{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ESFRDOHQ5BT3WOTCU54LZAX5RF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f04cdefb82a5866bfb0efaf8265fc64209345efb5b8ecbb4cf0fd857d0c4dc1","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-06-16T16:29:20Z","title_canon_sha256":"efc324b3ae23a189fbc6fee1b4360c124318da9c4bd895fc70ac45e84b15796b"},"schema_version":"1.0","source":{"id":"1406.4059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4059","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4059v1","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4059","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"ESFRDOHQ5BT3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"ESFRDOHQ5BT3WOTC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"ESFRDOHQ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:00135754e022b0cfab1bd833d09702cf21b8dffa99f660afa46d96a71c4c52f6","target":"graph","created_at":"2026-05-18T00:11:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper the author compares behaviors of systems which can be described by fractional differential and fractional difference equations using the fractional and fractional difference Caputo Standard $\\alpha$-Families of Maps as examples. The author shows that properties of fractional difference maps (systems with falling factorial-law memory) are similar to the properties of fractional maps (systems with power-law memory). The similarities (types of attractors, power-law convergence of trajectories, existence of cascade of bifurcations and intermittent cascade of bifurcations type traject","authors_text":"Mark Edelman","cross_cats":["physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-06-16T16:29:20Z","title":"Caputo Standard $\\alpha$-Family of Maps: Fractional Difference vs. Fractional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4059","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fb2b3724c4c2a02de9485811a90872b6ccdd3cd127d38d0f5e486b0d770b8c1a","target":"record","created_at":"2026-05-18T00:11:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1f04cdefb82a5866bfb0efaf8265fc64209345efb5b8ecbb4cf0fd857d0c4dc1","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-06-16T16:29:20Z","title_canon_sha256":"efc324b3ae23a189fbc6fee1b4360c124318da9c4bd895fc70ac45e84b15796b"},"schema_version":"1.0","source":{"id":"1406.4059","kind":"arxiv","version":1}},"canonical_sha256":"248b11b8f0e867bb3a62a778bc82fd8949f67499443b84fa02b825aa0697a657","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"248b11b8f0e867bb3a62a778bc82fd8949f67499443b84fa02b825aa0697a657","first_computed_at":"2026-05-18T00:11:29.113112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:29.113112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uv2mEqTaPoB6Y2RkN4M4abTdwbGAoH5oZlgBi6sR7eTs2xNwuRSja9jjSwwSKy2lyKjhQzaxJTgMdEgLYDTtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:29.113487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb2b3724c4c2a02de9485811a90872b6ccdd3cd127d38d0f5e486b0d770b8c1a","sha256:00135754e022b0cfab1bd833d09702cf21b8dffa99f660afa46d96a71c4c52f6"],"state_sha256":"dc842aa1708ac596db37a7b5aa644f0fd4d054f5012867dcd9d11bcc723c2732"}