{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VQ4P3N7P5UMMXID7B3BT2VOM7U","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":"f3161a82daf01e97342a75c6c2d1e175ecb02d8ff8c85317aee784af44acab6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2018-05-01T13:03:41Z","title_canon_sha256":"899254c0b421f39b0612737135cc2426d50fd8876620209e6dd2f5f960ea1122"},"schema_version":"1.0","source":{"id":"1805.00303","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00303","created_at":"2026-05-17T23:52:59Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00303v3","created_at":"2026-05-17T23:52:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00303","created_at":"2026-05-17T23:52:59Z"},{"alias_kind":"pith_short_12","alias_value":"VQ4P3N7P5UMM","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VQ4P3N7P5UMMXID7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VQ4P3N7P","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:d111828106b020a4b4e9bc51b0c0c74b05c3d9852c1dbfe7db2fbaf579f43f8f","target":"graph","created_at":"2026-05-17T23:52:59Z","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":"With the recent development of analytical methods for studying the collective dynamics of coupled oscillator systems, the dynamics of communities of coupled oscillators have received a great deal of attention in the nonlinear dynamics community. However, the majority of these works treat systems with a number of symmetries to simplify the analysis. In this work we study the role of symmetry and symmetry-breaking in the collective dynamics of coupled oscillator communities, allowing for a comparison between the macroscopic dynamics of symmetric and asymmetric systems. We begin by treating the s","authors_text":"Per Sebastian Skardal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2018-05-01T13:03:41Z","title":"Symmetry and symmetry breaking in coupled oscillator communities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00303","kind":"arxiv","version":3},"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":"sha256:78ae4996b4e2eb929a105465505092ea1721a24680e2df27d5c8525b466b73ea","target":"record","created_at":"2026-05-17T23:52:59Z","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":"f3161a82daf01e97342a75c6c2d1e175ecb02d8ff8c85317aee784af44acab6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2018-05-01T13:03:41Z","title_canon_sha256":"899254c0b421f39b0612737135cc2426d50fd8876620209e6dd2f5f960ea1122"},"schema_version":"1.0","source":{"id":"1805.00303","kind":"arxiv","version":3}},"canonical_sha256":"ac38fdb7efed18cba07f0ec33d55ccfd014481f39f903d1b3767927aea31c056","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac38fdb7efed18cba07f0ec33d55ccfd014481f39f903d1b3767927aea31c056","first_computed_at":"2026-05-17T23:52:59.225586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:59.225586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NcoUnaKQehf09fkg44Rfmzi8wL48XSBj5Rd1ryZtt6C81jk/RqFSmMsdnxXNO1FPuMAnBNqzg03rFFxoKd3oAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:59.226116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00303","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78ae4996b4e2eb929a105465505092ea1721a24680e2df27d5c8525b466b73ea","sha256:d111828106b020a4b4e9bc51b0c0c74b05c3d9852c1dbfe7db2fbaf579f43f8f"],"state_sha256":"16466de36ad84b92046fc89dc1c829f287120a850407b83e3f859ad5b7083ccb"}