{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7C6UVEF6PYYIJALPXMHYJ7JSWN","short_pith_number":"pith:7C6UVEF6","schema_version":"1.0","canonical_sha256":"f8bd4a90be7e3084816fbb0f84fd32b37029ddbf0562170ab5a9c05ba7cd5438","source":{"kind":"arxiv","id":"1409.3922","version":1},"attestation_state":"computed","paper":{"title":"Classifying invariant $\\sigma$-ideals with analytic base on good Cantor measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.LO"],"primary_cat":"math.GN","authors_text":"Robert Ralowski, Szymon Zeberski, Taras Banakh","submitted_at":"2014-09-13T07:31:38Z","abstract_excerpt":"Let $X$ be a zero-dimensional compact metrizable space endowed with a strictly positive continuous Borel $\\sigma$-additive measure $\\mu$ which is good in the sense that for any clopen subsets $U,V\\subset X$ with $\\mu(U)<\\mu(V)$ there is a clopen set $W\\subset V$ with $\\mu(W)=\\mu(U)$. We study $\\sigma$-ideals with Borel base on $X$ which are invariant under the action of the group $H_\\mu(X)$ of measure-preserving homeomorphisms of $(X,\\mu)$, and show that any such $\\sigma$-ideal $\\mathcal I$ is equal to one of seven $\\sigma$-ideals: $\\{\\emptyset\\}$, $[X]^{\\le\\omega}$, $\\mathcal E$, $\\mathcal M\\"},"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":"1409.3922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-09-13T07:31:38Z","cross_cats_sorted":["math.DS","math.LO"],"title_canon_sha256":"53129897175fc74ebc668f22b31acb4d201422f319971b21ecfef6927d123b74","abstract_canon_sha256":"f81159f7aef7423c618cb2a4ef85ed360c24ba34ec43e69119c5bbbf7b4ef8d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:26.441444Z","signature_b64":"GDh8tLAyQGlq3ABpqKfVAteZnnXzYjeJdve0QKpCM6XHd+FInry070BcKu8DwQlT97KT4F54YzqZiySUk2vfBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8bd4a90be7e3084816fbb0f84fd32b37029ddbf0562170ab5a9c05ba7cd5438","last_reissued_at":"2026-05-18T01:20:26.440762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:26.440762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classifying invariant $\\sigma$-ideals with analytic base on good Cantor measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.LO"],"primary_cat":"math.GN","authors_text":"Robert Ralowski, Szymon Zeberski, Taras Banakh","submitted_at":"2014-09-13T07:31:38Z","abstract_excerpt":"Let $X$ be a zero-dimensional compact metrizable space endowed with a strictly positive continuous Borel $\\sigma$-additive measure $\\mu$ which is good in the sense that for any clopen subsets $U,V\\subset X$ with $\\mu(U)<\\mu(V)$ there is a clopen set $W\\subset V$ with $\\mu(W)=\\mu(U)$. We study $\\sigma$-ideals with Borel base on $X$ which are invariant under the action of the group $H_\\mu(X)$ of measure-preserving homeomorphisms of $(X,\\mu)$, and show that any such $\\sigma$-ideal $\\mathcal I$ is equal to one of seven $\\sigma$-ideals: $\\{\\emptyset\\}$, $[X]^{\\le\\omega}$, $\\mathcal E$, $\\mathcal M\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3922","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":"1409.3922","created_at":"2026-05-18T01:20:26.440855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3922v1","created_at":"2026-05-18T01:20:26.440855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3922","created_at":"2026-05-18T01:20:26.440855+00:00"},{"alias_kind":"pith_short_12","alias_value":"7C6UVEF6PYYI","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7C6UVEF6PYYIJALP","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7C6UVEF6","created_at":"2026-05-18T12:28:16.859392+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/7C6UVEF6PYYIJALPXMHYJ7JSWN","json":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN.json","graph_json":"https://pith.science/api/pith-number/7C6UVEF6PYYIJALPXMHYJ7JSWN/graph.json","events_json":"https://pith.science/api/pith-number/7C6UVEF6PYYIJALPXMHYJ7JSWN/events.json","paper":"https://pith.science/paper/7C6UVEF6"},"agent_actions":{"view_html":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN","download_json":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN.json","view_paper":"https://pith.science/paper/7C6UVEF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3922&json=true","fetch_graph":"https://pith.science/api/pith-number/7C6UVEF6PYYIJALPXMHYJ7JSWN/graph.json","fetch_events":"https://pith.science/api/pith-number/7C6UVEF6PYYIJALPXMHYJ7JSWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN/action/storage_attestation","attest_author":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN/action/author_attestation","sign_citation":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN/action/citation_signature","submit_replication":"https://pith.science/pith/7C6UVEF6PYYIJALPXMHYJ7JSWN/action/replication_record"}},"created_at":"2026-05-18T01:20:26.440855+00:00","updated_at":"2026-05-18T01:20:26.440855+00:00"}