{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WKGTCGNTKZ7EBX3SH4NPP4O4BK","short_pith_number":"pith:WKGTCGNT","schema_version":"1.0","canonical_sha256":"b28d3119b3567e40df723f1af7f1dc0aabb3910b26d1fcd5b326d1a933f0f17f","source":{"kind":"arxiv","id":"1209.5681","version":1},"attestation_state":"computed","paper":{"title":"Fractional Maps and Fractional Attractors. Part I: $\\alpha$-Families of Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"nlin.CD","authors_text":"Mark Edelman","submitted_at":"2012-09-25T16:49:46Z","abstract_excerpt":"In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential equation $\\alpha > 0$. We investigate general properties of such families and how they vary with the increase in $\\alpha$ which represents increase in the space dimension and the memory of a system (increase in the weights of the earlier states). To demonstrate general properties of the $\\alpha$-families we use examples from physics (Standard $\\alpha$-family of "},"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":"1209.5681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-09-25T16:49:46Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"43465a811c8ddb9cb4c0f8d8a4785b99042682c27962b7c305581f5a234afebd","abstract_canon_sha256":"9e10c7d127f8aae4913a1bee6b5ed66d737c81ecc31b9df29f8814310464e7f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:32.400782Z","signature_b64":"QFlbfyNKyA8xlAcOJ9NjQA242F7RyQtSfLiabKPL90SZ5CMBV8x05632naHcS8fqDhEMsKZUz++ebP2yq0zKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b28d3119b3567e40df723f1af7f1dc0aabb3910b26d1fcd5b326d1a933f0f17f","last_reissued_at":"2026-05-18T03:26:32.400190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:32.400190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional Maps and Fractional Attractors. Part I: $\\alpha$-Families of Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"nlin.CD","authors_text":"Mark Edelman","submitted_at":"2012-09-25T16:49:46Z","abstract_excerpt":"In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential equation $\\alpha > 0$. We investigate general properties of such families and how they vary with the increase in $\\alpha$ which represents increase in the space dimension and the memory of a system (increase in the weights of the earlier states). To demonstrate general properties of the $\\alpha$-families we use examples from physics (Standard $\\alpha$-family of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5681","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":"1209.5681","created_at":"2026-05-18T03:26:32.400284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.5681v1","created_at":"2026-05-18T03:26:32.400284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5681","created_at":"2026-05-18T03:26:32.400284+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKGTCGNTKZ7E","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKGTCGNTKZ7EBX3S","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKGTCGNT","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/WKGTCGNTKZ7EBX3SH4NPP4O4BK","json":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK.json","graph_json":"https://pith.science/api/pith-number/WKGTCGNTKZ7EBX3SH4NPP4O4BK/graph.json","events_json":"https://pith.science/api/pith-number/WKGTCGNTKZ7EBX3SH4NPP4O4BK/events.json","paper":"https://pith.science/paper/WKGTCGNT"},"agent_actions":{"view_html":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK","download_json":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK.json","view_paper":"https://pith.science/paper/WKGTCGNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.5681&json=true","fetch_graph":"https://pith.science/api/pith-number/WKGTCGNTKZ7EBX3SH4NPP4O4BK/graph.json","fetch_events":"https://pith.science/api/pith-number/WKGTCGNTKZ7EBX3SH4NPP4O4BK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK/action/storage_attestation","attest_author":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK/action/author_attestation","sign_citation":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK/action/citation_signature","submit_replication":"https://pith.science/pith/WKGTCGNTKZ7EBX3SH4NPP4O4BK/action/replication_record"}},"created_at":"2026-05-18T03:26:32.400284+00:00","updated_at":"2026-05-18T03:26:32.400284+00:00"}