{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:B6CZ3ZQWG67IMBFYTVMM6N2KYE","short_pith_number":"pith:B6CZ3ZQW","schema_version":"1.0","canonical_sha256":"0f859de61637be8604b89d58cf374ac101d2c338f4b72e2b83d1362ecee5efad","source":{"kind":"arxiv","id":"1304.7529","version":1},"attestation_state":"computed","paper":{"title":"Micro and Macro Fractals generated by multi-valued dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.GN","authors_text":"Natalia Novosad, Taras Banakh","submitted_at":"2013-04-28T22:11:18Z","abstract_excerpt":"Given a multi-valued function $\\Phi$ on a topological space $X$ we study the properties of its fixed fractal, which is defined as the closure of the orbit $\\Phi^\\omega(Fix(\\Phi))=\\bigcup_{n\\in\\omega}\\Phi^n(Fix(\\Phi))$ of the set $Fix(\\Phi)=\\{x\\in X:x\\in\\Phi(x)\\}$ of fixed points of $\\Phi$. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals for a contracting compact-valued function $\\Phi$ on a complete metric space $X$ and its inverse multi-function $\\Phi^{-1}$. With help of algorithms (described in this paper) we generate various imag"},"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":"1304.7529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-04-28T22:11:18Z","cross_cats_sorted":["math.DS","math.MG"],"title_canon_sha256":"27b348f3f9e296437245b8b931e8f3bbadc4730e7a3f30965c0e0424dee01265","abstract_canon_sha256":"84c84e920d54bf78f7d49bf499f783da429faa061290b79e267605336b7e6f70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:14.457733Z","signature_b64":"1tOLN9IjTvfwW+OEk46NeIlvNaaQ5J7QhvFHXEHl7iXmp5nMd6YtixH26bUPFMyRmyYnhSOLy+tqOdhFUpwyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f859de61637be8604b89d58cf374ac101d2c338f4b72e2b83d1362ecee5efad","last_reissued_at":"2026-05-18T02:32:14.457031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:14.457031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Micro and Macro Fractals generated by multi-valued dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.GN","authors_text":"Natalia Novosad, Taras Banakh","submitted_at":"2013-04-28T22:11:18Z","abstract_excerpt":"Given a multi-valued function $\\Phi$ on a topological space $X$ we study the properties of its fixed fractal, which is defined as the closure of the orbit $\\Phi^\\omega(Fix(\\Phi))=\\bigcup_{n\\in\\omega}\\Phi^n(Fix(\\Phi))$ of the set $Fix(\\Phi)=\\{x\\in X:x\\in\\Phi(x)\\}$ of fixed points of $\\Phi$. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals for a contracting compact-valued function $\\Phi$ on a complete metric space $X$ and its inverse multi-function $\\Phi^{-1}$. With help of algorithms (described in this paper) we generate various imag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7529","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":"1304.7529","created_at":"2026-05-18T02:32:14.457142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7529v1","created_at":"2026-05-18T02:32:14.457142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7529","created_at":"2026-05-18T02:32:14.457142+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6CZ3ZQWG67I","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6CZ3ZQWG67IMBFY","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6CZ3ZQW","created_at":"2026-05-18T12:27:38.830355+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/B6CZ3ZQWG67IMBFYTVMM6N2KYE","json":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE.json","graph_json":"https://pith.science/api/pith-number/B6CZ3ZQWG67IMBFYTVMM6N2KYE/graph.json","events_json":"https://pith.science/api/pith-number/B6CZ3ZQWG67IMBFYTVMM6N2KYE/events.json","paper":"https://pith.science/paper/B6CZ3ZQW"},"agent_actions":{"view_html":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE","download_json":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE.json","view_paper":"https://pith.science/paper/B6CZ3ZQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7529&json=true","fetch_graph":"https://pith.science/api/pith-number/B6CZ3ZQWG67IMBFYTVMM6N2KYE/graph.json","fetch_events":"https://pith.science/api/pith-number/B6CZ3ZQWG67IMBFYTVMM6N2KYE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE/action/storage_attestation","attest_author":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE/action/author_attestation","sign_citation":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE/action/citation_signature","submit_replication":"https://pith.science/pith/B6CZ3ZQWG67IMBFYTVMM6N2KYE/action/replication_record"}},"created_at":"2026-05-18T02:32:14.457142+00:00","updated_at":"2026-05-18T02:32:14.457142+00:00"}