{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2AJS64QGRGK5HUB7FJB6MA2WZL","short_pith_number":"pith:2AJS64QG","schema_version":"1.0","canonical_sha256":"d0132f72068995d3d03f2a43e60356cafec8baf8426b7bcf7b4bd160c67fe357","source":{"kind":"arxiv","id":"1509.01273","version":1},"attestation_state":"computed","paper":{"title":"Subshifts with Slowly Growing Numbers of Follower Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nic Ormes, Ronnie Pavlov, Thomas French","submitted_at":"2015-09-03T20:39:07Z","abstract_excerpt":"For any subshift, define $F_X(n)$ to be the collection of distinct follower sets of words of length $n$ in $X$. Based on a similar result of the second and third authors, we conjecture that if there exists an $n$ for which $|F_X(n)| \\leq n$, then $X$ is sofic. In this paper, we prove several results related to this conjecture, including verifying it for $n \\leq 3$, proving that the conjecture is true for a large class of coded subshifts, and showing that if there exists $n$ for which $|F_X(n)| \\leq \\log_2(n+1)$, then $X$ is sofic."},"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":"1509.01273","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-03T20:39:07Z","cross_cats_sorted":[],"title_canon_sha256":"12865f9d2f6bd866a88c4218c21dac03264ec39e6b1f6345ad8a5fe1b5428b11","abstract_canon_sha256":"1584da9499dd12e39b4cac0f470881cd5893d94c01fa7cce025e4a029ce6b931"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:59.024005Z","signature_b64":"oifYpvRUHlc3l/rnbcgKDJBlzq0vRAn0cKt8zeP1NbFLA3Z/W/tGWGFj78an2WYbUr5cc6iJMFBAdE/qBMscAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0132f72068995d3d03f2a43e60356cafec8baf8426b7bcf7b4bd160c67fe357","last_reissued_at":"2026-05-18T01:33:59.023351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:59.023351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subshifts with Slowly Growing Numbers of Follower Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nic Ormes, Ronnie Pavlov, Thomas French","submitted_at":"2015-09-03T20:39:07Z","abstract_excerpt":"For any subshift, define $F_X(n)$ to be the collection of distinct follower sets of words of length $n$ in $X$. Based on a similar result of the second and third authors, we conjecture that if there exists an $n$ for which $|F_X(n)| \\leq n$, then $X$ is sofic. In this paper, we prove several results related to this conjecture, including verifying it for $n \\leq 3$, proving that the conjecture is true for a large class of coded subshifts, and showing that if there exists $n$ for which $|F_X(n)| \\leq \\log_2(n+1)$, then $X$ is sofic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01273","kind":"arxiv","version":1},"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":"1509.01273","created_at":"2026-05-18T01:33:59.023442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01273v1","created_at":"2026-05-18T01:33:59.023442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01273","created_at":"2026-05-18T01:33:59.023442+00:00"},{"alias_kind":"pith_short_12","alias_value":"2AJS64QGRGK5","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2AJS64QGRGK5HUB7","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2AJS64QG","created_at":"2026-05-18T12:28:59.999130+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/2AJS64QGRGK5HUB7FJB6MA2WZL","json":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL.json","graph_json":"https://pith.science/api/pith-number/2AJS64QGRGK5HUB7FJB6MA2WZL/graph.json","events_json":"https://pith.science/api/pith-number/2AJS64QGRGK5HUB7FJB6MA2WZL/events.json","paper":"https://pith.science/paper/2AJS64QG"},"agent_actions":{"view_html":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL","download_json":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL.json","view_paper":"https://pith.science/paper/2AJS64QG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01273&json=true","fetch_graph":"https://pith.science/api/pith-number/2AJS64QGRGK5HUB7FJB6MA2WZL/graph.json","fetch_events":"https://pith.science/api/pith-number/2AJS64QGRGK5HUB7FJB6MA2WZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL/action/storage_attestation","attest_author":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL/action/author_attestation","sign_citation":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL/action/citation_signature","submit_replication":"https://pith.science/pith/2AJS64QGRGK5HUB7FJB6MA2WZL/action/replication_record"}},"created_at":"2026-05-18T01:33:59.023442+00:00","updated_at":"2026-05-18T01:33:59.023442+00:00"}