{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VRF7PQTPJA6CAJOWSHEMRZEPFC","short_pith_number":"pith:VRF7PQTP","canonical_record":{"source":{"id":"1107.0843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T10:45:17Z","cross_cats_sorted":[],"title_canon_sha256":"5634f1c6c5a0a0a1b996296d7a562b0790d280fc151450598005d3d66c921ff5","abstract_canon_sha256":"8ff05e9f3718681439e7fbb238f9da3172fa7b87aa8919ef8a75dbc40d36eab6"},"schema_version":"1.0"},"canonical_sha256":"ac4bf7c26f483c2025d691c8c8e48f288ae8098bf4327cde77e06fcd7984e141","source":{"kind":"arxiv","id":"1107.0843","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0843","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0843v1","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0843","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"VRF7PQTPJA6C","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VRF7PQTPJA6CAJOW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VRF7PQTP","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VRF7PQTPJA6CAJOWSHEMRZEPFC","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T10:45:17Z","cross_cats_sorted":[],"title_canon_sha256":"5634f1c6c5a0a0a1b996296d7a562b0790d280fc151450598005d3d66c921ff5","abstract_canon_sha256":"8ff05e9f3718681439e7fbb238f9da3172fa7b87aa8919ef8a75dbc40d36eab6"},"schema_version":"1.0"},"canonical_sha256":"ac4bf7c26f483c2025d691c8c8e48f288ae8098bf4327cde77e06fcd7984e141","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:57.817713Z","signature_b64":"1w7bGLkPK9mZ1xM7+7PpU6UhQaWTZuPq72+bXaEa24ir2HEKLEqvP5yuD3mvYncIu96c3TIF6JcVFg38y9igDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac4bf7c26f483c2025d691c8c8e48f288ae8098bf4327cde77e06fcd7984e141","last_reissued_at":"2026-05-18T00:56:57.817208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:57.817208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0843","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":"2026-05-18T00:56:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xzzi58GMqsHV6Y+yihOIgh6OA2KO6jKxYxd3HAyplM5Y13NH3rP3CGNIS4ogznRixdGprr9d9glFDTwKe/8NCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:12:20.065730Z"},"content_sha256":"845fdfbda65d650e5e996448ebee9abba1e241ef1fbadfbab6ac59d055ba9473","schema_version":"1.0","event_id":"sha256:845fdfbda65d650e5e996448ebee9abba1e241ef1fbadfbab6ac59d055ba9473"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VRF7PQTPJA6CAJOWSHEMRZEPFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the lack of dispersion for a class of magnetic Dirac flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andoni Garc\\'ia, Luca Fanelli, Naiara Arrizabalaga","submitted_at":"2011-07-05T10:45:17Z","abstract_excerpt":"We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, i. e. with homogeneity-degree more than -1, such that the magnetic field points to a fixed direction, which does not depend on $x\\in \\mathbb{R}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0843","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":"2026-05-18T00:56:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4D3nTMPXxoIVNRSfo3fRTYa268nKzFHPBUbm8OdgavK18MsmDe5d5bsm38GbFJY5U+SrVCWC/svgeG1wV+tFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:12:20.066375Z"},"content_sha256":"8e9f52cf7218cc4cc718687222bb8d39d73058f10c61389f300cede3aa94011a","schema_version":"1.0","event_id":"sha256:8e9f52cf7218cc4cc718687222bb8d39d73058f10c61389f300cede3aa94011a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC/bundle.json","state_url":"https://pith.science/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC/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":"2026-05-31T18:12:20Z","links":{"resolver":"https://pith.science/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC","bundle":"https://pith.science/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC/bundle.json","state":"https://pith.science/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRF7PQTPJA6CAJOWSHEMRZEPFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VRF7PQTPJA6CAJOWSHEMRZEPFC","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":"8ff05e9f3718681439e7fbb238f9da3172fa7b87aa8919ef8a75dbc40d36eab6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T10:45:17Z","title_canon_sha256":"5634f1c6c5a0a0a1b996296d7a562b0790d280fc151450598005d3d66c921ff5"},"schema_version":"1.0","source":{"id":"1107.0843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0843","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0843v1","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0843","created_at":"2026-05-18T00:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"VRF7PQTPJA6C","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VRF7PQTPJA6CAJOW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VRF7PQTP","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:8e9f52cf7218cc4cc718687222bb8d39d73058f10c61389f300cede3aa94011a","target":"graph","created_at":"2026-05-18T00:56:57Z","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":"We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, i. e. with homogeneity-degree more than -1, such that the magnetic field points to a fixed direction, which does not depend on $x\\in \\mathbb{R}^3$.","authors_text":"Andoni Garc\\'ia, Luca Fanelli, Naiara Arrizabalaga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T10:45:17Z","title":"On the lack of dispersion for a class of magnetic Dirac flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0843","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":"sha256:845fdfbda65d650e5e996448ebee9abba1e241ef1fbadfbab6ac59d055ba9473","target":"record","created_at":"2026-05-18T00:56:57Z","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":"8ff05e9f3718681439e7fbb238f9da3172fa7b87aa8919ef8a75dbc40d36eab6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-05T10:45:17Z","title_canon_sha256":"5634f1c6c5a0a0a1b996296d7a562b0790d280fc151450598005d3d66c921ff5"},"schema_version":"1.0","source":{"id":"1107.0843","kind":"arxiv","version":1}},"canonical_sha256":"ac4bf7c26f483c2025d691c8c8e48f288ae8098bf4327cde77e06fcd7984e141","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4bf7c26f483c2025d691c8c8e48f288ae8098bf4327cde77e06fcd7984e141","first_computed_at":"2026-05-18T00:56:57.817208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:57.817208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1w7bGLkPK9mZ1xM7+7PpU6UhQaWTZuPq72+bXaEa24ir2HEKLEqvP5yuD3mvYncIu96c3TIF6JcVFg38y9igDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:57.817713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:845fdfbda65d650e5e996448ebee9abba1e241ef1fbadfbab6ac59d055ba9473","sha256:8e9f52cf7218cc4cc718687222bb8d39d73058f10c61389f300cede3aa94011a"],"state_sha256":"8c199543ac4021291c9501000361a228be64d5d96239a4b6ac95479ca3ce323a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UD6S+Poo2m6wA1i0GMQ/nGU3wyvQ1thr4kcmhZJBOJBBX6m7jFCFp7rzt3L5pQbABvPH5KVWTyNsxr6vFs78Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:12:20.071719Z","bundle_sha256":"86a9b9e2c4dabf24c4a08d34c5b9dec1a810804dd02f0da106fa163fe5835c96"}}