{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2TL5S4FRY36IQNTGBADA7LNBYE","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":"1722b12a0d9c17865eb0e83bf748c36af71914592835f10edc7a0bdd377f1c0a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-12T10:20:08Z","title_canon_sha256":"01626c46b4f44d9c408cbc2564533ff1d3c3dd13418dd5279742ab847a9c9b66"},"schema_version":"1.0","source":{"id":"2107.05299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.05299","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"2107.05299v1","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05299","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"2TL5S4FRY36I","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_16","alias_value":"2TL5S4FRY36IQNTG","created_at":"2026-07-05T02:57:01Z"},{"alias_kind":"pith_short_8","alias_value":"2TL5S4FR","created_at":"2026-07-05T02:57:01Z"}],"graph_snapshots":[{"event_id":"sha256:51be1142a47f5dfd32c7d1c7a49d8b05ecc8b668e90d31e9de1569234c87895b","target":"graph","created_at":"2026-07-05T02:57:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.05299/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\\\"odinger system in ${\\dot H}^1\\times{\\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\\rm u}_0$ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of ${\\rm u}_0$ is below or above that of the ground state.","authors_text":"Chengbin Xu, Chuanwei Gao, Fanfei Meng, Jiqiang Zheng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-12T10:20:08Z","title":"Scattering theory For Quadratic Nonlinear Schr\\\"odinger System in dimension six"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05299","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":"sha256:88d8367e997a6dcfd7d68a4b7f6bd9b362d796e70bf19f6ce9eca1259fac370b","target":"record","created_at":"2026-07-05T02:57:01Z","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":"1722b12a0d9c17865eb0e83bf748c36af71914592835f10edc7a0bdd377f1c0a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-12T10:20:08Z","title_canon_sha256":"01626c46b4f44d9c408cbc2564533ff1d3c3dd13418dd5279742ab847a9c9b66"},"schema_version":"1.0","source":{"id":"2107.05299","kind":"arxiv","version":1}},"canonical_sha256":"d4d7d970b1c6fc88366608060fada1c11b59588d8311b600d59f614db5322f9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4d7d970b1c6fc88366608060fada1c11b59588d8311b600d59f614db5322f9a","first_computed_at":"2026-07-05T02:57:01.484046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:57:01.484046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1/26af1A9teKdobd7/Z0DHplYCznH+AswaVEMeI7FSnPnuGY2fvgLBcmw/1108yD9uH2a+ax0XlGBFsGWf3jBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:57:01.484402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.05299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88d8367e997a6dcfd7d68a4b7f6bd9b362d796e70bf19f6ce9eca1259fac370b","sha256:51be1142a47f5dfd32c7d1c7a49d8b05ecc8b668e90d31e9de1569234c87895b"],"state_sha256":"c290f6773c70772afd5089b4afb7d503150935202a04fe3789f55ee7705c92b8"}