{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GAZK2AKKCQNI6FSW5IU2FNZN5O","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":"31ffb98706ddddbd6f148a5bd1630ab224e67851f14319677fb1d27c43fb193a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-04T18:32:50Z","title_canon_sha256":"8b8b98eddd8a36e87c9beb5943b5b1c8738139c378ffed5dcf9677167d78fd8f"},"schema_version":"1.0","source":{"id":"1304.1460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1460","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1460v1","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1460","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"GAZK2AKKCQNI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GAZK2AKKCQNI6FSW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GAZK2AKK","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:8983098db6ca7ce8e4765ad1e4f1c53016ee2a235bfa2b3a9f7fe9659fcb067d","target":"graph","created_at":"2026-05-18T03:28:56Z","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":"Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here for homogeneous networks, by showing that every homogeneous network dynamical system admits a semigroup of hidden symmetries. The synchronous solutions lie in the symmetry spaces of this semigroup and the spectral degeneracies of the network are determined by its indecomposable representations. Under a condition on the semigroup representation, we prove that a one-parameter synchrony breaking steady state bifurcatio","authors_text":"Bob Rink, Jan Sanders","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-04T18:32:50Z","title":"Coupled cell networks and their hidden symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1460","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":"sha256:3d1075e0246d90723d147033d326e5c8f99192f279b83bb6dcfc297add25a05d","target":"record","created_at":"2026-05-18T03:28:56Z","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":"31ffb98706ddddbd6f148a5bd1630ab224e67851f14319677fb1d27c43fb193a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-04T18:32:50Z","title_canon_sha256":"8b8b98eddd8a36e87c9beb5943b5b1c8738139c378ffed5dcf9677167d78fd8f"},"schema_version":"1.0","source":{"id":"1304.1460","kind":"arxiv","version":1}},"canonical_sha256":"3032ad014a141a8f1656ea29a2b72deba75ab2aef2cc15c57c2461f08b5f0382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3032ad014a141a8f1656ea29a2b72deba75ab2aef2cc15c57c2461f08b5f0382","first_computed_at":"2026-05-18T03:28:56.694363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:56.694363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cSyMUg+YWkTAhp6iwxGqAmrJVJlvfelWWjhsf2HxrHjVQ18Q0s/BKy/z1npNvdgaUN/u73abvD9EX+W+TNttCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:56.695083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d1075e0246d90723d147033d326e5c8f99192f279b83bb6dcfc297add25a05d","sha256:8983098db6ca7ce8e4765ad1e4f1c53016ee2a235bfa2b3a9f7fe9659fcb067d"],"state_sha256":"a45b162eff622d62e1decc87b83f4aea7391ae704c7741e182255336cd00a25e"}