{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TYN3HEAFCJIG6HTJPKNFW5YKJH","short_pith_number":"pith:TYN3HEAF","canonical_record":{"source":{"id":"1401.0048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-12-30T22:56:30Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"c23004e4e024f58da37ca975df5e36de93deed2609a402ef8cdf411bc1edcadd","abstract_canon_sha256":"a4928416e7be79bbb8fc6905f70f34beb69e6f2dae966abe223034abebf3a9fb"},"schema_version":"1.0"},"canonical_sha256":"9e1bb3900512506f1e697a9a5b770a49d6809f1add360ee3332d9c8bb2b4aee7","source":{"kind":"arxiv","id":"1401.0048","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0048","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0048v1","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0048","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"TYN3HEAFCJIG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TYN3HEAFCJIG6HTJ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TYN3HEAF","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TYN3HEAFCJIG6HTJPKNFW5YKJH","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-12-30T22:56:30Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"c23004e4e024f58da37ca975df5e36de93deed2609a402ef8cdf411bc1edcadd","abstract_canon_sha256":"a4928416e7be79bbb8fc6905f70f34beb69e6f2dae966abe223034abebf3a9fb"},"schema_version":"1.0"},"canonical_sha256":"9e1bb3900512506f1e697a9a5b770a49d6809f1add360ee3332d9c8bb2b4aee7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:29.141274Z","signature_b64":"O5mIot0XG8DgOuwo9UKsm4agDX4YWZ4RnEY0HtafrJJAjYr0uNDtmZuRX3Hmz5V9/6wZBi6+qHaTKZQg29aMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e1bb3900512506f1e697a9a5b770a49d6809f1add360ee3332d9c8bb2b4aee7","last_reissued_at":"2026-05-18T00:11:29.140904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:29.140904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0048","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":"2026-05-18T00:11:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MWQZHLA4pwe6UZrdUZbgMCpILeRDujg304iLiUy/gfQmb4EmRqfRPl4aLDSNr2S6senBRg229KOQXQUvdRBeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:28:10.256422Z"},"content_sha256":"f4ca6a460b7d3b4f1a5de23a07ce15468e31d16227f2ee727a803045b3b66ff3","schema_version":"1.0","event_id":"sha256:f4ca6a460b7d3b4f1a5de23a07ce15468e31d16227f2ee727a803045b3b66ff3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TYN3HEAFCJIG6HTJPKNFW5YKJH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Dynamical Systems","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":"2013-12-30T22:56:30Z","abstract_excerpt":"In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing systems experiencing periodic kicks. Their properties depend on the value of two parameters: the non-linearity parameter, which arises from the corresponding regular dynamical systems; and the memory parameter which is the order of the fractional derivative in the corresponding non-linear fractional differential equations. The examples of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0048","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":"2026-05-18T00:11:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLzDFWswMvcPtZHww2gmp4ypqijbb+VQ/+BFUVBSA9zqx8oquB0+S94yEt+BGQz3Dg5wb2mgovf6EZxlR1v2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:28:10.256765Z"},"content_sha256":"e63e52dfe72483073fc0abfa7cd09a181816e068ab22cb7f81c527394f836641","schema_version":"1.0","event_id":"sha256:e63e52dfe72483073fc0abfa7cd09a181816e068ab22cb7f81c527394f836641"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH/bundle.json","state_url":"https://pith.science/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH/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":"2026-06-27T15:28:10Z","links":{"resolver":"https://pith.science/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH","bundle":"https://pith.science/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH/bundle.json","state":"https://pith.science/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYN3HEAFCJIG6HTJPKNFW5YKJH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TYN3HEAFCJIG6HTJPKNFW5YKJH","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":"a4928416e7be79bbb8fc6905f70f34beb69e6f2dae966abe223034abebf3a9fb","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-12-30T22:56:30Z","title_canon_sha256":"c23004e4e024f58da37ca975df5e36de93deed2609a402ef8cdf411bc1edcadd"},"schema_version":"1.0","source":{"id":"1401.0048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0048","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0048v1","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0048","created_at":"2026-05-18T00:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"TYN3HEAFCJIG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TYN3HEAFCJIG6HTJ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TYN3HEAF","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:e63e52dfe72483073fc0abfa7cd09a181816e068ab22cb7f81c527394f836641","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 presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing systems experiencing periodic kicks. Their properties depend on the value of two parameters: the non-linearity parameter, which arises from the corresponding regular dynamical systems; and the memory parameter which is the order of the fractional derivative in the corresponding non-linear fractional differential equations. The examples of the","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":"2013-12-30T22:56:30Z","title":"Fractional Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0048","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:f4ca6a460b7d3b4f1a5de23a07ce15468e31d16227f2ee727a803045b3b66ff3","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":"a4928416e7be79bbb8fc6905f70f34beb69e6f2dae966abe223034abebf3a9fb","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-12-30T22:56:30Z","title_canon_sha256":"c23004e4e024f58da37ca975df5e36de93deed2609a402ef8cdf411bc1edcadd"},"schema_version":"1.0","source":{"id":"1401.0048","kind":"arxiv","version":1}},"canonical_sha256":"9e1bb3900512506f1e697a9a5b770a49d6809f1add360ee3332d9c8bb2b4aee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e1bb3900512506f1e697a9a5b770a49d6809f1add360ee3332d9c8bb2b4aee7","first_computed_at":"2026-05-18T00:11:29.140904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:29.140904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5mIot0XG8DgOuwo9UKsm4agDX4YWZ4RnEY0HtafrJJAjYr0uNDtmZuRX3Hmz5V9/6wZBi6+qHaTKZQg29aMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:29.141274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4ca6a460b7d3b4f1a5de23a07ce15468e31d16227f2ee727a803045b3b66ff3","sha256:e63e52dfe72483073fc0abfa7cd09a181816e068ab22cb7f81c527394f836641"],"state_sha256":"bc38259bd5ba6aa4f4bf6bef9d720b89acad8b31f5107f35e5e36bbcf505a1f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auk5w9QqI5L4Rwm5JHPl0X9AHCu4fjZiw50wR9rtE8XfQ6pjR6rHrb9sbt6sE0H99OUyW2YrFfMI+2eIynDbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:28:10.258631Z","bundle_sha256":"972712cfb13740ba6c92f6ff0a882c7b17d8d16ace90f173a6c8a9156b62c97b"}}