{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4AX5B2EWEBVVRFLNBNK6SWBJYX","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":"413dac531d6f99700f2ef820e3f0d1d60c57fbefc7abf352216b930b39e984e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-31T12:52:10Z","title_canon_sha256":"4179005c64ec6ead072a133b65ab7a54fd1e439f35720c541823ee8c3bc5bc8d"},"schema_version":"1.0","source":{"id":"1812.11777","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11777","created_at":"2026-05-17T23:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11777v1","created_at":"2026-05-17T23:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11777","created_at":"2026-05-17T23:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"4AX5B2EWEBVV","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AX5B2EWEBVVRFLN","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AX5B2EW","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:cd4f9392163783b119673e53e8cccba1ca0b36c20a7ce3912e48f540745dd9cd","target":"graph","created_at":"2026-05-17T23:39:55Z","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 consider the scattering problem for the nonlinear Schr\\\"{o}dinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator $A(s)$ appearing in commutator relations. The equivalence between the operators $\\left(-\\Delta_{V}\\right)^{\\frac{s}{2}}$ and $\\left(-\\Delta \\right)^{\\frac{s}{2}}$ in $L^{2}$ norm sense for $0\\leq s <1$ is investigated by using free resolvent estimates and Gaussian estimates for the heat kernel of the Schr\\\"{o}dinger operator $-\\Delta_{V}$. Our main result guarantees the global existence of solutio","authors_text":"Chunhua Li, Vladimir Georgiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-31T12:52:10Z","title":"On the scattering problem for the nonlinear Schr\\\"{o}dinger equation with a potential in 2D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11777","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":"sha256:9329c17c05b5b4163797cc8877836eac5bbe42aa269e796b5759fdfd8da65613","target":"record","created_at":"2026-05-17T23:39:55Z","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":"413dac531d6f99700f2ef820e3f0d1d60c57fbefc7abf352216b930b39e984e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-31T12:52:10Z","title_canon_sha256":"4179005c64ec6ead072a133b65ab7a54fd1e439f35720c541823ee8c3bc5bc8d"},"schema_version":"1.0","source":{"id":"1812.11777","kind":"arxiv","version":1}},"canonical_sha256":"e02fd0e896206b58956d0b55e95829c5f57483cc382b548e1b9247085d1ef272","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e02fd0e896206b58956d0b55e95829c5f57483cc382b548e1b9247085d1ef272","first_computed_at":"2026-05-17T23:39:55.423140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:55.423140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gy5OluSjhJmNnxjOYLzimwzz0bWuY4JzxZRAdScWT3bVQzuWTXFFslTMXD7laf5enyCd1tr49qUyHN33UXMoCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:55.423677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11777","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9329c17c05b5b4163797cc8877836eac5bbe42aa269e796b5759fdfd8da65613","sha256:cd4f9392163783b119673e53e8cccba1ca0b36c20a7ce3912e48f540745dd9cd"],"state_sha256":"3984f2f4e506fe232f09d7d84e816a7a42e08b7eba66ffd66942900607d87adb"}