{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DOG5DU2PEMX4LOMWJCLWQK5RQC","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f3fd1a7df2189fb2131ba0f43c2b352fad33ed6ec1f49c4d6af6c0bf195e8b57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-30T08:55:36Z","title_canon_sha256":"1ed0ae1da04804aecf53722e5b7e963ebfa80e489ebbf50eaa17085dcb383828"},"schema_version":"1.0","source":{"id":"2607.27880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27880","created_at":"2026-07-31T01:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27880v1","created_at":"2026-07-31T01:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27880","created_at":"2026-07-31T01:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"DOG5DU2PEMX4","created_at":"2026-07-31T01:34:32Z"},{"alias_kind":"pith_short_16","alias_value":"DOG5DU2PEMX4LOMW","created_at":"2026-07-31T01:34:32Z"},{"alias_kind":"pith_short_8","alias_value":"DOG5DU2P","created_at":"2026-07-31T01:34:32Z"}],"graph_snapshots":[{"event_id":"sha256:af9e87cb78606799fb8e54304ab0ebdad2e959bce1bd8680c629ae0db8fb31aa","target":"graph","created_at":"2026-07-31T01:34:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.27880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the aperiodic inverse-limit system constructed in our earlier work as an example of a finite-mean-dimensional dynamical system without the marker property. We prove that its mean dimension and Meyerovitch's dynamical dimension are both equal to $N$. Despite the absence of the marker property, the system admits an equivariant topological embedding into the cubical shift with alphabet dimension $3N+2$. As an auxiliary result, we prove that the dynamical dimension of the full shift over any compact metrizable alphabet is exactly the covering dimension of the alphabet, including when this","authors_text":"Ruxi Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-30T08:55:36Z","title":"Dynamical dimension and shift embeddability without the marker property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27880","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":"sha256:7612d5eab0ad0b901f4dc06b93457aae69bd7e72ec9136539337cbc3b35ff09e","target":"record","created_at":"2026-07-31T01:34:32Z","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":"f3fd1a7df2189fb2131ba0f43c2b352fad33ed6ec1f49c4d6af6c0bf195e8b57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-30T08:55:36Z","title_canon_sha256":"1ed0ae1da04804aecf53722e5b7e963ebfa80e489ebbf50eaa17085dcb383828"},"schema_version":"1.0","source":{"id":"2607.27880","kind":"arxiv","version":1}},"canonical_sha256":"1b8dd1d34f232fc5b9964897682bb18091508145806f9219e97bf8f8b0d74525","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b8dd1d34f232fc5b9964897682bb18091508145806f9219e97bf8f8b0d74525","first_computed_at":"2026-07-31T01:34:32.856901Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:34:32.856901Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7612d5eab0ad0b901f4dc06b93457aae69bd7e72ec9136539337cbc3b35ff09e","sha256:af9e87cb78606799fb8e54304ab0ebdad2e959bce1bd8680c629ae0db8fb31aa","sha256:e024dc399e7c85c9b84a54edbd516e4e787bf631e895c1a0a8bf650d73c34fd4"],"state_sha256":"505164ae7c3474bea29d7e8db73d23e601ed3c81c1b0e3ae869e8f009725f2af"}