{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AT4UTJGH5ZE24VHZACR3W7QEZS","short_pith_number":"pith:AT4UTJGH","schema_version":"1.0","canonical_sha256":"04f949a4c7ee49ae54f900a3bb7e04cc8587889a10391f88bf9acd28a4fa072d","source":{"kind":"arxiv","id":"1611.08482","version":1},"attestation_state":"computed","paper":{"title":"A Two-Soliton with Transient Turbulent Regime for the Cubic Half-wave Equation on The Real Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Oana Pocovnicu, Patrick G\\'erard (LM-Orsay), Pierre Rapha\\\"el (JAD)","submitted_at":"2016-11-25T15:11:26Z","abstract_excerpt":"We consider the focusing cubic half-wave equation on the real line $$i \\partial_t u + |D| u = |u|^2 u, \\ \\ \\widehat{|D|u}(\\xi)=|\\xi|\\hat{u}(\\xi), \\ \\ (t,x)\\in \\Bbb R_+\\times \\Bbb R.$$ We construct an asymptotic global-in-time compact two-soliton solution with arbitrarily small $L^2$-norm which exhibits the following two regimes: (i) a transient turbulent regime characterized by a dramatic and explicit growth of its $H^1$-norm on a finite time interval, followed by (ii) a saturation regime in which the $H^1$-norm remains stationary large forever in time."},"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":"1611.08482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-25T15:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"ef1dc65c98aec809139cb4ab9172de5e9e1fe881cb325b657bb3bbcd5aa20694","abstract_canon_sha256":"2e24f616c39225c6d2311e75c8e0bf8a57b9726b67f2d4318c202469707c981b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:38.906487Z","signature_b64":"FXtXrIMFnDLfOkRAvkn2RS9MDonwjK7f7/ok2VEIZjhIaYORYmDSf8DIapdSCNBDPoENxFZWqYgaqgXTO/RhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04f949a4c7ee49ae54f900a3bb7e04cc8587889a10391f88bf9acd28a4fa072d","last_reissued_at":"2026-05-18T00:56:38.905713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:38.905713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Two-Soliton with Transient Turbulent Regime for the Cubic Half-wave Equation on The Real Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Oana Pocovnicu, Patrick G\\'erard (LM-Orsay), Pierre Rapha\\\"el (JAD)","submitted_at":"2016-11-25T15:11:26Z","abstract_excerpt":"We consider the focusing cubic half-wave equation on the real line $$i \\partial_t u + |D| u = |u|^2 u, \\ \\ \\widehat{|D|u}(\\xi)=|\\xi|\\hat{u}(\\xi), \\ \\ (t,x)\\in \\Bbb R_+\\times \\Bbb R.$$ We construct an asymptotic global-in-time compact two-soliton solution with arbitrarily small $L^2$-norm which exhibits the following two regimes: (i) a transient turbulent regime characterized by a dramatic and explicit growth of its $H^1$-norm on a finite time interval, followed by (ii) a saturation regime in which the $H^1$-norm remains stationary large forever in time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08482","kind":"arxiv","version":1},"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":"1611.08482","created_at":"2026-05-18T00:56:38.905844+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.08482v1","created_at":"2026-05-18T00:56:38.905844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08482","created_at":"2026-05-18T00:56:38.905844+00:00"},{"alias_kind":"pith_short_12","alias_value":"AT4UTJGH5ZE2","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AT4UTJGH5ZE24VHZ","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AT4UTJGH","created_at":"2026-05-18T12:30:07.202191+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/AT4UTJGH5ZE24VHZACR3W7QEZS","json":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS.json","graph_json":"https://pith.science/api/pith-number/AT4UTJGH5ZE24VHZACR3W7QEZS/graph.json","events_json":"https://pith.science/api/pith-number/AT4UTJGH5ZE24VHZACR3W7QEZS/events.json","paper":"https://pith.science/paper/AT4UTJGH"},"agent_actions":{"view_html":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS","download_json":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS.json","view_paper":"https://pith.science/paper/AT4UTJGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.08482&json=true","fetch_graph":"https://pith.science/api/pith-number/AT4UTJGH5ZE24VHZACR3W7QEZS/graph.json","fetch_events":"https://pith.science/api/pith-number/AT4UTJGH5ZE24VHZACR3W7QEZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS/action/storage_attestation","attest_author":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS/action/author_attestation","sign_citation":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS/action/citation_signature","submit_replication":"https://pith.science/pith/AT4UTJGH5ZE24VHZACR3W7QEZS/action/replication_record"}},"created_at":"2026-05-18T00:56:38.905844+00:00","updated_at":"2026-05-18T00:56:38.905844+00:00"}