{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CA4JUIBOFP2DVCBKKT2OJJB3TT","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":"09116fa1e8c50adef22781e6c60d548be6873875bfe50bf0d2f092ccdefd590c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-09T17:07:06Z","title_canon_sha256":"93141d0e7ac62c36c7be28ecbd72be76cab0e4171eeda26b37d2838fb01192ce"},"schema_version":"1.0","source":{"id":"1811.04013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04013","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04013v1","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04013","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"CA4JUIBOFP2D","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CA4JUIBOFP2DVCBK","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CA4JUIBO","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:2bcb3fb7448691b4454851b5871077488fffafaf1d3350f840bb5e58ee188919","target":"graph","created_at":"2026-05-18T00:01:11Z","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":"A major motivation for the development of semigroup theory was, and still is, its applications to the study of formal languages. Therefore, it is not surprising that the correspondence $\\mathcal X\\mapsto B(\\mathcal X)$, associating to each symbolic dynamical system $\\mathcal X$ the formal language $B(\\mathcal X)$ of its blocks, entails a connection between symbolic dynamics and semigroup theory. In this article we survey some developments on this connection, since when it was noticed in an article by Almeida, published in the CIM bulletin, in 2003.","authors_text":"Alfredo Costa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-09T17:07:06Z","title":"Symbolic dynamics and semigroup theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04013","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:d49c72ef7c141c80573ed22f7d2a1daee2f843c08552bb11b7c1efff30553bcb","target":"record","created_at":"2026-05-18T00:01:11Z","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":"09116fa1e8c50adef22781e6c60d548be6873875bfe50bf0d2f092ccdefd590c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-09T17:07:06Z","title_canon_sha256":"93141d0e7ac62c36c7be28ecbd72be76cab0e4171eeda26b37d2838fb01192ce"},"schema_version":"1.0","source":{"id":"1811.04013","kind":"arxiv","version":1}},"canonical_sha256":"10389a202e2bf43a882a54f4e4a43b9cda2ad0e3f5f2280264931a84e6789b24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10389a202e2bf43a882a54f4e4a43b9cda2ad0e3f5f2280264931a84e6789b24","first_computed_at":"2026-05-18T00:01:11.296897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:11.296897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MuyQm9eO43omVvKDQOqiK7/dNvuSNPbv7kbVz1w7APjIeE80VsLOLOaWtqV3Lxv/Jvgtx0ccfC6wNfVs/BWiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:11.297467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d49c72ef7c141c80573ed22f7d2a1daee2f843c08552bb11b7c1efff30553bcb","sha256:2bcb3fb7448691b4454851b5871077488fffafaf1d3350f840bb5e58ee188919"],"state_sha256":"3cbeb869a8e0807802b29d4c6f001777330592a1e711b314d7f7cbe969deb8a9"}