{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FAQ3E4C3Q4UZU43O7MGWV76STW","short_pith_number":"pith:FAQ3E4C3","schema_version":"1.0","canonical_sha256":"2821b2705b87299a736efb0d6affd29dae6301f6e1de4baae9ca84e0deb964dc","source":{"kind":"arxiv","id":"1212.5027","version":2},"attestation_state":"computed","paper":{"title":"Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Smets (LJLL), Fabrice B\\'ethuel (LJLL), Philippe Gravejat (CMLS-EcolePolytechnique)","submitted_at":"2012-12-20T13:31:38Z","abstract_excerpt":"We pursue our work on the dynamical stability of dark solitons for the one-dimensional Gross-Pitaevskii equation. In this paper, we prove their asymptotic stability under small perturbations in the energy space. In particular, our results do not require smallness in some weighted spaces or a priori spectral assumptions. Our strategy is reminiscent of the one used by Martel and Merle in various works regarding generalized Korteweg-de Vries equations. The important feature of our contribution is related to the fact that while Korteweg-de Vries equations possess unidirectional dispersion, Schr\\\"o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.5027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-20T13:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"86097b7d498b3d51361d817437cae0fecbaee9e0fe3a980137978ff7c3e498d9","abstract_canon_sha256":"312c502be9e207599a0ccbbf7b5bfad0c5aa67eede4094ec7e2fc8aa249921e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:51.583794Z","signature_b64":"KBRvuCvvlmVmMtC321MBhUYK4e0w7UnffoUx5fMUXMaqQsdwZ8RrurgKBP3xfSbuAeWjLtwqwZgfzhSndJFbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2821b2705b87299a736efb0d6affd29dae6301f6e1de4baae9ca84e0deb964dc","last_reissued_at":"2026-05-18T03:18:51.583063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:51.583063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Smets (LJLL), Fabrice B\\'ethuel (LJLL), Philippe Gravejat (CMLS-EcolePolytechnique)","submitted_at":"2012-12-20T13:31:38Z","abstract_excerpt":"We pursue our work on the dynamical stability of dark solitons for the one-dimensional Gross-Pitaevskii equation. In this paper, we prove their asymptotic stability under small perturbations in the energy space. In particular, our results do not require smallness in some weighted spaces or a priori spectral assumptions. Our strategy is reminiscent of the one used by Martel and Merle in various works regarding generalized Korteweg-de Vries equations. The important feature of our contribution is related to the fact that while Korteweg-de Vries equations possess unidirectional dispersion, Schr\\\"o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5027","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.5027","created_at":"2026-05-18T03:18:51.583193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5027v2","created_at":"2026-05-18T03:18:51.583193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5027","created_at":"2026-05-18T03:18:51.583193+00:00"},{"alias_kind":"pith_short_12","alias_value":"FAQ3E4C3Q4UZ","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"FAQ3E4C3Q4UZU43O","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"FAQ3E4C3","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW","json":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW.json","graph_json":"https://pith.science/api/pith-number/FAQ3E4C3Q4UZU43O7MGWV76STW/graph.json","events_json":"https://pith.science/api/pith-number/FAQ3E4C3Q4UZU43O7MGWV76STW/events.json","paper":"https://pith.science/paper/FAQ3E4C3"},"agent_actions":{"view_html":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW","download_json":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW.json","view_paper":"https://pith.science/paper/FAQ3E4C3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5027&json=true","fetch_graph":"https://pith.science/api/pith-number/FAQ3E4C3Q4UZU43O7MGWV76STW/graph.json","fetch_events":"https://pith.science/api/pith-number/FAQ3E4C3Q4UZU43O7MGWV76STW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW/action/storage_attestation","attest_author":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW/action/author_attestation","sign_citation":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW/action/citation_signature","submit_replication":"https://pith.science/pith/FAQ3E4C3Q4UZU43O7MGWV76STW/action/replication_record"}},"created_at":"2026-05-18T03:18:51.583193+00:00","updated_at":"2026-05-18T03:18:51.583193+00:00"}