{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5TULLU5BK5SVFGDROJXYR6DSZE","short_pith_number":"pith:5TULLU5B","canonical_record":{"source":{"id":"1401.6059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-01-23T17:19:23Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"c8d727f2a6600e0890971a720ff0fc2e2d60b3c54d1dd9ddd61178c452b6302f","abstract_canon_sha256":"fe53f1863ea725424b9071c6c9bd4965f246064b68b36bdfafe165bea8bc3487"},"schema_version":"1.0"},"canonical_sha256":"ece8b5d3a15765529871726f88f872c91047c17a5f279ff7c1c34b44f5b05435","source":{"kind":"arxiv","id":"1401.6059","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6059","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6059v1","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6059","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"5TULLU5BK5SV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5TULLU5BK5SVFGDR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5TULLU5B","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5TULLU5BK5SVFGDROJXYR6DSZE","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-01-23T17:19:23Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"c8d727f2a6600e0890971a720ff0fc2e2d60b3c54d1dd9ddd61178c452b6302f","abstract_canon_sha256":"fe53f1863ea725424b9071c6c9bd4965f246064b68b36bdfafe165bea8bc3487"},"schema_version":"1.0"},"canonical_sha256":"ece8b5d3a15765529871726f88f872c91047c17a5f279ff7c1c34b44f5b05435","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:00.997039Z","signature_b64":"t7XMt0POVAPLkaqRfRbx/KePSW+IN/niPvPtki2CzwUfDdJHQvEtFMfhj07Tr/GZ78UctHpQM9WRcohlFWraBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ece8b5d3a15765529871726f88f872c91047c17a5f279ff7c1c34b44f5b05435","last_reissued_at":"2026-05-18T02:51:00.996586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:00.996586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6059","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qfK0DvquSFCvLHmvVYMgF5sIhLpiwh9nTkmh208hZPFa/dUIRQacO3jQOu3FCXvcUgioCHdAKw/+vv4fSLIgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:54:17.496611Z"},"content_sha256":"b437410eba1a7d05b12f61f782d8b2ae215a8a251b3e78a6b0d952cdea0016e4","schema_version":"1.0","event_id":"sha256:b437410eba1a7d05b12f61f782d8b2ae215a8a251b3e78a6b0d952cdea0016e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5TULLU5BK5SVFGDROJXYR6DSZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"physics.optics","authors_text":"D. Gomila, L. Gelens, M. A. Matias, P. Parra-Rivas, S. Coen","submitted_at":"2014-01-23T17:19:23Z","abstract_excerpt":"It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6059","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyrtsNgbEZ0jQiEHNvZJHOH9TAyDNoTDwul9m6A4UZUQ5uQeUXGgnB/3ac8Sk2mLkBOnE78Ugv9FldwSue/QCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:54:17.496973Z"},"content_sha256":"4d6fcffc06ef8f338420f4a25c90fb9f8820443c1ed21171d9de61ca344c4896","schema_version":"1.0","event_id":"sha256:4d6fcffc06ef8f338420f4a25c90fb9f8820443c1ed21171d9de61ca344c4896"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TULLU5BK5SVFGDROJXYR6DSZE/bundle.json","state_url":"https://pith.science/pith/5TULLU5BK5SVFGDROJXYR6DSZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TULLU5BK5SVFGDROJXYR6DSZE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T00:54:17Z","links":{"resolver":"https://pith.science/pith/5TULLU5BK5SVFGDROJXYR6DSZE","bundle":"https://pith.science/pith/5TULLU5BK5SVFGDROJXYR6DSZE/bundle.json","state":"https://pith.science/pith/5TULLU5BK5SVFGDROJXYR6DSZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TULLU5BK5SVFGDROJXYR6DSZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5TULLU5BK5SVFGDROJXYR6DSZE","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":"fe53f1863ea725424b9071c6c9bd4965f246064b68b36bdfafe165bea8bc3487","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-01-23T17:19:23Z","title_canon_sha256":"c8d727f2a6600e0890971a720ff0fc2e2d60b3c54d1dd9ddd61178c452b6302f"},"schema_version":"1.0","source":{"id":"1401.6059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6059","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6059v1","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6059","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"5TULLU5BK5SV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5TULLU5BK5SVFGDR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5TULLU5B","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:4d6fcffc06ef8f338420f4a25c90fb9f8820443c1ed21171d9de61ca344c4896","target":"graph","created_at":"2026-05-18T02:51:00Z","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":"It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and ","authors_text":"D. Gomila, L. Gelens, M. A. Matias, P. Parra-Rivas, S. Coen","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-01-23T17:19:23Z","title":"Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6059","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:b437410eba1a7d05b12f61f782d8b2ae215a8a251b3e78a6b0d952cdea0016e4","target":"record","created_at":"2026-05-18T02:51:00Z","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":"fe53f1863ea725424b9071c6c9bd4965f246064b68b36bdfafe165bea8bc3487","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2014-01-23T17:19:23Z","title_canon_sha256":"c8d727f2a6600e0890971a720ff0fc2e2d60b3c54d1dd9ddd61178c452b6302f"},"schema_version":"1.0","source":{"id":"1401.6059","kind":"arxiv","version":1}},"canonical_sha256":"ece8b5d3a15765529871726f88f872c91047c17a5f279ff7c1c34b44f5b05435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ece8b5d3a15765529871726f88f872c91047c17a5f279ff7c1c34b44f5b05435","first_computed_at":"2026-05-18T02:51:00.996586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:00.996586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t7XMt0POVAPLkaqRfRbx/KePSW+IN/niPvPtki2CzwUfDdJHQvEtFMfhj07Tr/GZ78UctHpQM9WRcohlFWraBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:00.997039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b437410eba1a7d05b12f61f782d8b2ae215a8a251b3e78a6b0d952cdea0016e4","sha256:4d6fcffc06ef8f338420f4a25c90fb9f8820443c1ed21171d9de61ca344c4896"],"state_sha256":"bdf9e4df9b1f611437fa287b953b650baf61c8cfe2a3f2e75254dd0627624937"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CtERExnagUemJzo4oYIHP0nX07sfmcuxWsHzTQ4G558SlrlR6uvwj//zt7DingWe9S3Cyzj05NACfOncuGZSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:54:17.501588Z","bundle_sha256":"cc4bc373fc3b7528f0c0f5ab78e59c8b90552851e9b918e85c801089046c558f"}}