{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:E6ZC6YZ2YWXD7A5ADBYE5RRUZM","short_pith_number":"pith:E6ZC6YZ2","schema_version":"1.0","canonical_sha256":"27b22f633ac5ae3f83a018704ec634cb30034f85d9d941bfe81ff026115df72d","source":{"kind":"arxiv","id":"1603.02206","version":5},"attestation_state":"computed","paper":{"title":"A priori bounds and global bifurcation results for frequency combs modeled by the Lugiato-Lefever equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel, Wolfgang Reichel","submitted_at":"2016-03-07T19:06:12Z","abstract_excerpt":"In nonlinear optics $2\\pi$-periodic solutions $a\\in C^2([0,2\\pi];\\mathbb{C})$ of the stationary Lugiato-Lefever equation $-d a\"= ({\\rm i} -\\zeta)a +|a|^2a-{\\rm i} f$ serve as a model for frequency combs, which are optical signals consisting of a superposition of modes with equally spaced frequencies. We prove that nontrivial frequency combs can only be observed for special ranges of values of the forcing and detuning parameters $f$ and $\\zeta$, as it has been previously documented in experiments and numerical simulations. E.g., if the detuning parameter $\\zeta$ is too large then nontrivial fre"},"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":"1603.02206","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-07T19:06:12Z","cross_cats_sorted":[],"title_canon_sha256":"fe158e33a7fe6755aed466c5b2f95cfe537911e05a2a038e8e199581648f0e5e","abstract_canon_sha256":"7feaff7f753301d4c750c9dde10b2d0eae1eccbb072e9461b606a96cdde84d5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:00.277484Z","signature_b64":"zchd4VFb12wBLT3zZ7Q9NQmh09coGYGoO5Ckn/HtQ21kLLM8qv3WTZ4tP0vkdmvfSB+wF3Qr9n4SY8caga9YAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27b22f633ac5ae3f83a018704ec634cb30034f85d9d941bfe81ff026115df72d","last_reissued_at":"2026-05-18T01:01:00.276673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:00.276673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A priori bounds and global bifurcation results for frequency combs modeled by the Lugiato-Lefever equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel, Wolfgang Reichel","submitted_at":"2016-03-07T19:06:12Z","abstract_excerpt":"In nonlinear optics $2\\pi$-periodic solutions $a\\in C^2([0,2\\pi];\\mathbb{C})$ of the stationary Lugiato-Lefever equation $-d a\"= ({\\rm i} -\\zeta)a +|a|^2a-{\\rm i} f$ serve as a model for frequency combs, which are optical signals consisting of a superposition of modes with equally spaced frequencies. We prove that nontrivial frequency combs can only be observed for special ranges of values of the forcing and detuning parameters $f$ and $\\zeta$, as it has been previously documented in experiments and numerical simulations. E.g., if the detuning parameter $\\zeta$ is too large then nontrivial fre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02206","kind":"arxiv","version":5},"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":"1603.02206","created_at":"2026-05-18T01:01:00.276821+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.02206v5","created_at":"2026-05-18T01:01:00.276821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02206","created_at":"2026-05-18T01:01:00.276821+00:00"},{"alias_kind":"pith_short_12","alias_value":"E6ZC6YZ2YWXD","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"E6ZC6YZ2YWXD7A5A","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"E6ZC6YZ2","created_at":"2026-05-18T12:30:12.583610+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/E6ZC6YZ2YWXD7A5ADBYE5RRUZM","json":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM.json","graph_json":"https://pith.science/api/pith-number/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/graph.json","events_json":"https://pith.science/api/pith-number/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/events.json","paper":"https://pith.science/paper/E6ZC6YZ2"},"agent_actions":{"view_html":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM","download_json":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM.json","view_paper":"https://pith.science/paper/E6ZC6YZ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.02206&json=true","fetch_graph":"https://pith.science/api/pith-number/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/graph.json","fetch_events":"https://pith.science/api/pith-number/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/action/storage_attestation","attest_author":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/action/author_attestation","sign_citation":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/action/citation_signature","submit_replication":"https://pith.science/pith/E6ZC6YZ2YWXD7A5ADBYE5RRUZM/action/replication_record"}},"created_at":"2026-05-18T01:01:00.276821+00:00","updated_at":"2026-05-18T01:01:00.276821+00:00"}