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The natural projection $\\pi: \\mathbb{M} \\rightarrow \\mathbb N$, which sends $(n,x)$ to $n$, induces a projection mapping $\\pi^*: \\mathbb{M}^* \\rightarrow \\mathbb N^*$, where $\\mathbb{M}^*$ and $\\mathbb N^*$ denote the \\v{C}ech-Stone remainders of $\\mathbb{M}$ and $\\mathbb N$, respectively.\n  We show that $\\mathsf{CH}$ implies every autohomeomorphism of $\\mathbb N^*$ lifts through the natural projection to an autohomeomorphism of $\\mathbb{M}^*$. That is, for every homeomorphism $h: \\mathbb N^* \\rightarrow \\mathbb N^*$ there is a homeomorphism $H: \\math"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.04425","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2025-05-07T13:58:04Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"940a0f7c652253b8152544077ae5186d60b11f516675f5f7010de308aef55c08","abstract_canon_sha256":"226cae8795557ac14c9cd5579dbea3101c684731d1a2acbc4a38c04e8adbbe90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:51:26.713575Z","signature_b64":"77rWYqVDMYQhn7B4qUWe3c5fzObvC+IgLbvSTGvOq7yV+uu4HOPuLhzexn/dWh2odDF1T5bwxbHnp18cgPN1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6611aea4c1eeb0b7c05d3eeb3fb592dec886389ae2bb22391a811b19f67837ef","last_reissued_at":"2026-07-05T11:51:26.712149Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:51:26.712149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathbb{M}^*$, $\\mathbb{N}^*$, and $\\mathbb{H}^*$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Alan Dow, Klaas Pieter Hart, Will Brian","submitted_at":"2025-05-07T13:58:04Z","abstract_excerpt":"Let $\\mathbb{M} = \\mathbb N \\times [0,1]$. The natural projection $\\pi: \\mathbb{M} \\rightarrow \\mathbb N$, which sends $(n,x)$ to $n$, induces a projection mapping $\\pi^*: \\mathbb{M}^* \\rightarrow \\mathbb N^*$, where $\\mathbb{M}^*$ and $\\mathbb N^*$ denote the \\v{C}ech-Stone remainders of $\\mathbb{M}$ and $\\mathbb N$, respectively.\n  We show that $\\mathsf{CH}$ implies every autohomeomorphism of $\\mathbb N^*$ lifts through the natural projection to an autohomeomorphism of $\\mathbb{M}^*$. That is, for every homeomorphism $h: \\mathbb N^* \\rightarrow \\mathbb N^*$ there is a homeomorphism $H: \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04425","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/2505.04425/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":"2505.04425","created_at":"2026-07-05T11:51:26.713013+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.04425v1","created_at":"2026-07-05T11:51:26.713013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04425","created_at":"2026-07-05T11:51:26.713013+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYI25JGB52YL","created_at":"2026-07-05T11:51:26.713013+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYI25JGB52YLPQC5","created_at":"2026-07-05T11:51:26.713013+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYI25JGB","created_at":"2026-07-05T11:51:26.713013+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/MYI25JGB52YLPQC5H3VT7NMS33","json":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33.json","graph_json":"https://pith.science/api/pith-number/MYI25JGB52YLPQC5H3VT7NMS33/graph.json","events_json":"https://pith.science/api/pith-number/MYI25JGB52YLPQC5H3VT7NMS33/events.json","paper":"https://pith.science/paper/MYI25JGB"},"agent_actions":{"view_html":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33","download_json":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33.json","view_paper":"https://pith.science/paper/MYI25JGB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.04425&json=true","fetch_graph":"https://pith.science/api/pith-number/MYI25JGB52YLPQC5H3VT7NMS33/graph.json","fetch_events":"https://pith.science/api/pith-number/MYI25JGB52YLPQC5H3VT7NMS33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33/action/storage_attestation","attest_author":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33/action/author_attestation","sign_citation":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33/action/citation_signature","submit_replication":"https://pith.science/pith/MYI25JGB52YLPQC5H3VT7NMS33/action/replication_record"}},"created_at":"2026-07-05T11:51:26.713013+00:00","updated_at":"2026-07-05T11:51:26.713013+00:00"}