{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EJVVSHFUOFATCUVX7PLP4CRI7Z","short_pith_number":"pith:EJVVSHFU","canonical_record":{"source":{"id":"1306.6361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-06-26T21:02:55Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"4aa5175b115f8194ac2def953301fda6fbc16b2e61b9a63b482fd8b6f4ee6902","abstract_canon_sha256":"e32090b8a48898bceeaca221b9ca0b77bf4ffb27bfa695d86a8af5e23fb17a91"},"schema_version":"1.0"},"canonical_sha256":"226b591cb471413152b7fbd6fe0a28fe4a61d1618dec2f8ff3a94460a44b5aa9","source":{"kind":"arxiv","id":"1306.6361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6361","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6361v1","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6361","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"EJVVSHFUOFAT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EJVVSHFUOFATCUVX","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EJVVSHFU","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EJVVSHFUOFATCUVX7PLP4CRI7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1306.6361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-06-26T21:02:55Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"4aa5175b115f8194ac2def953301fda6fbc16b2e61b9a63b482fd8b6f4ee6902","abstract_canon_sha256":"e32090b8a48898bceeaca221b9ca0b77bf4ffb27bfa695d86a8af5e23fb17a91"},"schema_version":"1.0"},"canonical_sha256":"226b591cb471413152b7fbd6fe0a28fe4a61d1618dec2f8ff3a94460a44b5aa9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.279663Z","signature_b64":"yxnrx9Ic6j7n6sccOhzV+ssGwuMJ7qODPdKsoEk9yGZxwRFp6D8wTBE7G9mMwBXq0T/Ex6mEQFgeICfSDc5vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"226b591cb471413152b7fbd6fe0a28fe4a61d1618dec2f8ff3a94460a44b5aa9","last_reissued_at":"2026-05-18T02:51:42.279210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.279210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.6361","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vcfPRNGdxcNjcdrMl+Q1WdBOVQUr40gg+GEFa8TZpQxUwvY5LBrISmwobjfNhOGRNdZkc7fNcyH+6OP1YH3rAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:27:52.471980Z"},"content_sha256":"6e89021f765a3f93b6c32e62a38731804f30552d5b79c3cf6053b0d9c181afe4","schema_version":"1.0","event_id":"sha256:6e89021f765a3f93b6c32e62a38731804f30552d5b79c3cf6053b0d9c181afe4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EJVVSHFUOFATCUVX7PLP4CRI7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Maps as Maps with Power-Law Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"nlin.CD","authors_text":"Mark Edelman","submitted_at":"2013-06-26T21:02:55Z","abstract_excerpt":"The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are integro-differential equations. To study the general properties of nonlinear fractional dynamical systems we use fractional maps, which are discrete nonlinear systems with power-law memory derived from fractional differential equations. To study fractional maps we use the notion of $\\alpha$-families of maps depending on a single parameter $\\alpha > 0$ which is the order of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6361","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNB7y6qoinuazO/0AzZ+62sbzgPEp10CbwaSyRXsijv/VbsAyIrCRTRAp/cQ7XUuWgSrb1+1LuCNgvwmIrPMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:27:52.472326Z"},"content_sha256":"a97d57a91bfa3f2d14925d9f8ccf9cd9b8a192ead64aa203e870ee4f56d2e812","schema_version":"1.0","event_id":"sha256:a97d57a91bfa3f2d14925d9f8ccf9cd9b8a192ead64aa203e870ee4f56d2e812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z/bundle.json","state_url":"https://pith.science/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T15:27:52Z","links":{"resolver":"https://pith.science/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z","bundle":"https://pith.science/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z/bundle.json","state":"https://pith.science/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJVVSHFUOFATCUVX7PLP4CRI7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EJVVSHFUOFATCUVX7PLP4CRI7Z","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":"e32090b8a48898bceeaca221b9ca0b77bf4ffb27bfa695d86a8af5e23fb17a91","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-06-26T21:02:55Z","title_canon_sha256":"4aa5175b115f8194ac2def953301fda6fbc16b2e61b9a63b482fd8b6f4ee6902"},"schema_version":"1.0","source":{"id":"1306.6361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6361","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6361v1","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6361","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"EJVVSHFUOFAT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EJVVSHFUOFATCUVX","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EJVVSHFU","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:a97d57a91bfa3f2d14925d9f8ccf9cd9b8a192ead64aa203e870ee4f56d2e812","target":"graph","created_at":"2026-05-18T02:51:42Z","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":"The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are integro-differential equations. To study the general properties of nonlinear fractional dynamical systems we use fractional maps, which are discrete nonlinear systems with power-law memory derived from fractional differential equations. To study fractional maps we use the notion of $\\alpha$-families of maps depending on a single parameter $\\alpha > 0$ which is the order of th","authors_text":"Mark Edelman","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-06-26T21:02:55Z","title":"Fractional Maps as Maps with Power-Law Memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6361","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":"sha256:6e89021f765a3f93b6c32e62a38731804f30552d5b79c3cf6053b0d9c181afe4","target":"record","created_at":"2026-05-18T02:51:42Z","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":"e32090b8a48898bceeaca221b9ca0b77bf4ffb27bfa695d86a8af5e23fb17a91","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-06-26T21:02:55Z","title_canon_sha256":"4aa5175b115f8194ac2def953301fda6fbc16b2e61b9a63b482fd8b6f4ee6902"},"schema_version":"1.0","source":{"id":"1306.6361","kind":"arxiv","version":1}},"canonical_sha256":"226b591cb471413152b7fbd6fe0a28fe4a61d1618dec2f8ff3a94460a44b5aa9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"226b591cb471413152b7fbd6fe0a28fe4a61d1618dec2f8ff3a94460a44b5aa9","first_computed_at":"2026-05-18T02:51:42.279210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.279210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxnrx9Ic6j7n6sccOhzV+ssGwuMJ7qODPdKsoEk9yGZxwRFp6D8wTBE7G9mMwBXq0T/Ex6mEQFgeICfSDc5vAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.279663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e89021f765a3f93b6c32e62a38731804f30552d5b79c3cf6053b0d9c181afe4","sha256:a97d57a91bfa3f2d14925d9f8ccf9cd9b8a192ead64aa203e870ee4f56d2e812"],"state_sha256":"0f8fb0ff35b08ff4c66615a1ad2357c80a45dc211e63a783b284dfceb288e34c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RiuRQKHXHE9hjfhKYfoCeIBQ5gm/dCRTT/TTqOYeam9fhmlN1Q8B676yCRlvkpZUlMOgd0xO+gyglIsUDYA2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:27:52.474113Z","bundle_sha256":"9001621d5fff55da7b4e588cef1f10d338883e0b743f88410ec93cbd64e07877"}}