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Furthermore, countable dense homogeneity can be proven without assuming the space is connected.\n  This theorem has the following two consequences.\n  COROLLARY 1. If $X$ is a homogeneous compact suspension, then $X$ is an absolute suspension (i.e., for any two distinct points $p$ and $q$ of $X$, there is a homeomorphism from $X$ to a suspension that maps $p$ and $q$ to the sus"},"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":"1607.00103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-07-01T03:22:35Z","cross_cats_sorted":[],"title_canon_sha256":"baf24efbce0bcfa65988e032cb77fb82f17ca3020f40f3d94ff44eab86ce7885","abstract_canon_sha256":"783244da96630dbec87a916ae0267624f7f7fbb908b616815e1a92a76d2c4e07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:18.506129Z","signature_b64":"rVmzyoQApMHlGenePfVeFC4E0YxX6KSlFo8F39AHAvO5mi8SIoqdZZKiCN+LyRvSyNyEZ71OaZ/9xqxXPuQOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db1230ca34a0701fb0ac5aa0931f980f676494470bf324416ed1bbcc3bd83b89","last_reissued_at":"2026-05-18T00:43:18.505421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:18.505421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On homogeneous locally conical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"David P. 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If $X$ is a homogeneous compact suspension, then $X$ is an absolute suspension (i.e., for any two distinct points $p$ and $q$ of $X$, there is a homeomorphism from $X$ to a suspension that maps $p$ and $q$ to the sus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00103","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":""},"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":"1607.00103","created_at":"2026-05-18T00:43:18.505537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.00103v2","created_at":"2026-05-18T00:43:18.505537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00103","created_at":"2026-05-18T00:43:18.505537+00:00"},{"alias_kind":"pith_short_12","alias_value":"3MJDBSRUUBYB","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3MJDBSRUUBYB7MFM","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3MJDBSRU","created_at":"2026-05-18T12:29:55.572404+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/3MJDBSRUUBYB7MFMLKQJGH4YB5","json":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5.json","graph_json":"https://pith.science/api/pith-number/3MJDBSRUUBYB7MFMLKQJGH4YB5/graph.json","events_json":"https://pith.science/api/pith-number/3MJDBSRUUBYB7MFMLKQJGH4YB5/events.json","paper":"https://pith.science/paper/3MJDBSRU"},"agent_actions":{"view_html":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5","download_json":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5.json","view_paper":"https://pith.science/paper/3MJDBSRU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.00103&json=true","fetch_graph":"https://pith.science/api/pith-number/3MJDBSRUUBYB7MFMLKQJGH4YB5/graph.json","fetch_events":"https://pith.science/api/pith-number/3MJDBSRUUBYB7MFMLKQJGH4YB5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5/action/storage_attestation","attest_author":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5/action/author_attestation","sign_citation":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5/action/citation_signature","submit_replication":"https://pith.science/pith/3MJDBSRUUBYB7MFMLKQJGH4YB5/action/replication_record"}},"created_at":"2026-05-18T00:43:18.505537+00:00","updated_at":"2026-05-18T00:43:18.505537+00:00"}