{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NCYVCF5H2ZEM35YBHZYEI3UILF","short_pith_number":"pith:NCYVCF5H","schema_version":"1.0","canonical_sha256":"68b15117a7d648cdf7013e70446e8859710a28adb1a47b89e9f57668a8e2d116","source":{"kind":"arxiv","id":"2606.28873","version":1},"attestation_state":"computed","paper":{"title":"Devil's terraces: determining the organization of resonance tongues in a periodically forced dynamical system","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernd Krauskopf, John Bailie, Priya Subramanian","submitted_at":"2026-06-27T11:33:14Z","abstract_excerpt":"In periodically forced dynamical systems, resonance tongues are open regions of a parameter plane in which the dynamics on an invariant torus locks to a stable periodic orbit. While individual resonance tongues are well understood, the principles governing their global arrangement remain largely unexplored. We develop a topological framework, grounded in applied topology and Morse theory, whose central object is the two-dimensional resonance surface, defined as the graph of the rotation number $\\rho$ over a parameter plane. Within this framework, resonance tongues appear as terraces of the res"},"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":"2606.28873","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-27T11:33:14Z","cross_cats_sorted":[],"title_canon_sha256":"a58812f1e5519a616a169fd677e8bb29bf182357efbc8de96c6d9d15d78ae5f8","abstract_canon_sha256":"c9c8f00f403c221912c7a743f9dc25028faf271588a62e6c718a76265c1ccc2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:16:55.406420Z","signature_b64":"QSWy67/vUZvBrQMlg6Z0OrYswbEn0GwHfWiRrN0pOPjcRJkvR4xTiQRfzSeV5RPgABoooKzoJlJFvXZoeTfJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68b15117a7d648cdf7013e70446e8859710a28adb1a47b89e9f57668a8e2d116","last_reissued_at":"2026-06-30T01:16:55.405825Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:16:55.405825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Devil's terraces: determining the organization of resonance tongues in a periodically forced dynamical system","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernd Krauskopf, John Bailie, Priya Subramanian","submitted_at":"2026-06-27T11:33:14Z","abstract_excerpt":"In periodically forced dynamical systems, resonance tongues are open regions of a parameter plane in which the dynamics on an invariant torus locks to a stable periodic orbit. While individual resonance tongues are well understood, the principles governing their global arrangement remain largely unexplored. We develop a topological framework, grounded in applied topology and Morse theory, whose central object is the two-dimensional resonance surface, defined as the graph of the rotation number $\\rho$ over a parameter plane. Within this framework, resonance tongues appear as terraces of the res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28873","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28873/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.28873","created_at":"2026-06-30T01:16:55.405912+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.28873v1","created_at":"2026-06-30T01:16:55.405912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28873","created_at":"2026-06-30T01:16:55.405912+00:00"},{"alias_kind":"pith_short_12","alias_value":"NCYVCF5H2ZEM","created_at":"2026-06-30T01:16:55.405912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NCYVCF5H2ZEM35YB","created_at":"2026-06-30T01:16:55.405912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NCYVCF5H","created_at":"2026-06-30T01:16:55.405912+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/NCYVCF5H2ZEM35YBHZYEI3UILF","json":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF.json","graph_json":"https://pith.science/api/pith-number/NCYVCF5H2ZEM35YBHZYEI3UILF/graph.json","events_json":"https://pith.science/api/pith-number/NCYVCF5H2ZEM35YBHZYEI3UILF/events.json","paper":"https://pith.science/paper/NCYVCF5H"},"agent_actions":{"view_html":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF","download_json":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF.json","view_paper":"https://pith.science/paper/NCYVCF5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.28873&json=true","fetch_graph":"https://pith.science/api/pith-number/NCYVCF5H2ZEM35YBHZYEI3UILF/graph.json","fetch_events":"https://pith.science/api/pith-number/NCYVCF5H2ZEM35YBHZYEI3UILF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF/action/storage_attestation","attest_author":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF/action/author_attestation","sign_citation":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF/action/citation_signature","submit_replication":"https://pith.science/pith/NCYVCF5H2ZEM35YBHZYEI3UILF/action/replication_record"}},"created_at":"2026-06-30T01:16:55.405912+00:00","updated_at":"2026-06-30T01:16:55.405912+00:00"}