{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EB6XLKBFHQHXCO2NSDNK2N37P2","short_pith_number":"pith:EB6XLKBF","canonical_record":{"source":{"id":"1709.03847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T13:57:08Z","cross_cats_sorted":[],"title_canon_sha256":"09d8d196f631e359529c2f624bb0ce96806217f52c087f3ae9efee741838793f","abstract_canon_sha256":"8a25f7f8ed594c5df3dbd5c0050f131391bd2c68efe746317fbe8c9b956111bb"},"schema_version":"1.0"},"canonical_sha256":"207d75a8253c0f713b4d90daad377f7e92e446dfb81cdeca141ed05c8ca0faac","source":{"kind":"arxiv","id":"1709.03847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03847","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03847v1","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03847","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"EB6XLKBFHQHX","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EB6XLKBFHQHXCO2N","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EB6XLKBF","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EB6XLKBFHQHXCO2NSDNK2N37P2","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T13:57:08Z","cross_cats_sorted":[],"title_canon_sha256":"09d8d196f631e359529c2f624bb0ce96806217f52c087f3ae9efee741838793f","abstract_canon_sha256":"8a25f7f8ed594c5df3dbd5c0050f131391bd2c68efe746317fbe8c9b956111bb"},"schema_version":"1.0"},"canonical_sha256":"207d75a8253c0f713b4d90daad377f7e92e446dfb81cdeca141ed05c8ca0faac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:50.591278Z","signature_b64":"SAB+FmChgXI4Bdb24NX6H05G9h7DRyFYWe/hykdkkuMcRhju7nGZaBrEbO/xjuO1Tv/0k+MR5qaidGJS3i6KBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"207d75a8253c0f713b4d90daad377f7e92e446dfb81cdeca141ed05c8ca0faac","last_reissued_at":"2026-05-18T00:11:50.590634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:50.590634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03847","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":"2026-05-18T00:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vH3vycOTNTr5jiQuz0UePbZRSw8ETfdxyWj+8JwqEjHjtVAIPCqDh3KP3wuvbcePxQSMByLqlnfu2A2MGQOoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:45:23.948655Z"},"content_sha256":"80f4f359fbf908e498aec2408eed04ddc880e2f7ccff6941532dc21bf8855274","schema_version":"1.0","event_id":"sha256:80f4f359fbf908e498aec2408eed04ddc880e2f7ccff6941532dc21bf8855274"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EB6XLKBFHQHXCO2NSDNK2N37P2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scattering theory for the Schr\\\"odinger-Debye System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira, Sim\\~ao Correia","submitted_at":"2017-09-12T13:57:08Z","abstract_excerpt":"We study the Schr\\\"odinger-Debye system over $\\mathbb{R}^d$ iu_t+\\frac 12\\Delta u=uv,\\quad \\mu v_t+v=\\lambda |u|^2 and establish the global existence and scattering of small solutions for initial data in several function spaces in dimensions $d=2,3,4$. Moreover, in dimension $d=1$, we prove a Hayashi-Naumkin modified scattering result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03847","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":"2026-05-18T00:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3aErTTUy3tjw5laS1WMagVmZgS1qR+dfC9E27+J5Z7P+qu6owSQpWMMZkdE5KgFJDrWLKpiIsim8DKMKg7N6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:45:23.948996Z"},"content_sha256":"de99ee65218038893debbe39117fcb974ae8241cf3e0f12e658e0ab70be39f19","schema_version":"1.0","event_id":"sha256:de99ee65218038893debbe39117fcb974ae8241cf3e0f12e658e0ab70be39f19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EB6XLKBFHQHXCO2NSDNK2N37P2/bundle.json","state_url":"https://pith.science/pith/EB6XLKBFHQHXCO2NSDNK2N37P2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EB6XLKBFHQHXCO2NSDNK2N37P2/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":"2026-06-24T18:45:23Z","links":{"resolver":"https://pith.science/pith/EB6XLKBFHQHXCO2NSDNK2N37P2","bundle":"https://pith.science/pith/EB6XLKBFHQHXCO2NSDNK2N37P2/bundle.json","state":"https://pith.science/pith/EB6XLKBFHQHXCO2NSDNK2N37P2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EB6XLKBFHQHXCO2NSDNK2N37P2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EB6XLKBFHQHXCO2NSDNK2N37P2","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":"8a25f7f8ed594c5df3dbd5c0050f131391bd2c68efe746317fbe8c9b956111bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T13:57:08Z","title_canon_sha256":"09d8d196f631e359529c2f624bb0ce96806217f52c087f3ae9efee741838793f"},"schema_version":"1.0","source":{"id":"1709.03847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03847","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03847v1","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03847","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"EB6XLKBFHQHX","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EB6XLKBFHQHXCO2N","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EB6XLKBF","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:de99ee65218038893debbe39117fcb974ae8241cf3e0f12e658e0ab70be39f19","target":"graph","created_at":"2026-05-18T00:11:50Z","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 study the Schr\\\"odinger-Debye system over $\\mathbb{R}^d$ iu_t+\\frac 12\\Delta u=uv,\\quad \\mu v_t+v=\\lambda |u|^2 and establish the global existence and scattering of small solutions for initial data in several function spaces in dimensions $d=2,3,4$. Moreover, in dimension $d=1$, we prove a Hayashi-Naumkin modified scattering result.","authors_text":"Filipe Oliveira, Sim\\~ao Correia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T13:57:08Z","title":"Scattering theory for the Schr\\\"odinger-Debye System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03847","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":"sha256:80f4f359fbf908e498aec2408eed04ddc880e2f7ccff6941532dc21bf8855274","target":"record","created_at":"2026-05-18T00:11:50Z","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":"8a25f7f8ed594c5df3dbd5c0050f131391bd2c68efe746317fbe8c9b956111bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T13:57:08Z","title_canon_sha256":"09d8d196f631e359529c2f624bb0ce96806217f52c087f3ae9efee741838793f"},"schema_version":"1.0","source":{"id":"1709.03847","kind":"arxiv","version":1}},"canonical_sha256":"207d75a8253c0f713b4d90daad377f7e92e446dfb81cdeca141ed05c8ca0faac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"207d75a8253c0f713b4d90daad377f7e92e446dfb81cdeca141ed05c8ca0faac","first_computed_at":"2026-05-18T00:11:50.590634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:50.590634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SAB+FmChgXI4Bdb24NX6H05G9h7DRyFYWe/hykdkkuMcRhju7nGZaBrEbO/xjuO1Tv/0k+MR5qaidGJS3i6KBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:50.591278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80f4f359fbf908e498aec2408eed04ddc880e2f7ccff6941532dc21bf8855274","sha256:de99ee65218038893debbe39117fcb974ae8241cf3e0f12e658e0ab70be39f19"],"state_sha256":"fce8bfff88c2a5c6e36ad9111cd7f8acab7f79f8067d70d8dc6fc06c2303e1c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fb2QGALiqt4jAgme7XDSUve1tPGmRx1mFF3WA9bCz52WAWeFqsGxoqBE76Fmi+NBSpOsL9ZBxw2BvVBx8JU7Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:45:23.950905Z","bundle_sha256":"7ea6a7309243cc7864cccd913b80997f7eada5e85c0e15d5ed3fa6d21ee9794c"}}