, Karlheinz Gr\\\"ochenig, Luigi Rodino","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-22T09:04:22Z","title":"Generalized Metaplectic Operators and the Schr\\\"odinger Equation with a Potential in the Sj\\\"ostrand Class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5301","kind":"arxiv","version":3},"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":"sha256:5966d4b943fcb3f4aa9a27a45c2deef6ed968f6091617435fd6b4b0be292a6a6","target":"record","created_at":"2026-05-18T01:49:13Z","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":"7531e82ce44e5cef7641774a1144d3e0c33c9f78efa7a0f897004cfce7a8afe8","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-22T09:04:22Z","title_canon_sha256":"4f643f9fd9dc865270d4512b06d5d3feb04a5b2117fb9ee23e856678aea9917a"},"schema_version":"1.0","source":{"id":"1306.5301","kind":"arxiv","version":3}},"canonical_sha256":"2728e6f987110fd5bbe50128192fda9b470cc51b38a81d9fed45045645865c0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2728e6f987110fd5bbe50128192fda9b470cc51b38a81d9fed45045645865c0d","first_computed_at":"2026-05-18T01:49:13.709805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:13.709805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CIi/MluxKACWII9yO75SDUdOUw+EYMyDFZTqjj1s+9GIOmxRUh411o1tJ+lyVCdAWwVe65vzEXq+SphAFjtBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:13.710426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5301","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5966d4b943fcb3f4aa9a27a45c2deef6ed968f6091617435fd6b4b0be292a6a6","sha256:6dfb4290c2558eee3b2cf4a78f0a9eb8834108abeb65a752aafb5e6d1c0b2d17"],"state_sha256":"6cb226dad74a7853461ef300926205b0d5507d0ac8b25cf6a5a30c3d21d058fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkMtpYRLnT+PMR0yiEdJfX0k869FU8gZz2uE5eoHrqKEzbdWPFos4pNbvF/YceZA07ICgyIWT8e46Ozq/Qx+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:11:03.820105Z","bundle_sha256":"0e149fd8222df75d98eb6f5a8564d1705b79b20476b0a72d2768d0291d359062"}}