{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:XALKNI3WERMXJWPR2P3XX7SUS2","short_pith_number":"pith:XALKNI3W","schema_version":"1.0","canonical_sha256":"b816a6a376245974d9f1d3f77bfe5496a7c0a58fefac3411069e5ca68dd81bc8","source":{"kind":"arxiv","id":"2305.04817","version":2},"attestation_state":"computed","paper":{"title":"On word complexity and topological entropy of random substitution subshifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Mitchell","submitted_at":"2023-05-08T16:15:59Z","abstract_excerpt":"We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random substitution has zero topological entropy if and only if it can be obtained as the subshift of a deterministic substitution, answering in the affirmative an open question of Rust and Spindeler. For constant length primitive random substitutions, we develop a systematic approach to calculating the topological entropy of the associated subshift. Further, we prove"},"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":"2305.04817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-05-08T16:15:59Z","cross_cats_sorted":[],"title_canon_sha256":"08c19f4022789f68021909558a102245449052f1f469ba1774bf12bf8a2c4226","abstract_canon_sha256":"fbd71ed8117710b734c71f414f82b0ad7f222933e778bd5c510e7882f03e6409"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:10:13.644695Z","signature_b64":"ulnVtttPPpPQ48TE1FHzM040SnLaxcMULDEVnNq97nr/dUHg+7F8HabPrybuqSuBIlVe8hCAdNUd4+k6uhDnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b816a6a376245974d9f1d3f77bfe5496a7c0a58fefac3411069e5ca68dd81bc8","last_reissued_at":"2026-07-05T08:10:13.644302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:10:13.644302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On word complexity and topological entropy of random substitution subshifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Mitchell","submitted_at":"2023-05-08T16:15:59Z","abstract_excerpt":"We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random substitution has zero topological entropy if and only if it can be obtained as the subshift of a deterministic substitution, answering in the affirmative an open question of Rust and Spindeler. For constant length primitive random substitutions, we develop a systematic approach to calculating the topological entropy of the associated subshift. Further, we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.04817","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.04817/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.04817","created_at":"2026-07-05T08:10:13.644370+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.04817v2","created_at":"2026-07-05T08:10:13.644370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.04817","created_at":"2026-07-05T08:10:13.644370+00:00"},{"alias_kind":"pith_short_12","alias_value":"XALKNI3WERMX","created_at":"2026-07-05T08:10:13.644370+00:00"},{"alias_kind":"pith_short_16","alias_value":"XALKNI3WERMXJWPR","created_at":"2026-07-05T08:10:13.644370+00:00"},{"alias_kind":"pith_short_8","alias_value":"XALKNI3W","created_at":"2026-07-05T08:10:13.644370+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/XALKNI3WERMXJWPR2P3XX7SUS2","json":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2.json","graph_json":"https://pith.science/api/pith-number/XALKNI3WERMXJWPR2P3XX7SUS2/graph.json","events_json":"https://pith.science/api/pith-number/XALKNI3WERMXJWPR2P3XX7SUS2/events.json","paper":"https://pith.science/paper/XALKNI3W"},"agent_actions":{"view_html":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2","download_json":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2.json","view_paper":"https://pith.science/paper/XALKNI3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.04817&json=true","fetch_graph":"https://pith.science/api/pith-number/XALKNI3WERMXJWPR2P3XX7SUS2/graph.json","fetch_events":"https://pith.science/api/pith-number/XALKNI3WERMXJWPR2P3XX7SUS2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2/action/storage_attestation","attest_author":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2/action/author_attestation","sign_citation":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2/action/citation_signature","submit_replication":"https://pith.science/pith/XALKNI3WERMXJWPR2P3XX7SUS2/action/replication_record"}},"created_at":"2026-07-05T08:10:13.644370+00:00","updated_at":"2026-07-05T08:10:13.644370+00:00"}