{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M7B4EM4HH2OWGVWHYJXFUU5K73","short_pith_number":"pith:M7B4EM4H","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"},"canonical_sha256":"67c3c233873e9d6356c7c26e5a53aafefd6d9c9c005a22b115f07081398d6deb","source":{"kind":"arxiv","id":"1502.00937","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00937","created_at":"2026-05-18T02:27:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00937v1","created_at":"2026-05-18T02:27:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00937","created_at":"2026-05-18T02:27:59Z"},{"alias_kind":"pith_short_12","alias_value":"M7B4EM4HH2OW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M7B4EM4HH2OWGVWH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M7B4EM4H","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M7B4EM4HH2OWGVWHYJXFUU5K73","target":"record","payload":{"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"},"canonical_sha256":"67c3c233873e9d6356c7c26e5a53aafefd6d9c9c005a22b115f07081398d6deb","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"},"source_kind":"arxiv","source_id":"1502.00937","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":"2026-05-18T02:27:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1IrA6geyQKXf6NfUoA/5ErGErWi6IAzg8xQxtiXjTJuJEqhQpipRsHLCCop5QioOwBjaMbEihlpwOiDGIbNoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:18:50.791663Z"},"content_sha256":"8f9e8d38ce0e81aae439dcb7e90ae3c62024451859cd503dc1ca18d00f99391b","schema_version":"1.0","event_id":"sha256:8f9e8d38ce0e81aae439dcb7e90ae3c62024451859cd503dc1ca18d00f99391b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M7B4EM4HH2OWGVWHYJXFUU5K73","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMMi/PzW1paGm6D5wKtmZDhP7FnNQl9ql9nHfvqHxKO+PgrECE6CibrjQKCFL/5WglrG7BtMTsUCYgg437nZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:18:50.792044Z"},"content_sha256":"76250ae83e0d71c05e95fa065bd9f073961cb3a1f56d27b7b706409cf18ef23b","schema_version":"1.0","event_id":"sha256:76250ae83e0d71c05e95fa065bd9f073961cb3a1f56d27b7b706409cf18ef23b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/bundle.json","state_url":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/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":"2026-05-27T11:18:50Z","links":{"resolver":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73","bundle":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/bundle.json","state":"https://pith.science/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7B4EM4HH2OWGVWHYJXFUU5K73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M7B4EM4HH2OWGVWHYJXFUU5K73","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":"cc557d50eeb6756fdf263ed77f629a8848cb443fb9f809e75a1d08203194d208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-03T17:33:26Z","title_canon_sha256":"b3d27b8698e405931cb4c4d2ea5a858caaed9cf8e74ce92d4c42da88f12a05be"},"schema_version":"1.0","source":{"id":"1502.00937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00937","created_at":"2026-05-18T02:27:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00937v1","created_at":"2026-05-18T02:27:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00937","created_at":"2026-05-18T02:27:59Z"},{"alias_kind":"pith_short_12","alias_value":"M7B4EM4HH2OW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M7B4EM4HH2OWGVWH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M7B4EM4H","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:76250ae83e0d71c05e95fa065bd9f073961cb3a1f56d27b7b706409cf18ef23b","target":"graph","created_at":"2026-05-18T02:27:59Z","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 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","authors_text":"Biagio Cassano, Piero D'Ancona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-03T17:33:26Z","title":"Scattering in the energy space for the NLS with variable coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00937","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":"sha256:8f9e8d38ce0e81aae439dcb7e90ae3c62024451859cd503dc1ca18d00f99391b","target":"record","created_at":"2026-05-18T02:27:59Z","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":"cc557d50eeb6756fdf263ed77f629a8848cb443fb9f809e75a1d08203194d208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-03T17:33:26Z","title_canon_sha256":"b3d27b8698e405931cb4c4d2ea5a858caaed9cf8e74ce92d4c42da88f12a05be"},"schema_version":"1.0","source":{"id":"1502.00937","kind":"arxiv","version":1}},"canonical_sha256":"67c3c233873e9d6356c7c26e5a53aafefd6d9c9c005a22b115f07081398d6deb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67c3c233873e9d6356c7c26e5a53aafefd6d9c9c005a22b115f07081398d6deb","first_computed_at":"2026-05-18T02:27:59.205771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:59.205771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pp/+axeOrCcUrHSGfMu7YhYrFlkeFpV+g8YmHXShsF+7Hx3ERxQS00CCjx/KyojXBImQFV80O9KHrdY0IJODAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:59.206311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f9e8d38ce0e81aae439dcb7e90ae3c62024451859cd503dc1ca18d00f99391b","sha256:76250ae83e0d71c05e95fa065bd9f073961cb3a1f56d27b7b706409cf18ef23b"],"state_sha256":"e43ea5d45db75487dbcb5edcc2cb81376ea4d24bc6b30eda396f914db66353cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkGiUD4Wv7M/5ljsEdCUF8gW9I7sEOFGUs85+B/AFazp1Z/0PwRGy2CBS9fI7w/AU32E2K0r0Av/erYbnWUgBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:18:50.794825Z","bundle_sha256":"14e5f6def63de2b633b39429b46c72079c7efc3dfe38c67d7483fe9814728426"}}