{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:REYSTXHI3CWHY2WJAQCQZYBXP5","short_pith_number":"pith:REYSTXHI","schema_version":"1.0","canonical_sha256":"893129dce8d8ac7c6ac904050ce0377f4f89e5190fee0cdcbb482e2ae3a56642","source":{"kind":"arxiv","id":"1812.02480","version":1},"attestation_state":"computed","paper":{"title":"Connected neighborhoods in Cartesian products of solenoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GN","authors_text":"Alejandro Illanes, Emanuel R. M\\'arquez, Jan P. Boro\\'nski","submitted_at":"2018-12-06T11:51:21Z","abstract_excerpt":"Given a collection of pairwise co-prime integers $% m_{1},\\ldots ,m_{r}$, greater than $1$, we consider the product $\\Sigma =\\Sigma _{m_{1}}\\times \\cdots \\times \\Sigma _{m_{r}}$, where each $\\Sigma _{m_{i}}$ is the $m_{i}$-adic solenoid. Answering a question of D. P. Bellamy and J. M. \\L ysko, in this paper we prove that if $M$ is a subcontinuum of $\\Sigma $ such that the projections of $M$ on each $\\Sigma _{m_{i}}$ are onto, then for each open subset $U$ in $\\Sigma $ with $M\\subset U$, there exists an open connected subset $V$ of $\\Sigma $ such that $M\\subset V\\subset U$; i.e. any such $M$ is"},"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":"1812.02480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-06T11:51:21Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"a1a6b3d6186da147e389f84db3e84afa4d3159ab994ca0f918503a12300aaa8e","abstract_canon_sha256":"faf20001bb5d1d92f4287fef42fbc0be08c6f3652fcef467b7e54d8f49c53024"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.579289Z","signature_b64":"zVZj9DN/FyVYSejDE8IyWsWkD605z8lM6DpDFVux+hWSTSRBjs5eXgKNi+u5YQKx6MvYG5R6E/z7r3fG95a4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"893129dce8d8ac7c6ac904050ce0377f4f89e5190fee0cdcbb482e2ae3a56642","last_reissued_at":"2026-05-17T23:58:55.578828Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.578828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connected neighborhoods in Cartesian products of solenoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GN","authors_text":"Alejandro Illanes, Emanuel R. M\\'arquez, Jan P. Boro\\'nski","submitted_at":"2018-12-06T11:51:21Z","abstract_excerpt":"Given a collection of pairwise co-prime integers $% m_{1},\\ldots ,m_{r}$, greater than $1$, we consider the product $\\Sigma =\\Sigma _{m_{1}}\\times \\cdots \\times \\Sigma _{m_{r}}$, where each $\\Sigma _{m_{i}}$ is the $m_{i}$-adic solenoid. Answering a question of D. P. Bellamy and J. M. \\L ysko, in this paper we prove that if $M$ is a subcontinuum of $\\Sigma $ such that the projections of $M$ on each $\\Sigma _{m_{i}}$ are onto, then for each open subset $U$ in $\\Sigma $ with $M\\subset U$, there exists an open connected subset $V$ of $\\Sigma $ such that $M\\subset V\\subset U$; i.e. any such $M$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02480","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":"1812.02480","created_at":"2026-05-17T23:58:55.578892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.02480v1","created_at":"2026-05-17T23:58:55.578892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02480","created_at":"2026-05-17T23:58:55.578892+00:00"},{"alias_kind":"pith_short_12","alias_value":"REYSTXHI3CWH","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"REYSTXHI3CWHY2WJ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"REYSTXHI","created_at":"2026-05-18T12:32:50.500415+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/REYSTXHI3CWHY2WJAQCQZYBXP5","json":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5.json","graph_json":"https://pith.science/api/pith-number/REYSTXHI3CWHY2WJAQCQZYBXP5/graph.json","events_json":"https://pith.science/api/pith-number/REYSTXHI3CWHY2WJAQCQZYBXP5/events.json","paper":"https://pith.science/paper/REYSTXHI"},"agent_actions":{"view_html":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5","download_json":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5.json","view_paper":"https://pith.science/paper/REYSTXHI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.02480&json=true","fetch_graph":"https://pith.science/api/pith-number/REYSTXHI3CWHY2WJAQCQZYBXP5/graph.json","fetch_events":"https://pith.science/api/pith-number/REYSTXHI3CWHY2WJAQCQZYBXP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5/action/storage_attestation","attest_author":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5/action/author_attestation","sign_citation":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5/action/citation_signature","submit_replication":"https://pith.science/pith/REYSTXHI3CWHY2WJAQCQZYBXP5/action/replication_record"}},"created_at":"2026-05-17T23:58:55.578892+00:00","updated_at":"2026-05-17T23:58:55.578892+00:00"}