{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:EFMPUWPGAQRINT7QVTEMQN46OW","short_pith_number":"pith:EFMPUWPG","canonical_record":{"source":{"id":"math/0509416","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-09-19T08:32:03Z","cross_cats_sorted":[],"title_canon_sha256":"a92f67f5bd3783cf0d845cebeb6f6eb6dfbaec732dd4f8e1cafc323604f8a132","abstract_canon_sha256":"59026d1e81675889fe199c7167b41897b9cce47525a5914b35e169ca06325b02"},"schema_version":"1.0"},"canonical_sha256":"2158fa59e6042286cff0acc8c8379e759a7d6bb5e97f5dbd479323b331e9d117","source":{"kind":"arxiv","id":"math/0509416","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509416","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509416v2","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509416","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"EFMPUWPGAQRI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EFMPUWPGAQRINT7Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EFMPUWPG","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:EFMPUWPGAQRINT7QVTEMQN46OW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0509416","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-09-19T08:32:03Z","cross_cats_sorted":[],"title_canon_sha256":"a92f67f5bd3783cf0d845cebeb6f6eb6dfbaec732dd4f8e1cafc323604f8a132","abstract_canon_sha256":"59026d1e81675889fe199c7167b41897b9cce47525a5914b35e169ca06325b02"},"schema_version":"1.0"},"canonical_sha256":"2158fa59e6042286cff0acc8c8379e759a7d6bb5e97f5dbd479323b331e9d117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.031167Z","signature_b64":"4KSENkQcHvmEOt56HN3tCvsONrf45pve1YIOai1eSiwVyIuoG8+86ZqXm9f6mypk7/m2DKhumx84hGuGOSYBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2158fa59e6042286cff0acc8c8379e759a7d6bb5e97f5dbd479323b331e9d117","last_reissued_at":"2026-05-18T04:41:54.030483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.030483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0509416","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aS4iJ4xmejjl1uqh57UTYdeULMGo12xHqpI8HZf8Ujq0AMcLjYJCuc3wUlnpw124OaoJ+FgN6ExryzAmq8V9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:17:29.539413Z"},"content_sha256":"d89cef4e54791be128d0c47d81bdc71de221dd2000d9302faf999640481e2996","schema_version":"1.0","event_id":"sha256:d89cef4e54791be128d0c47d81bdc71de221dd2000d9302faf999640481e2996"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:EFMPUWPGAQRINT7QVTEMQN46OW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothing - Strichartz Estimates for the Schrodinger Equation with small Magnetic Potential","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Atanas Stefanov, Mirko Tarulli, Vladimir Georgiev","submitted_at":"2005-09-19T08:32:03Z","abstract_excerpt":"The work treats smoothing and dispersive properties of solutions to the Schrodinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509416","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CUfdG1ujBAw1G0/kb/w/IqhvSY95FnsdTKIkY/fROk8hnH4PuSjtcVvCkBEJL9QSpG72Ki6oP1I6ixgII3jHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:17:29.539761Z"},"content_sha256":"fe535d7c38b9853c6168acadc06dcc0f9e9f7d2a5f8979eb43332f59842e4e0d","schema_version":"1.0","event_id":"sha256:fe535d7c38b9853c6168acadc06dcc0f9e9f7d2a5f8979eb43332f59842e4e0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFMPUWPGAQRINT7QVTEMQN46OW/bundle.json","state_url":"https://pith.science/pith/EFMPUWPGAQRINT7QVTEMQN46OW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFMPUWPGAQRINT7QVTEMQN46OW/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":"2026-06-03T21:17:29Z","links":{"resolver":"https://pith.science/pith/EFMPUWPGAQRINT7QVTEMQN46OW","bundle":"https://pith.science/pith/EFMPUWPGAQRINT7QVTEMQN46OW/bundle.json","state":"https://pith.science/pith/EFMPUWPGAQRINT7QVTEMQN46OW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFMPUWPGAQRINT7QVTEMQN46OW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:EFMPUWPGAQRINT7QVTEMQN46OW","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":"59026d1e81675889fe199c7167b41897b9cce47525a5914b35e169ca06325b02","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2005-09-19T08:32:03Z","title_canon_sha256":"a92f67f5bd3783cf0d845cebeb6f6eb6dfbaec732dd4f8e1cafc323604f8a132"},"schema_version":"1.0","source":{"id":"math/0509416","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509416","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509416v2","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509416","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"EFMPUWPGAQRI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EFMPUWPGAQRINT7Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EFMPUWPG","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:fe535d7c38b9853c6168acadc06dcc0f9e9f7d2a5f8979eb43332f59842e4e0d","target":"graph","created_at":"2026-05-18T04:41:54Z","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":"The work treats smoothing and dispersive properties of solutions to the Schrodinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too.","authors_text":"Atanas Stefanov, Mirko Tarulli, Vladimir Georgiev","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2005-09-19T08:32:03Z","title":"Smoothing - Strichartz Estimates for the Schrodinger Equation with small Magnetic Potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509416","kind":"arxiv","version":2},"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:d89cef4e54791be128d0c47d81bdc71de221dd2000d9302faf999640481e2996","target":"record","created_at":"2026-05-18T04:41:54Z","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":"59026d1e81675889fe199c7167b41897b9cce47525a5914b35e169ca06325b02","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2005-09-19T08:32:03Z","title_canon_sha256":"a92f67f5bd3783cf0d845cebeb6f6eb6dfbaec732dd4f8e1cafc323604f8a132"},"schema_version":"1.0","source":{"id":"math/0509416","kind":"arxiv","version":2}},"canonical_sha256":"2158fa59e6042286cff0acc8c8379e759a7d6bb5e97f5dbd479323b331e9d117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2158fa59e6042286cff0acc8c8379e759a7d6bb5e97f5dbd479323b331e9d117","first_computed_at":"2026-05-18T04:41:54.030483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:54.030483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4KSENkQcHvmEOt56HN3tCvsONrf45pve1YIOai1eSiwVyIuoG8+86ZqXm9f6mypk7/m2DKhumx84hGuGOSYBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:54.031167Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509416","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d89cef4e54791be128d0c47d81bdc71de221dd2000d9302faf999640481e2996","sha256:fe535d7c38b9853c6168acadc06dcc0f9e9f7d2a5f8979eb43332f59842e4e0d"],"state_sha256":"b937a23baff789b6e86ce79d911e158a5de86787699ea71659ac4e77d88a39d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4J5ljdRCRIQLhGoFkh2IojApWKMO2+9kio7UApjDBm1FVQwFu58cZPxq03jGlrUGmK4jdZEOBNq09nkIkqnwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:17:29.541816Z","bundle_sha256":"9c2f4b1163d21b34e3d0eb2dae05f0b44241b4d490bc054889d71f2d540333dd"}}