{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OEQQ4WGIEQ25XAX6XVBLTBYYSW","short_pith_number":"pith:OEQQ4WGI","schema_version":"1.0","canonical_sha256":"71210e58c82435db82febd42b987189584c7d8c51e1805db4ee52f05bfac5552","source":{"kind":"arxiv","id":"1603.00667","version":2},"attestation_state":"computed","paper":{"title":"How sticky is the chaos/order boundary?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.CD","authors_text":"Carl P. Dettmann","submitted_at":"2016-03-02T11:55:25Z","abstract_excerpt":"In dynamical systems with divided phase space, the vicinity of the boundary between regular and chaotic regions is often \"sticky,\" that is, trapping orbits from the chaotic region for long times. Here, we investigate the stickiness in the simplest mushroom billiard, which has a smooth such boundary, but surprisingly subtle behaviour. As a measure of stickiness, we investigate P(t), the probability of remaining in the mushroom cap for at least time t given uniform initial conditions in the chaotic part of the cap. The stickiness is sensitively dependent on the radius of the stem r via the Dioph"},"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":"1603.00667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-03-02T11:55:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d69527c3c6608fdb30e25f3a47f179dd5949b806a38c87966a315240d8cf95e8","abstract_canon_sha256":"cd4bbfeb533bce09406da4a8769b2f72edca63457b4e7b128a59ea70fba052ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:35.437981Z","signature_b64":"n20/2WJlm+sS9xuQzNqEbzHvcDcU7DPt6xdLaGaSp0/ajOM4vXK/fZuMDGLFk4r/ZYNx5AE10J3vkLS51XxeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71210e58c82435db82febd42b987189584c7d8c51e1805db4ee52f05bfac5552","last_reissued_at":"2026-05-18T00:34:35.437391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:35.437391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How sticky is the chaos/order boundary?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.CD","authors_text":"Carl P. Dettmann","submitted_at":"2016-03-02T11:55:25Z","abstract_excerpt":"In dynamical systems with divided phase space, the vicinity of the boundary between regular and chaotic regions is often \"sticky,\" that is, trapping orbits from the chaotic region for long times. Here, we investigate the stickiness in the simplest mushroom billiard, which has a smooth such boundary, but surprisingly subtle behaviour. As a measure of stickiness, we investigate P(t), the probability of remaining in the mushroom cap for at least time t given uniform initial conditions in the chaotic part of the cap. The stickiness is sensitively dependent on the radius of the stem r via the Dioph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00667","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.00667","created_at":"2026-05-18T00:34:35.437469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00667v2","created_at":"2026-05-18T00:34:35.437469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00667","created_at":"2026-05-18T00:34:35.437469+00:00"},{"alias_kind":"pith_short_12","alias_value":"OEQQ4WGIEQ25","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OEQQ4WGIEQ25XAX6","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OEQQ4WGI","created_at":"2026-05-18T12:30:36.002864+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/OEQQ4WGIEQ25XAX6XVBLTBYYSW","json":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW.json","graph_json":"https://pith.science/api/pith-number/OEQQ4WGIEQ25XAX6XVBLTBYYSW/graph.json","events_json":"https://pith.science/api/pith-number/OEQQ4WGIEQ25XAX6XVBLTBYYSW/events.json","paper":"https://pith.science/paper/OEQQ4WGI"},"agent_actions":{"view_html":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW","download_json":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW.json","view_paper":"https://pith.science/paper/OEQQ4WGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00667&json=true","fetch_graph":"https://pith.science/api/pith-number/OEQQ4WGIEQ25XAX6XVBLTBYYSW/graph.json","fetch_events":"https://pith.science/api/pith-number/OEQQ4WGIEQ25XAX6XVBLTBYYSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW/action/storage_attestation","attest_author":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW/action/author_attestation","sign_citation":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW/action/citation_signature","submit_replication":"https://pith.science/pith/OEQQ4WGIEQ25XAX6XVBLTBYYSW/action/replication_record"}},"created_at":"2026-05-18T00:34:35.437469+00:00","updated_at":"2026-05-18T00:34:35.437469+00:00"}