{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2BJ4PEUS5JC7RT4SZIBLIVJ5L5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f5668e8ce6f2a1f07263f93d4bd297a586fa35e2c8ca45c85905394ed4a1a13d","cross_cats_sorted":["math.AT","math.CO"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GT","submitted_at":"2009-03-23T18:50:36Z","title_canon_sha256":"44caad0e61984d685b63ef56d7fc8b972ae9ee7991cf8abc1f47067569d30880"},"schema_version":"1.0","source":{"id":"0903.3653","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3653","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3653v3","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3653","created_at":"2026-05-18T04:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"2BJ4PEUS5JC7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2BJ4PEUS5JC7RT4S","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2BJ4PEUS","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7384b0b1a8a0bab5625e248a032bbcb89599b798d37e5c06845e7c21df68aa35","target":"graph","created_at":"2026-05-18T04:28:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch (1976) \\cite[Chapter 8, \\S 2 Gluing Manifolds Together]{h}, we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimensional prism $P^3(m)$ with $m\\geq 3$. We introduce two invariants from colored prisms and other two invariants from ordinary cohomology rings with ${\\Bbb Z}_2$-coefficients of small covers. These invariants can form a complete invariant system of homeomorphism types of all small co","authors_text":"Xiangyu Cao, Zhi L\\\"u","cross_cats":["math.AT","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GT","submitted_at":"2009-03-23T18:50:36Z","title":"Cohomological rigidity and the number of homeomorphism types for small covers over prisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3653","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:54a0f97053adbd6500fa344333aa7f4540bcddd38ee4ce1b76f2cf8093abb6d5","target":"record","created_at":"2026-05-18T04:28:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f5668e8ce6f2a1f07263f93d4bd297a586fa35e2c8ca45c85905394ed4a1a13d","cross_cats_sorted":["math.AT","math.CO"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GT","submitted_at":"2009-03-23T18:50:36Z","title_canon_sha256":"44caad0e61984d685b63ef56d7fc8b972ae9ee7991cf8abc1f47067569d30880"},"schema_version":"1.0","source":{"id":"0903.3653","kind":"arxiv","version":3}},"canonical_sha256":"d053c79292ea45f8cf92ca02b4553d5f7a50f8e256b60744586ca91c33b6b925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d053c79292ea45f8cf92ca02b4553d5f7a50f8e256b60744586ca91c33b6b925","first_computed_at":"2026-05-18T04:28:20.506020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:20.506020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZxflzWG4YdXnzA8A05zyNroG3+dFUoGjVd0vnYWIvK5V4d/i4WtNZ4JUF++7XJr2KBfJcOismW8qN2wGFujuBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:20.506462Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3653","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54a0f97053adbd6500fa344333aa7f4540bcddd38ee4ce1b76f2cf8093abb6d5","sha256:7384b0b1a8a0bab5625e248a032bbcb89599b798d37e5c06845e7c21df68aa35"],"state_sha256":"643270fa6e340085e4b54e636ca35ebc8e059b185e5732615774cb27272bf204"}