{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:M7B4EM4HH2OWGVWHYJXFUU5K73","short_pith_number":"pith:M7B4EM4H","schema_version":"1.0","canonical_sha256":"67c3c233873e9d6356c7c26e5a53aafefd6d9c9c005a22b115f07081398d6deb","source":{"kind":"arxiv","id":"1502.00937","version":1},"attestation_state":"computed","paper":{"title":"Scattering in the energy space for the NLS with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Biagio Cassano, Piero D'Ancona","submitted_at":"2015-02-03T17:33:26Z","abstract_excerpt":"We consider the NLS with variable coefficients in dimension $n\\ge3$ \\begin{equation*} i \\partial_t u - Lu +f(u)=0, \\qquad Lv=\\nabla^{b}\\cdot(a(x)\\nabla^{b}v)-c(x)v, \\qquad \\nabla^{b}=\\nabla+ib(x), \\end{equation*} on $\\mathbb{R}^{n}$ or more generally on an exterior domain with Dirichlet boundary conditions, for a gauge invariant, defocusing nonlinearity of power type $f(u)\\simeq|u|^{\\gamma-1}u$. We assume that $L$ is a small, long range perturbation of $\\Delta$, plus a potential with a large positive part. The first main result of the paper is a bilinear smoothing (interaction Morawetz) estima"},"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":"1502.00937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-03T17:33:26Z","cross_cats_sorted":[],"title_canon_sha256":"b3d27b8698e405931cb4c4d2ea5a858caaed9cf8e74ce92d4c42da88f12a05be","abstract_canon_sha256":"cc557d50eeb6756fdf263ed77f629a8848cb443fb9f809e75a1d08203194d208"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:59.206311Z","signature_b64":"pp/+axeOrCcUrHSGfMu7YhYrFlkeFpV+g8YmHXShsF+7Hx3ERxQS00CCjx/KyojXBImQFV80O9KHrdY0IJODAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67c3c233873e9d6356c7c26e5a53aafefd6d9c9c005a22b115f07081398d6deb","last_reissued_at":"2026-05-18T02:27:59.205771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:59.205771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering in the energy space for the NLS with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Biagio Cassano, Piero D'Ancona","submitted_at":"2015-02-03T17:33:26Z","abstract_excerpt":"We consider the NLS with variable coefficients in dimension $n\\ge3$ \\begin{equation*} i \\partial_t u - Lu +f(u)=0, \\qquad Lv=\\nabla^{b}\\cdot(a(x)\\nabla^{b}v)-c(x)v, \\qquad \\nabla^{b}=\\nabla+ib(x), \\end{equation*} on $\\mathbb{R}^{n}$ or more generally on an exterior domain with Dirichlet boundary conditions, for a gauge invariant, defocusing nonlinearity of power type $f(u)\\simeq|u|^{\\gamma-1}u$. We assume that $L$ is a small, long range perturbation of $\\Delta$, plus a potential with a large positive part. The first main result of the paper is a bilinear smoothing (interaction Morawetz) estima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00937","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":"1502.00937","created_at":"2026-05-18T02:27:59.205856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.00937v1","created_at":"2026-05-18T02:27:59.205856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00937","created_at":"2026-05-18T02:27:59.205856+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7B4EM4HH2OW","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7B4EM4HH2OWGVWH","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7B4EM4H","created_at":"2026-05-18T12:29:32.376354+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/M7B4EM4HH2OWGVWHYJXFUU5K73","json":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73.json","graph_json":"https://pith.science/api/pith-number/M7B4EM4HH2OWGVWHYJXFUU5K73/graph.json","events_json":"https://pith.science/api/pith-number/M7B4EM4HH2OWGVWHYJXFUU5K73/events.json","paper":"https://pith.science/paper/M7B4EM4H"},"agent_actions":{"view_html":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73","download_json":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73.json","view_paper":"https://pith.science/paper/M7B4EM4H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.00937&json=true","fetch_graph":"https://pith.science/api/pith-number/M7B4EM4HH2OWGVWHYJXFUU5K73/graph.json","fetch_events":"https://pith.science/api/pith-number/M7B4EM4HH2OWGVWHYJXFUU5K73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/action/storage_attestation","attest_author":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/action/author_attestation","sign_citation":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/action/citation_signature","submit_replication":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/action/replication_record"}},"created_at":"2026-05-18T02:27:59.205856+00:00","updated_at":"2026-05-18T02:27:59.205856+00:00"}