{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JZ5E2EAEV55K4B2HLAEBSE32K6","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":"952ba80105a6d5e0901fb33f03e8f0df7bb9af20623e45e994b06d48346f70cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-29T15:18:59Z","title_canon_sha256":"36aeb06484f01f4c0f8ba9789ef66fea12f62f94e9a056913bb5ecbdead73f49"},"schema_version":"1.0","source":{"id":"1410.8011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8011","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8011v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8011","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"JZ5E2EAEV55K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JZ5E2EAEV55K4B2H","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JZ5E2EAE","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:6565167f75a55a1d0f5b6201b0ba0bbb3974f544c82a53953bb59bf6b2d23c89","target":"graph","created_at":"2026-05-18T02:39:07Z","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 nonlinear Schr\\\"odinger equation with $L^2$-critical exponent and an inhomogeneous damping term. By using the tools developed by Merle and Raphael, we prove the existence of blowup phenomena in the energy space $H^1(\\mathbb{R})$.","authors_text":"Sim\\~ao Correia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-29T15:18:59Z","title":"Blowup for the nonlinear Schr\\\"odinger equation with an inhomogeneous damping term in the $L^2$ critical case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8011","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:a3e9a805c8368a8c628091b2e229a1bb1982c7cd50de26957c58650695661b4d","target":"record","created_at":"2026-05-18T02:39:07Z","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":"952ba80105a6d5e0901fb33f03e8f0df7bb9af20623e45e994b06d48346f70cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-29T15:18:59Z","title_canon_sha256":"36aeb06484f01f4c0f8ba9789ef66fea12f62f94e9a056913bb5ecbdead73f49"},"schema_version":"1.0","source":{"id":"1410.8011","kind":"arxiv","version":1}},"canonical_sha256":"4e7a4d1004af7aae0747580819137a57ad645f1b54258c668bb856c7fe7a8943","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e7a4d1004af7aae0747580819137a57ad645f1b54258c668bb856c7fe7a8943","first_computed_at":"2026-05-18T02:39:07.569923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:07.569923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DxSgRx/Jopuqmhwf5+GkSSowvOuSqq7Q89+WoBmA9QVVooB6ZDNdGiMKr764Hbft7C9DNMqzozDWbkXDtwRzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:07.570420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3e9a805c8368a8c628091b2e229a1bb1982c7cd50de26957c58650695661b4d","sha256:6565167f75a55a1d0f5b6201b0ba0bbb3974f544c82a53953bb59bf6b2d23c89"],"state_sha256":"9f17de8fcb5263cfcff51dcdceb92d6f6604f593a844f9052d1ca12c5c9b2269"}