{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:D63BRE36RCDA2DOWUQCHXEI4OB","short_pith_number":"pith:D63BRE36","schema_version":"1.0","canonical_sha256":"1fb618937e88860d0dd6a4047b911c704d45e3b3a12a40fa69982e3cba276e5b","source":{"kind":"arxiv","id":"2606.05832","version":1},"attestation_state":"computed","paper":{"title":"A choice-free approach to Wallman compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Cerene Rathilal, Ranjitha Raviprakash, Sebastian D Melzer","submitted_at":"2026-06-04T08:10:36Z","abstract_excerpt":"The classical Wallman compactification of a $T_1$-space and the Stone--\\v{C}ech compactification of a completely regular space rely on choice principles. We show that, by representing a space by its powerset MT-algebra (McKinsey--Tarski algebra), both constructions admit choice-free compactifications. More generally, from any Wallman basis of a spatial $T_1$ MT-algebra we construct a compact $T_1$ MT-algebra which is a compactification of the original algebra. Taking the basis of all closed elements yields a choice-free Wallman compactification of every spatial $T_1$ MT-algebra, while taking t"},"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":"2606.05832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2026-06-04T08:10:36Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"28ffab9bedddd7f85ab446c62ff8a0866e05ce5f740cb7ede056dbd71349e813","abstract_canon_sha256":"3dfb1407e4879a2a5daf2a668afaec5870fa1a7fa44538f31df866404bc700af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:04.942688Z","signature_b64":"4cxYYN0bWSNXMPc2h0qgffF3EsEN2v69pl1e5bkwygNxKs/oaHGVnYduWvlJaSNciYr2AUy0fjvPxiMguXVEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fb618937e88860d0dd6a4047b911c704d45e3b3a12a40fa69982e3cba276e5b","last_reissued_at":"2026-06-05T01:15:04.942146Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:04.942146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A choice-free approach to Wallman compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Cerene Rathilal, Ranjitha Raviprakash, Sebastian D Melzer","submitted_at":"2026-06-04T08:10:36Z","abstract_excerpt":"The classical Wallman compactification of a $T_1$-space and the Stone--\\v{C}ech compactification of a completely regular space rely on choice principles. We show that, by representing a space by its powerset MT-algebra (McKinsey--Tarski algebra), both constructions admit choice-free compactifications. More generally, from any Wallman basis of a spatial $T_1$ MT-algebra we construct a compact $T_1$ MT-algebra which is a compactification of the original algebra. Taking the basis of all closed elements yields a choice-free Wallman compactification of every spatial $T_1$ MT-algebra, while taking t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05832","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05832/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":"2606.05832","created_at":"2026-06-05T01:15:04.942217+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.05832v1","created_at":"2026-06-05T01:15:04.942217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05832","created_at":"2026-06-05T01:15:04.942217+00:00"},{"alias_kind":"pith_short_12","alias_value":"D63BRE36RCDA","created_at":"2026-06-05T01:15:04.942217+00:00"},{"alias_kind":"pith_short_16","alias_value":"D63BRE36RCDA2DOW","created_at":"2026-06-05T01:15:04.942217+00:00"},{"alias_kind":"pith_short_8","alias_value":"D63BRE36","created_at":"2026-06-05T01:15:04.942217+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/D63BRE36RCDA2DOWUQCHXEI4OB","json":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB.json","graph_json":"https://pith.science/api/pith-number/D63BRE36RCDA2DOWUQCHXEI4OB/graph.json","events_json":"https://pith.science/api/pith-number/D63BRE36RCDA2DOWUQCHXEI4OB/events.json","paper":"https://pith.science/paper/D63BRE36"},"agent_actions":{"view_html":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB","download_json":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB.json","view_paper":"https://pith.science/paper/D63BRE36","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.05832&json=true","fetch_graph":"https://pith.science/api/pith-number/D63BRE36RCDA2DOWUQCHXEI4OB/graph.json","fetch_events":"https://pith.science/api/pith-number/D63BRE36RCDA2DOWUQCHXEI4OB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB/action/storage_attestation","attest_author":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB/action/author_attestation","sign_citation":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB/action/citation_signature","submit_replication":"https://pith.science/pith/D63BRE36RCDA2DOWUQCHXEI4OB/action/replication_record"}},"created_at":"2026-06-05T01:15:04.942217+00:00","updated_at":"2026-06-05T01:15:04.942217+00:00"}