{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NR774WXKZQV4B7CMAQF44V2CJK","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":"21e31ddc81dae6c8c7ae67d86b59d7ca239033e59fb8a61e7bd9062d6ff42a8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T09:17:15Z","title_canon_sha256":"8202f8f7ddc50d70a0ce87a32f3cb0f32f09e99a642a7bec96fa24eed2d322b9"},"schema_version":"1.0","source":{"id":"1703.02288","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02288","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02288v2","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02288","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"NR774WXKZQV4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NR774WXKZQV4B7CM","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NR774WXK","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:5c52a4c0c68e89c0bb05c1dd18501f0e468435967abb448fc23731199ab849be","target":"graph","created_at":"2026-05-18T00:09:53Z","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 the following text we introduce specification property (stroboscopical property) for dynamical systems on uniform space. We focus on two classes of dynamical systems: generalized shifts and dynamical systems with Alexandroff compactification of a discrete space as phase space. We prove that for a discrete finite topological space $X$ with at least two elements, a nonempty set $\\Gamma$ and a self--map $\\varphi:\\Gamma\\to\\Gamma$ the generalized shift dynamical system $(X^\\Gamma,\\sigma_\\varphi)$: \\begin{itemize} \\item has (almost) weak specification property if and only if $\\varphi:\\Gamma\\to\\Ga","authors_text":"Bahman Taherkhani, Fatemah Ayatollah Zadeh Shirazi, Khosro Tajbakhsh, Zahra Nili Ahmadabadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T09:17:15Z","title":"Specification properties on uniform spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02288","kind":"arxiv","version":2},"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:acfd01b60a0c819154fb413e28b0c87034423c0302b592cafc83ef509de4ae7d","target":"record","created_at":"2026-05-18T00:09:53Z","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":"21e31ddc81dae6c8c7ae67d86b59d7ca239033e59fb8a61e7bd9062d6ff42a8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T09:17:15Z","title_canon_sha256":"8202f8f7ddc50d70a0ce87a32f3cb0f32f09e99a642a7bec96fa24eed2d322b9"},"schema_version":"1.0","source":{"id":"1703.02288","kind":"arxiv","version":2}},"canonical_sha256":"6c7ffe5aeacc2bc0fc4c040bce57424aac27499265db49bb4c2af022fcf7d8e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c7ffe5aeacc2bc0fc4c040bce57424aac27499265db49bb4c2af022fcf7d8e7","first_computed_at":"2026-05-18T00:09:53.161455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:53.161455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hG8NG2lndmlE1tepBGKAeSr/jx7PQitYZc5iamstrkrCHzuefC3Vhu+SKuewhxx+D1FLbfkDq2KTIqARkXWeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:53.162115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02288","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acfd01b60a0c819154fb413e28b0c87034423c0302b592cafc83ef509de4ae7d","sha256:5c52a4c0c68e89c0bb05c1dd18501f0e468435967abb448fc23731199ab849be"],"state_sha256":"1d854debe191c07d6f4b8e3d167898d6cefc7567e31cc45fa10f18d3da1c3dec"}