{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A6ILUIJVNZSEYIUSQOED77ARMX","short_pith_number":"pith:A6ILUIJV","canonical_record":{"source":{"id":"1306.3327","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T08:20:26Z","cross_cats_sorted":["math.MP","nlin.CD","physics.optics"],"title_canon_sha256":"66ba03026893469815ffae2621842b50e9376e2150309441e03a020a21f05f80","abstract_canon_sha256":"7d482aea6c62158a87cb333067837746fdbd57c181f5331e6003a8f5c5fcb6b5"},"schema_version":"1.0"},"canonical_sha256":"0790ba21356e644c229283883ffc1165d68182ccd99d038293fa639e5779e4d8","source":{"kind":"arxiv","id":"1306.3327","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3327","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3327v2","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3327","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"A6ILUIJVNZSE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A6ILUIJVNZSEYIUS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A6ILUIJV","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A6ILUIJVNZSEYIUSQOED77ARMX","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3327","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T08:20:26Z","cross_cats_sorted":["math.MP","nlin.CD","physics.optics"],"title_canon_sha256":"66ba03026893469815ffae2621842b50e9376e2150309441e03a020a21f05f80","abstract_canon_sha256":"7d482aea6c62158a87cb333067837746fdbd57c181f5331e6003a8f5c5fcb6b5"},"schema_version":"1.0"},"canonical_sha256":"0790ba21356e644c229283883ffc1165d68182ccd99d038293fa639e5779e4d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:58.869014Z","signature_b64":"02dmolBRqmyQqKuQo8yUQzJVToYITNBMWUcq+mSdBxj+1iNKueQrGpl7d2P8VI25DtVOZ//Z27zdOvlDH9PFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0790ba21356e644c229283883ffc1165d68182ccd99d038293fa639e5779e4d8","last_reissued_at":"2026-05-18T00:55:58.868513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:58.868513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3327","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opeeJ48W7g6k6vX1sn/1MOIcsJdHhZ/vtCFP0oM7thUgLYr3xNW4e0raumcVqlb4DsgC6e+Fa4AcWuKJnayLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:39:01.460878Z"},"content_sha256":"9ae47baba43dc37e4f66a02edba448e172d500d8049787ccdbef966f6aafe2ae","schema_version":"1.0","event_id":"sha256:9ae47baba43dc37e4f66a02edba448e172d500d8049787ccdbef966f6aafe2ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A6ILUIJVNZSEYIUSQOED77ARMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative equilibria and relative periodic solutions in systems with time-delay and $S^{1}$ symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.CD","physics.optics"],"primary_cat":"math-ph","authors_text":"Jan Sieber, Serhiy Yanchuk","submitted_at":"2013-06-14T08:20:26Z","abstract_excerpt":"We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the number of CW solutions grows generically linearly with time delay $\\tau$. Here we show, in particular, that the number of relative periodic solutions grows generically as $\\tau^2$ when delay increases. Thus, in such systems, the relative periodic solutions are more abundant than relative equilibria. The results are directly applicable to, e.g., Lang-Kobayash"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3327","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bl+yT4DaI4rgJ8fks5fMA3DUTa6mcWomDZUotyB2sjhgglcWxIUWabCmz5IkAVUXCh1ToQOFmb/s0xJ5oGBxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:39:01.461573Z"},"content_sha256":"3d5ca26789b2b606536b99dd9b117f58f81ab4bc73e48e050338539aa6940092","schema_version":"1.0","event_id":"sha256:3d5ca26789b2b606536b99dd9b117f58f81ab4bc73e48e050338539aa6940092"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6ILUIJVNZSEYIUSQOED77ARMX/bundle.json","state_url":"https://pith.science/pith/A6ILUIJVNZSEYIUSQOED77ARMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6ILUIJVNZSEYIUSQOED77ARMX/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":"2026-05-27T14:39:01Z","links":{"resolver":"https://pith.science/pith/A6ILUIJVNZSEYIUSQOED77ARMX","bundle":"https://pith.science/pith/A6ILUIJVNZSEYIUSQOED77ARMX/bundle.json","state":"https://pith.science/pith/A6ILUIJVNZSEYIUSQOED77ARMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6ILUIJVNZSEYIUSQOED77ARMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A6ILUIJVNZSEYIUSQOED77ARMX","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":"7d482aea6c62158a87cb333067837746fdbd57c181f5331e6003a8f5c5fcb6b5","cross_cats_sorted":["math.MP","nlin.CD","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T08:20:26Z","title_canon_sha256":"66ba03026893469815ffae2621842b50e9376e2150309441e03a020a21f05f80"},"schema_version":"1.0","source":{"id":"1306.3327","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3327","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3327v2","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3327","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"A6ILUIJVNZSE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A6ILUIJVNZSEYIUS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A6ILUIJV","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:3d5ca26789b2b606536b99dd9b117f58f81ab4bc73e48e050338539aa6940092","target":"graph","created_at":"2026-05-18T00:55:58Z","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 study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the number of CW solutions grows generically linearly with time delay $\\tau$. Here we show, in particular, that the number of relative periodic solutions grows generically as $\\tau^2$ when delay increases. Thus, in such systems, the relative periodic solutions are more abundant than relative equilibria. The results are directly applicable to, e.g., Lang-Kobayash","authors_text":"Jan Sieber, Serhiy Yanchuk","cross_cats":["math.MP","nlin.CD","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T08:20:26Z","title":"Relative equilibria and relative periodic solutions in systems with time-delay and $S^{1}$ symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3327","kind":"arxiv","version":2},"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":"sha256:9ae47baba43dc37e4f66a02edba448e172d500d8049787ccdbef966f6aafe2ae","target":"record","created_at":"2026-05-18T00:55:58Z","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":"7d482aea6c62158a87cb333067837746fdbd57c181f5331e6003a8f5c5fcb6b5","cross_cats_sorted":["math.MP","nlin.CD","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-14T08:20:26Z","title_canon_sha256":"66ba03026893469815ffae2621842b50e9376e2150309441e03a020a21f05f80"},"schema_version":"1.0","source":{"id":"1306.3327","kind":"arxiv","version":2}},"canonical_sha256":"0790ba21356e644c229283883ffc1165d68182ccd99d038293fa639e5779e4d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0790ba21356e644c229283883ffc1165d68182ccd99d038293fa639e5779e4d8","first_computed_at":"2026-05-18T00:55:58.868513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:58.868513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02dmolBRqmyQqKuQo8yUQzJVToYITNBMWUcq+mSdBxj+1iNKueQrGpl7d2P8VI25DtVOZ//Z27zdOvlDH9PFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:58.869014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3327","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ae47baba43dc37e4f66a02edba448e172d500d8049787ccdbef966f6aafe2ae","sha256:3d5ca26789b2b606536b99dd9b117f58f81ab4bc73e48e050338539aa6940092"],"state_sha256":"bc2033377ab690ba538e0199103e950c11b500ef7fad9d9be958abde5733309b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AG0UAucsU5iJ/tAcPxdjsR6sTrnpxaB0f3e+VbaGWwKXFEPXLffexC2JoLfoMGXBAuxQpBPIWiJwnNXV5lqsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:39:01.465177Z","bundle_sha256":"51e6f843dbf8eb2179ff261c8ab218cdfcafbbde2e77fec2b131352865e1f4c1"}}