{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YZB247X7MMNDEF5AWQDINVUN67","short_pith_number":"pith:YZB247X7","schema_version":"1.0","canonical_sha256":"c643ae7eff631a3217a0b40686d68df7d512b2c2c5ff2be6a799637c535886c1","source":{"kind":"arxiv","id":"1006.4776","version":2},"attestation_state":"computed","paper":{"title":"Skew Category Algebras Associated with Partially Defined Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Patrik Lundstr\\\"om","submitted_at":"2010-06-24T12:39:14Z","abstract_excerpt":"We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor $s$ from a category $G$ to $\\Top^{\\op}$ and show that it defines what we call a skew category algebra $A \\rtimes^{\\sigma} G$. We study the connection between topological freeness of $s$ and, on the one hand, ideal properties of $A \\rtimes^{\\sigma} G$ and, on the other hand, maximal commutativity of $A$ in $A \\rtimes^{\\sigma} G$. In particular, we show that if $G$ is a groupoid and for each $e \\in \\ob(G)$ the group of all morphisms $e \\rightarrow e$ is countable and the to"},"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":"1006.4776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-06-24T12:39:14Z","cross_cats_sorted":[],"title_canon_sha256":"708a8f24ac9629d66af8deb160cf07029c3b02fed22b39d7a89c00bb8b9ae84f","abstract_canon_sha256":"611165ca65b8be318dabee84f8632e8ee40028e58ecceba4a425558d4d8eec81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:09.390062Z","signature_b64":"FHVd47nmMC/SF0YI+os4IhBpzB6j4fMX53G0Lyr7i9FFov0qqzPLyiZZl4buzbHevd6gDfdbjp3poyf0havnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c643ae7eff631a3217a0b40686d68df7d512b2c2c5ff2be6a799637c535886c1","last_reissued_at":"2026-05-18T03:37:09.389298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:09.389298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew Category Algebras Associated with Partially Defined Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Patrik Lundstr\\\"om","submitted_at":"2010-06-24T12:39:14Z","abstract_excerpt":"We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor $s$ from a category $G$ to $\\Top^{\\op}$ and show that it defines what we call a skew category algebra $A \\rtimes^{\\sigma} G$. We study the connection between topological freeness of $s$ and, on the one hand, ideal properties of $A \\rtimes^{\\sigma} G$ and, on the other hand, maximal commutativity of $A$ in $A \\rtimes^{\\sigma} G$. In particular, we show that if $G$ is a groupoid and for each $e \\in \\ob(G)$ the group of all morphisms $e \\rightarrow e$ is countable and the to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4776","kind":"arxiv","version":2},"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":"1006.4776","created_at":"2026-05-18T03:37:09.389446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.4776v2","created_at":"2026-05-18T03:37:09.389446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4776","created_at":"2026-05-18T03:37:09.389446+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZB247X7MMND","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZB247X7MMNDEF5A","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZB247X7","created_at":"2026-05-18T12:26:17.028572+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/YZB247X7MMNDEF5AWQDINVUN67","json":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67.json","graph_json":"https://pith.science/api/pith-number/YZB247X7MMNDEF5AWQDINVUN67/graph.json","events_json":"https://pith.science/api/pith-number/YZB247X7MMNDEF5AWQDINVUN67/events.json","paper":"https://pith.science/paper/YZB247X7"},"agent_actions":{"view_html":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67","download_json":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67.json","view_paper":"https://pith.science/paper/YZB247X7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.4776&json=true","fetch_graph":"https://pith.science/api/pith-number/YZB247X7MMNDEF5AWQDINVUN67/graph.json","fetch_events":"https://pith.science/api/pith-number/YZB247X7MMNDEF5AWQDINVUN67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67/action/storage_attestation","attest_author":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67/action/author_attestation","sign_citation":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67/action/citation_signature","submit_replication":"https://pith.science/pith/YZB247X7MMNDEF5AWQDINVUN67/action/replication_record"}},"created_at":"2026-05-18T03:37:09.389446+00:00","updated_at":"2026-05-18T03:37:09.389446+00:00"}