{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2M27LSFILWTXJRBPTMK3UU2JB4","short_pith_number":"pith:2M27LSFI","schema_version":"1.0","canonical_sha256":"d335f5c8a85da774c42f9b15ba53490f105f2115e7743442734605be831d5df8","source":{"kind":"arxiv","id":"1510.04930","version":4},"attestation_state":"computed","paper":{"title":"Linear sequential dynamical systems, incidence algebras, and M\\\"{o}bius functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Ricky X. F. Chen","submitted_at":"2015-10-16T16:20:43Z","abstract_excerpt":"A sequential dynamical system (SDS) consists of a graph, a set of local functions and an update schedule. A linear sequential dynamical system is an SDS whose local functions are linear. In this paper, we derive an explicit closed formula for any linear SDS as a synchronous dynamical system. We also show constructively, that any synchronous linear system can be expressed as a linear SDS, i.e. it can be written as a product of linear local functions. Furthermore, we study the connection between linear SDS and the incidence algebras of partially ordered sets (posets). Specifically, we show that "},"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":"1510.04930","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-16T16:20:43Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"bb0bf86392e09eeab3f3a423c77a172e3d655cc27addbf520edb07f87fd04d64","abstract_canon_sha256":"1ee07193d9d9545b88e862a58818cc97612ddfe5f241fddbc294e156987e3586"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:42.454671Z","signature_b64":"0ACvfdx5HrUBDgRBsk3ZfkKj8EA8TU8ECPVu6jBm3rg4Lu/sAPmZehT3Ai7dcEm2mQIrgnB+PabqU22qgUDoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d335f5c8a85da774c42f9b15ba53490f105f2115e7743442734605be831d5df8","last_reissued_at":"2026-05-18T00:15:42.454117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:42.454117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear sequential dynamical systems, incidence algebras, and M\\\"{o}bius functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Ricky X. F. Chen","submitted_at":"2015-10-16T16:20:43Z","abstract_excerpt":"A sequential dynamical system (SDS) consists of a graph, a set of local functions and an update schedule. A linear sequential dynamical system is an SDS whose local functions are linear. In this paper, we derive an explicit closed formula for any linear SDS as a synchronous dynamical system. We also show constructively, that any synchronous linear system can be expressed as a linear SDS, i.e. it can be written as a product of linear local functions. Furthermore, we study the connection between linear SDS and the incidence algebras of partially ordered sets (posets). Specifically, we show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04930","kind":"arxiv","version":4},"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":"1510.04930","created_at":"2026-05-18T00:15:42.454217+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04930v4","created_at":"2026-05-18T00:15:42.454217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04930","created_at":"2026-05-18T00:15:42.454217+00:00"},{"alias_kind":"pith_short_12","alias_value":"2M27LSFILWTX","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2M27LSFILWTXJRBP","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2M27LSFI","created_at":"2026-05-18T12:29:02.477457+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/2M27LSFILWTXJRBPTMK3UU2JB4","json":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4.json","graph_json":"https://pith.science/api/pith-number/2M27LSFILWTXJRBPTMK3UU2JB4/graph.json","events_json":"https://pith.science/api/pith-number/2M27LSFILWTXJRBPTMK3UU2JB4/events.json","paper":"https://pith.science/paper/2M27LSFI"},"agent_actions":{"view_html":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4","download_json":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4.json","view_paper":"https://pith.science/paper/2M27LSFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04930&json=true","fetch_graph":"https://pith.science/api/pith-number/2M27LSFILWTXJRBPTMK3UU2JB4/graph.json","fetch_events":"https://pith.science/api/pith-number/2M27LSFILWTXJRBPTMK3UU2JB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4/action/storage_attestation","attest_author":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4/action/author_attestation","sign_citation":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4/action/citation_signature","submit_replication":"https://pith.science/pith/2M27LSFILWTXJRBPTMK3UU2JB4/action/replication_record"}},"created_at":"2026-05-18T00:15:42.454217+00:00","updated_at":"2026-05-18T00:15:42.454217+00:00"}