{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZJNBLY7CCENLZBCK2MFSFCHHYO","short_pith_number":"pith:ZJNBLY7C","schema_version":"1.0","canonical_sha256":"ca5a15e3e2111abc844ad30b2288e7c3bac527dbd584e5e3b81c16d07a62413d","source":{"kind":"arxiv","id":"1310.5417","version":1},"attestation_state":"computed","paper":{"title":"Strange Attractors for Asymptotically Zero Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Denis Blackmore, Yogesh Joshi","submitted_at":"2013-10-21T04:20:32Z","abstract_excerpt":"A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional hypotheses are sufficient to guarantee that A has a minimal (invariant) subset A* that is a chaotic strange attractor is answered in detail for a few types of asymptotically zero maps. These special cases happen to have many applications (especially as mathematical models for a variety of processes in ecological and population dynamics), some of which are pr"},"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":"1310.5417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-21T04:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"a63bcb250d14b61cfbc0bb55404d5dab137a0207cb48016ca512f6d04781fbf9","abstract_canon_sha256":"68d54c54a30016c9cb7eb0d4bd7b42a4e1832002c048eb064055054d78f91f48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:57.241782Z","signature_b64":"QSstr8YHMuoA4ek5xAMuXkZaMXWAXa2nzWxyKbkw8GW4IasLP1I6/UuMIgHEX1p78mmF+bm2emDifuSB8N2XAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca5a15e3e2111abc844ad30b2288e7c3bac527dbd584e5e3b81c16d07a62413d","last_reissued_at":"2026-05-18T01:46:57.241010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:57.241010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strange Attractors for Asymptotically Zero Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Denis Blackmore, Yogesh Joshi","submitted_at":"2013-10-21T04:20:32Z","abstract_excerpt":"A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional hypotheses are sufficient to guarantee that A has a minimal (invariant) subset A* that is a chaotic strange attractor is answered in detail for a few types of asymptotically zero maps. These special cases happen to have many applications (especially as mathematical models for a variety of processes in ecological and population dynamics), some of which are pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5417","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":"1310.5417","created_at":"2026-05-18T01:46:57.241126+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5417v1","created_at":"2026-05-18T01:46:57.241126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5417","created_at":"2026-05-18T01:46:57.241126+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZJNBLY7CCENL","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZJNBLY7CCENLZBCK","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZJNBLY7C","created_at":"2026-05-18T12:28:09.283467+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/ZJNBLY7CCENLZBCK2MFSFCHHYO","json":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO.json","graph_json":"https://pith.science/api/pith-number/ZJNBLY7CCENLZBCK2MFSFCHHYO/graph.json","events_json":"https://pith.science/api/pith-number/ZJNBLY7CCENLZBCK2MFSFCHHYO/events.json","paper":"https://pith.science/paper/ZJNBLY7C"},"agent_actions":{"view_html":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO","download_json":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO.json","view_paper":"https://pith.science/paper/ZJNBLY7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5417&json=true","fetch_graph":"https://pith.science/api/pith-number/ZJNBLY7CCENLZBCK2MFSFCHHYO/graph.json","fetch_events":"https://pith.science/api/pith-number/ZJNBLY7CCENLZBCK2MFSFCHHYO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO/action/storage_attestation","attest_author":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO/action/author_attestation","sign_citation":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO/action/citation_signature","submit_replication":"https://pith.science/pith/ZJNBLY7CCENLZBCK2MFSFCHHYO/action/replication_record"}},"created_at":"2026-05-18T01:46:57.241126+00:00","updated_at":"2026-05-18T01:46:57.241126+00:00"}