{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VQDW6XFE4OHDNHFBDPO2BUPM4H","short_pith_number":"pith:VQDW6XFE","schema_version":"1.0","canonical_sha256":"ac076f5ca4e38e369ca11bdda0d1ece1df6c259b7a988367e16f16024e3271ab","source":{"kind":"arxiv","id":"1208.5437","version":1},"attestation_state":"computed","paper":{"title":"Positive topological entropy for multi-bump magnetic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Andreas Knauf, Frank Schulz, Karl Friedrich Siburg","submitted_at":"2012-08-27T16:35:04Z","abstract_excerpt":"We study the dynamics of a charged particle in a planar magnetic field which consists of $n\\geq 2$ disjoint localized peaks. We show that, under mild geometric conditions, this system is semi-conjugated to the full shift on $n$ symbols and, hence, carries positive topological entropy."},"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":"1208.5437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-27T16:35:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1612c94537f1e05b8e6191144cbef6e2598ef3b9e5e34953374d3d3e8675c763","abstract_canon_sha256":"af80e8c5b6ce168d38c809bd3baffa12fe6215b5999b8276b48638d8920920ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:57.725646Z","signature_b64":"2jBnd7uPrDL0TM4Fbmd3IVWfD7aW9Ctetrc1MkaaRDzcqQLUeJvKefGbGO+qwg5JNhUijcc5nH1sKrYbkq92CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac076f5ca4e38e369ca11bdda0d1ece1df6c259b7a988367e16f16024e3271ab","last_reissued_at":"2026-05-18T01:54:57.724949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:57.724949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive topological entropy for multi-bump magnetic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Andreas Knauf, Frank Schulz, Karl Friedrich Siburg","submitted_at":"2012-08-27T16:35:04Z","abstract_excerpt":"We study the dynamics of a charged particle in a planar magnetic field which consists of $n\\geq 2$ disjoint localized peaks. We show that, under mild geometric conditions, this system is semi-conjugated to the full shift on $n$ symbols and, hence, carries positive topological entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5437","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":"1208.5437","created_at":"2026-05-18T01:54:57.725043+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5437v1","created_at":"2026-05-18T01:54:57.725043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5437","created_at":"2026-05-18T01:54:57.725043+00:00"},{"alias_kind":"pith_short_12","alias_value":"VQDW6XFE4OHD","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VQDW6XFE4OHDNHFB","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VQDW6XFE","created_at":"2026-05-18T12:27:25.539911+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/VQDW6XFE4OHDNHFBDPO2BUPM4H","json":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H.json","graph_json":"https://pith.science/api/pith-number/VQDW6XFE4OHDNHFBDPO2BUPM4H/graph.json","events_json":"https://pith.science/api/pith-number/VQDW6XFE4OHDNHFBDPO2BUPM4H/events.json","paper":"https://pith.science/paper/VQDW6XFE"},"agent_actions":{"view_html":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H","download_json":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H.json","view_paper":"https://pith.science/paper/VQDW6XFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5437&json=true","fetch_graph":"https://pith.science/api/pith-number/VQDW6XFE4OHDNHFBDPO2BUPM4H/graph.json","fetch_events":"https://pith.science/api/pith-number/VQDW6XFE4OHDNHFBDPO2BUPM4H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H/action/storage_attestation","attest_author":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H/action/author_attestation","sign_citation":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H/action/citation_signature","submit_replication":"https://pith.science/pith/VQDW6XFE4OHDNHFBDPO2BUPM4H/action/replication_record"}},"created_at":"2026-05-18T01:54:57.725043+00:00","updated_at":"2026-05-18T01:54:57.725043+00:00"}