{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DD3POHVRDACXZRE6PSV7MX2KXK","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":"7aaf5d5e62d7cab8efe00440f25aee2620579372ccf19dd3a72aef203515b11f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-19T01:33:51Z","title_canon_sha256":"800923a4a8231365d6d14b9375973e3d851e919fbb2b288857ca622754c5f070"},"schema_version":"1.0","source":{"id":"1512.06175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06175","created_at":"2026-05-18T01:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06175v2","created_at":"2026-05-18T01:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06175","created_at":"2026-05-18T01:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"DD3POHVRDACX","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DD3POHVRDACXZRE6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DD3POHVR","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:0d2aaba58e3648a588b4de2c1569f64c616f82944bc0a0947bf9f0d716f825d2","target":"graph","created_at":"2026-05-18T01:15:06Z","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 long time well-posedness of the Cauchy problem with large Sobolev data for a class of nonlinear Schr\\\"odinger equations (NLS) on $\\mathbb{R}^2$ with power nonlinearities of arbitrary odd degree. Specifically, the method in this paper applies to those NLS equations having either elliptic signature with a defocusing nonlinearity, or else having an indefinite signature. By rigorously justifying that these equations govern the modulation of wave packet-like solutions to an artificially constructed equation with an advantageous structure, we show that a priori every subcritical inho","authors_text":"Nathan Totz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-19T01:33:51Z","title":"Global Well-Posedness of 2D Non-Focusing Schr\\\"odinger Equations via Rigorous Modulation Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06175","kind":"arxiv","version":2},"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":"sha256:31f4f6d185dfd2dfc2346b6a71610c648481ba22724f3581a1edcb1293f7c4f9","target":"record","created_at":"2026-05-18T01:15:06Z","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":"7aaf5d5e62d7cab8efe00440f25aee2620579372ccf19dd3a72aef203515b11f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-19T01:33:51Z","title_canon_sha256":"800923a4a8231365d6d14b9375973e3d851e919fbb2b288857ca622754c5f070"},"schema_version":"1.0","source":{"id":"1512.06175","kind":"arxiv","version":2}},"canonical_sha256":"18f6f71eb118057cc49e7cabf65f4abaaac342015a3998bf767ab34ba8a8194f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18f6f71eb118057cc49e7cabf65f4abaaac342015a3998bf767ab34ba8a8194f","first_computed_at":"2026-05-18T01:15:06.433387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:06.433387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w8EvLXdSC0WYQtJhHzuBaXcAFbizlgbFO0qszhCFnsp5ip0VJyQ7br1MAB6J8E5gPq8QmaEq7M7vKrj5rCzHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:06.433921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31f4f6d185dfd2dfc2346b6a71610c648481ba22724f3581a1edcb1293f7c4f9","sha256:0d2aaba58e3648a588b4de2c1569f64c616f82944bc0a0947bf9f0d716f825d2"],"state_sha256":"fdfdcea4b541b6c9df336eb116fca4d57e54cec1dd7eeac06bd639263eca5f51"}