{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JPAEN47S2ABEPQ2T3ETHZGCRKD","short_pith_number":"pith:JPAEN47S","schema_version":"1.0","canonical_sha256":"4bc046f3f2d00247c353d9267c985150c36c41389fd50d449e29412128dbec33","source":{"kind":"arxiv","id":"1710.07152","version":1},"attestation_state":"computed","paper":{"title":"Transversality in Dynamical Systems with Generalized Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bob Rink, Eddie Nijholt","submitted_at":"2017-10-19T14:20:14Z","abstract_excerpt":"We prove that a generic $k$-parameter bifurcation of a dynamical system with a monoid symmetry occurs along a generalized kernel or center subspace of a particular type. More precisely, any (complementable) subrepresentation $U$ is given a number $K_U$ and a number $C_U$. A $k$-parameter bifurcation can generically only occur along a generalized kernel isomorphic to $U$ if $k \\geq K_U$. It can generically only occur along a center subspace isomorphic to $U$ if $k \\geq C_U$. The numbers $K_U$ and $C_U$ depend only on the decomposition of $U$ into indecomposable subrepresentations. In particular"},"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":"1710.07152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-19T14:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"339c3ba5ecde304e9c2a09338f7a4cce88462578bc012c0682e4ca7b5c5f2f4d","abstract_canon_sha256":"a33ac0a9bca8ffa06b2d158b4398b252d09641a10ead1912dc21bdafb0652830"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:26.831461Z","signature_b64":"nqIuI+y7P99QzSeq8NccH+uojHhfEtQnr+pmBEHH/1TFK0lEwy1gSFaEYq1DtkLHNyn96i4HcG2BTbH7HfDfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc046f3f2d00247c353d9267c985150c36c41389fd50d449e29412128dbec33","last_reissued_at":"2026-05-18T00:32:26.830882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:26.830882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transversality in Dynamical Systems with Generalized Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bob Rink, Eddie Nijholt","submitted_at":"2017-10-19T14:20:14Z","abstract_excerpt":"We prove that a generic $k$-parameter bifurcation of a dynamical system with a monoid symmetry occurs along a generalized kernel or center subspace of a particular type. More precisely, any (complementable) subrepresentation $U$ is given a number $K_U$ and a number $C_U$. A $k$-parameter bifurcation can generically only occur along a generalized kernel isomorphic to $U$ if $k \\geq K_U$. It can generically only occur along a center subspace isomorphic to $U$ if $k \\geq C_U$. The numbers $K_U$ and $C_U$ depend only on the decomposition of $U$ into indecomposable subrepresentations. In particular"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07152","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.07152","created_at":"2026-05-18T00:32:26.830987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.07152v1","created_at":"2026-05-18T00:32:26.830987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07152","created_at":"2026-05-18T00:32:26.830987+00:00"},{"alias_kind":"pith_short_12","alias_value":"JPAEN47S2ABE","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JPAEN47S2ABEPQ2T","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JPAEN47S","created_at":"2026-05-18T12:31:24.725408+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/JPAEN47S2ABEPQ2T3ETHZGCRKD","json":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD.json","graph_json":"https://pith.science/api/pith-number/JPAEN47S2ABEPQ2T3ETHZGCRKD/graph.json","events_json":"https://pith.science/api/pith-number/JPAEN47S2ABEPQ2T3ETHZGCRKD/events.json","paper":"https://pith.science/paper/JPAEN47S"},"agent_actions":{"view_html":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD","download_json":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD.json","view_paper":"https://pith.science/paper/JPAEN47S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.07152&json=true","fetch_graph":"https://pith.science/api/pith-number/JPAEN47S2ABEPQ2T3ETHZGCRKD/graph.json","fetch_events":"https://pith.science/api/pith-number/JPAEN47S2ABEPQ2T3ETHZGCRKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD/action/storage_attestation","attest_author":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD/action/author_attestation","sign_citation":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD/action/citation_signature","submit_replication":"https://pith.science/pith/JPAEN47S2ABEPQ2T3ETHZGCRKD/action/replication_record"}},"created_at":"2026-05-18T00:32:26.830987+00:00","updated_at":"2026-05-18T00:32:26.830987+00:00"}