{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IPQJL5HSZNDNW3KEUJTI3WCWP6","short_pith_number":"pith:IPQJL5HS","schema_version":"1.0","canonical_sha256":"43e095f4f2cb46db6d44a2668dd8567f9a7b9549b83432cc28a0968dec4e256b","source":{"kind":"arxiv","id":"1312.1030","version":3},"attestation_state":"computed","paper":{"title":"On the Shrinkable U.S.C. Decomposition Spaces of Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Shijie Gu","submitted_at":"2013-12-04T05:41:54Z","abstract_excerpt":"Let $G$ be a u.s.c decomposition of $S^n$, $H_G$ denote the set of nondegenerate elements and $\\pi$ be the projection of $S^n$ onto $S^n/G$. Suppose that each point in the decomposition space has arbitrarily small neighborhoods with ($n-1$)-sphere frontiers which miss $\\pi(H_G)$, and such frontiers satisfies the Mismatch Property. Then this paper shows that this condition implies $S^n/G$ is homeomorphic to $S^n$ ($n\\geq 4$). This answers a weakened form of a conjecture asked by Daverman [3, p. 61]. In the case $n=3$, the strong form of the conjecture has an affirmative answer from Woodruff [12"},"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":"1312.1030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-04T05:41:54Z","cross_cats_sorted":[],"title_canon_sha256":"4ac26888a24170604fdcebdc5da634e772959a56adc515682ce47cf78dda2b4f","abstract_canon_sha256":"6a73923379d39d49f92ebe596775792894314c2d692c027eb29deef2d1b79ef5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:33.907066Z","signature_b64":"9doiF+7MdGJmyG0FQl30YPC5G1wdDU2HFmNKGTXfNwMVJW/qEhZy0sZhMoWRAD8COdUb7Lk2GRFYuA4FUh7+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43e095f4f2cb46db6d44a2668dd8567f9a7b9549b83432cc28a0968dec4e256b","last_reissued_at":"2026-05-18T02:50:33.906586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:33.906586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Shrinkable U.S.C. Decomposition Spaces of Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Shijie Gu","submitted_at":"2013-12-04T05:41:54Z","abstract_excerpt":"Let $G$ be a u.s.c decomposition of $S^n$, $H_G$ denote the set of nondegenerate elements and $\\pi$ be the projection of $S^n$ onto $S^n/G$. Suppose that each point in the decomposition space has arbitrarily small neighborhoods with ($n-1$)-sphere frontiers which miss $\\pi(H_G)$, and such frontiers satisfies the Mismatch Property. Then this paper shows that this condition implies $S^n/G$ is homeomorphic to $S^n$ ($n\\geq 4$). This answers a weakened form of a conjecture asked by Daverman [3, p. 61]. In the case $n=3$, the strong form of the conjecture has an affirmative answer from Woodruff [12"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1030","kind":"arxiv","version":3},"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":"1312.1030","created_at":"2026-05-18T02:50:33.906669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1030v3","created_at":"2026-05-18T02:50:33.906669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1030","created_at":"2026-05-18T02:50:33.906669+00:00"},{"alias_kind":"pith_short_12","alias_value":"IPQJL5HSZNDN","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IPQJL5HSZNDNW3KE","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IPQJL5HS","created_at":"2026-05-18T12:27:46.883200+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/IPQJL5HSZNDNW3KEUJTI3WCWP6","json":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6.json","graph_json":"https://pith.science/api/pith-number/IPQJL5HSZNDNW3KEUJTI3WCWP6/graph.json","events_json":"https://pith.science/api/pith-number/IPQJL5HSZNDNW3KEUJTI3WCWP6/events.json","paper":"https://pith.science/paper/IPQJL5HS"},"agent_actions":{"view_html":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6","download_json":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6.json","view_paper":"https://pith.science/paper/IPQJL5HS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1030&json=true","fetch_graph":"https://pith.science/api/pith-number/IPQJL5HSZNDNW3KEUJTI3WCWP6/graph.json","fetch_events":"https://pith.science/api/pith-number/IPQJL5HSZNDNW3KEUJTI3WCWP6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6/action/storage_attestation","attest_author":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6/action/author_attestation","sign_citation":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6/action/citation_signature","submit_replication":"https://pith.science/pith/IPQJL5HSZNDNW3KEUJTI3WCWP6/action/replication_record"}},"created_at":"2026-05-18T02:50:33.906669+00:00","updated_at":"2026-05-18T02:50:33.906669+00:00"}