{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5BR2BRZO5ZDWQFHUZ2GPFR2YQN","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":"8cfca3c3948de850feea5396f28b3750b952918efc745ea7667a5c67a554a4ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-30T08:00:49Z","title_canon_sha256":"8af905967090b4ce5724207f06977c05aa47e650f59d2436342e7f37d3259edb"},"schema_version":"1.0","source":{"id":"1409.8416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8416","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8416v1","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8416","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"5BR2BRZO5ZDW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5BR2BRZO5ZDWQFHU","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5BR2BRZO","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:3293a6136320d97761c6099063f4980215819395b0c0f5f9841493969f38e6f6","target":"graph","created_at":"2026-05-18T02:41:25Z","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 prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schr\\\"odinger equations\n  $$ \\begin{cases} i\\partial_t u_\\mu + \\Delta u_\\mu - \\sum_{\\mu,\\nu=1 }^N \\beta_{\\mu\\nu}|u_\\nu|^{p+1}|u_\\mu|^{p-1}u_\\mu=0, \\quad\\quad \\mu=1,\\dots,N,\\\\(u_\\mu(0,\\cdot))_{\\mu=1}^N= (u_{\\mu,0})_{\\mu=1}^N \\in H^1(\\mathbb R^d)^N. \\end{cases} $$ with $N\\geq 2$, $\\beta_{\\mu\\nu} \\geq 0$, $\\beta_{\\mu\\mu}\\neq 0$ for $p>2 $ if $d=1$, $p>1 $ if $d=2$ and $ 1 \\leq p < 2$ if $d=3$.","authors_text":"Biagio Cassano, Mirko Tarulli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-30T08:00:49Z","title":"$H^1$-scattering for systems of $N$-defocusing weakly coupled NLS equations in low space dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8416","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":"sha256:1bddef0e38a68154819779ce6ff8a8d38542a9e37fc8340639859fbef4a10089","target":"record","created_at":"2026-05-18T02:41:25Z","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":"8cfca3c3948de850feea5396f28b3750b952918efc745ea7667a5c67a554a4ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-30T08:00:49Z","title_canon_sha256":"8af905967090b4ce5724207f06977c05aa47e650f59d2436342e7f37d3259edb"},"schema_version":"1.0","source":{"id":"1409.8416","kind":"arxiv","version":1}},"canonical_sha256":"e863a0c72eee476814f4ce8cf2c7588379df55e9d505e40ead27fd97c755bc12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e863a0c72eee476814f4ce8cf2c7588379df55e9d505e40ead27fd97c755bc12","first_computed_at":"2026-05-18T02:41:25.398041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:25.398041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IzeVj6p2iBxS3hvaGpu6IV2t22CwJIuobNRlok2+4mvdSmUub6/xxf5elaQdOynSeYQkk5ZCJ9WtqxLKAVAdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:25.398620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bddef0e38a68154819779ce6ff8a8d38542a9e37fc8340639859fbef4a10089","sha256:3293a6136320d97761c6099063f4980215819395b0c0f5f9841493969f38e6f6"],"state_sha256":"7a997eb0c4bd65caed7f0467935f42b4d77f2d7696b4b726574df107192fb22c"}