{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RHI5IH4SB3S4ORVIGNNS7LOK25","short_pith_number":"pith:RHI5IH4S","schema_version":"1.0","canonical_sha256":"89d1d41f920ee5c746a8335b2fadcad77234317089b90125e96d6eaa079c3e88","source":{"kind":"arxiv","id":"1311.2088","version":1},"attestation_state":"computed","paper":{"title":"Decay and Scattering for the Chern-Simons-Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabio Pusateri, Sung-Jin Oh","submitted_at":"2013-11-08T21:35:46Z","abstract_excerpt":"We consider the Chern-Simons-Schr\\\"odinger model in 1+2 dimensions, and prove scattering for small solutions of the Cauchy problem in the Coulomb gauge. This model is a gauge covariant Schr\\\"odinger equation, with a potential decaying like $r^{-1}$ at infinity. To overcome the difficulties due to this long range decay we start by performing $L^2$-based estimates covariantly. This gives favorable commutation identities so that only curvature terms, which decay faster than $r^{-1}$, appear in our weighted energy estimates. We then select the Coulomb gauge to reveal a genuinely cubic null structu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.2088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-08T21:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"fe5e9f4a4b62c1304a1cab28b98f2f82fa37d6e92b5a641948a9605dfb7c1958","abstract_canon_sha256":"588a62c9aa450294f95fb890728f1e6809ed4639a3788982435ed3a62ff40f57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:33.560911Z","signature_b64":"DHnRj6RCFI1rQ7/7bzmj4j26q02EuvDMUNmsJ4PyBBlKTMZoopiObZLTxPTqXsX2t71mgRkLsGb1am0XFv11Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d1d41f920ee5c746a8335b2fadcad77234317089b90125e96d6eaa079c3e88","last_reissued_at":"2026-05-18T03:07:33.560400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:33.560400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decay and Scattering for the Chern-Simons-Schr\\\"odinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabio Pusateri, Sung-Jin Oh","submitted_at":"2013-11-08T21:35:46Z","abstract_excerpt":"We consider the Chern-Simons-Schr\\\"odinger model in 1+2 dimensions, and prove scattering for small solutions of the Cauchy problem in the Coulomb gauge. This model is a gauge covariant Schr\\\"odinger equation, with a potential decaying like $r^{-1}$ at infinity. To overcome the difficulties due to this long range decay we start by performing $L^2$-based estimates covariantly. This gives favorable commutation identities so that only curvature terms, which decay faster than $r^{-1}$, appear in our weighted energy estimates. We then select the Coulomb gauge to reveal a genuinely cubic null structu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2088","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.2088","created_at":"2026-05-18T03:07:33.560475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.2088v1","created_at":"2026-05-18T03:07:33.560475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2088","created_at":"2026-05-18T03:07:33.560475+00:00"},{"alias_kind":"pith_short_12","alias_value":"RHI5IH4SB3S4","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"RHI5IH4SB3S4ORVI","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"RHI5IH4S","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25","json":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25.json","graph_json":"https://pith.science/api/pith-number/RHI5IH4SB3S4ORVIGNNS7LOK25/graph.json","events_json":"https://pith.science/api/pith-number/RHI5IH4SB3S4ORVIGNNS7LOK25/events.json","paper":"https://pith.science/paper/RHI5IH4S"},"agent_actions":{"view_html":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25","download_json":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25.json","view_paper":"https://pith.science/paper/RHI5IH4S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.2088&json=true","fetch_graph":"https://pith.science/api/pith-number/RHI5IH4SB3S4ORVIGNNS7LOK25/graph.json","fetch_events":"https://pith.science/api/pith-number/RHI5IH4SB3S4ORVIGNNS7LOK25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25/action/storage_attestation","attest_author":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25/action/author_attestation","sign_citation":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25/action/citation_signature","submit_replication":"https://pith.science/pith/RHI5IH4SB3S4ORVIGNNS7LOK25/action/replication_record"}},"created_at":"2026-05-18T03:07:33.560475+00:00","updated_at":"2026-05-18T03:07:33.560475+00:00"}