{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4A2PROR6GYZZTAMBEPNLUREQVL","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":"be56c40a8108be08cd59ce154118c91c74f3d6577794a14f20f481b129a7b1c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-01T17:21:31Z","title_canon_sha256":"37317c4b6a3aec5b0c3bfd1226004020711cd86fe308f2eb47d6ae9f2ac445b4"},"schema_version":"1.0","source":{"id":"1111.0249","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0249","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0249v2","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0249","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"4A2PROR6GYZZ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4A2PROR6GYZZTAMB","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4A2PROR6","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:66fccd1c6b810a1eaa3f6ef720e204708898a3acebb099d3c90448c4fe83097b","target":"graph","created_at":"2026-05-18T02:58:00Z","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":"We show that in every codimension greater than one there exists a mod 2 homology class in some closed manifold (of sufficiently high dimension) which cannot be realized by an immersion of closed manifolds. The proof gives explicit obstructions (in terms of cohomology operations) for realizability of mod 2 homology classes by immersions. We also prove the corresponding result in which the word `immersion' is replaced by `map with some restricted set of multi-singularities'.","authors_text":"Andras Szucs, Mark Grant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-01T17:21:31Z","title":"On realizing homology classes by maps of restricted complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0249","kind":"arxiv","version":2},"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":"sha256:9c86d30ff0e9ac76b73d36749a4327a45950b0c8777e9bff363e60003342ae9f","target":"record","created_at":"2026-05-18T02:58:00Z","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":"be56c40a8108be08cd59ce154118c91c74f3d6577794a14f20f481b129a7b1c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-01T17:21:31Z","title_canon_sha256":"37317c4b6a3aec5b0c3bfd1226004020711cd86fe308f2eb47d6ae9f2ac445b4"},"schema_version":"1.0","source":{"id":"1111.0249","kind":"arxiv","version":2}},"canonical_sha256":"e034f8ba3e363399818123daba4490aacac22a21e5413f5b18388d6191d10b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e034f8ba3e363399818123daba4490aacac22a21e5413f5b18388d6191d10b21","first_computed_at":"2026-05-18T02:58:00.273413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.273413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RyFWwMka4lCbeEUw9DZ/+IeJ9gbs43rKJX46ht12cH27511nv1TiNoug9fEMyUyGYjN0k7iWSfQYIw4Q2PzDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.274096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0249","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c86d30ff0e9ac76b73d36749a4327a45950b0c8777e9bff363e60003342ae9f","sha256:66fccd1c6b810a1eaa3f6ef720e204708898a3acebb099d3c90448c4fe83097b"],"state_sha256":"6371ce7a92372a282897a8da027d12995439d09fa952489487f6e6caa4f6d215"}