{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3JIP7N7HYTB53DI6HJKWDATCKF","short_pith_number":"pith:3JIP7N7H","canonical_record":{"source":{"id":"1201.4823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-23T19:22:45Z","cross_cats_sorted":["math.GR","math.MG"],"title_canon_sha256":"feefa7e08e6220c833e8b5cb7dc6768d712c938a93cb0f9795d27572fbbd2ce6","abstract_canon_sha256":"5eb43dfebd62017cb320973f35aa3240987ce340b05cc1063ef37f58e65345c2"},"schema_version":"1.0"},"canonical_sha256":"da50ffb7e7c4c3dd8d1e3a55618262517ce4a1c035f291a24c6a5af5f630d5a3","source":{"kind":"arxiv","id":"1201.4823","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4823","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4823v2","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4823","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"3JIP7N7HYTB5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3JIP7N7HYTB53DI6","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3JIP7N7H","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3JIP7N7HYTB53DI6HJKWDATCKF","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-23T19:22:45Z","cross_cats_sorted":["math.GR","math.MG"],"title_canon_sha256":"feefa7e08e6220c833e8b5cb7dc6768d712c938a93cb0f9795d27572fbbd2ce6","abstract_canon_sha256":"5eb43dfebd62017cb320973f35aa3240987ce340b05cc1063ef37f58e65345c2"},"schema_version":"1.0"},"canonical_sha256":"da50ffb7e7c4c3dd8d1e3a55618262517ce4a1c035f291a24c6a5af5f630d5a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.633968Z","signature_b64":"9l9mW1G8+7eVmO2jK7acWPkwKovoEmy9wHu5+tDLb9K5sJHtab/KwDWGo/TKptwIcivQrhF7K0ZZnN9ua5FaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da50ffb7e7c4c3dd8d1e3a55618262517ce4a1c035f291a24c6a5af5f630d5a3","last_reissued_at":"2026-05-18T02:51:42.633446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.633446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4823","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uXsf2yjh2NxdNSvp+Kd9qIn/3zdCzMZBs0deAt3HLnp2FCUb5+0x6+kVyjRnwvtbaHMWRXKpCF1JzPOjQjihDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:39:48.133289Z"},"content_sha256":"43c5c604a6ef5052efdf738a437e42383748d8069ba850368f888d1f26fc84c4","schema_version":"1.0","event_id":"sha256:43c5c604a6ef5052efdf738a437e42383748d8069ba850368f888d1f26fc84c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3JIP7N7HYTB53DI6HJKWDATCKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Realisators for Homology Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG"],"primary_cat":"math.AT","authors_text":"Alexander A. Gaifullin","submitted_at":"2012-01-23T19:22:45Z","abstract_excerpt":"We study oriented closed manifolds M^n possessing the following Universal Realisation of Cycles (URC) Property: For each topological space X and each integral homology class z of it, there exist a finite-sheeted covering \\hM^n of M^n and a continuous mapping f of \\hM^n to X such that f takes the fundamental class [\\hM^n] to kz for a non-zero integer k. We find wide class of examples of such manifolds M^n among so-called small covers of simple polytopes. In particular, we find 4-dimensional hyperbolic manifolds possessing the URC property. As a consequence, we prove that for each 4-dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4823","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOWqkA01DF4j0N0DvHN5Nl8jrESW/GlKfsh8oKSRVlNtPaJNuumFN8ZUPf0NyBUVXBrkjh2DbEooQOyjB1iMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:39:48.134051Z"},"content_sha256":"9bb11e52c92ecf3dd0526f54ac944866a71d60147a51b774f28bd77085a8ba31","schema_version":"1.0","event_id":"sha256:9bb11e52c92ecf3dd0526f54ac944866a71d60147a51b774f28bd77085a8ba31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JIP7N7HYTB53DI6HJKWDATCKF/bundle.json","state_url":"https://pith.science/pith/3JIP7N7HYTB53DI6HJKWDATCKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JIP7N7HYTB53DI6HJKWDATCKF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T00:39:48Z","links":{"resolver":"https://pith.science/pith/3JIP7N7HYTB53DI6HJKWDATCKF","bundle":"https://pith.science/pith/3JIP7N7HYTB53DI6HJKWDATCKF/bundle.json","state":"https://pith.science/pith/3JIP7N7HYTB53DI6HJKWDATCKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JIP7N7HYTB53DI6HJKWDATCKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3JIP7N7HYTB53DI6HJKWDATCKF","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":"5eb43dfebd62017cb320973f35aa3240987ce340b05cc1063ef37f58e65345c2","cross_cats_sorted":["math.GR","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-23T19:22:45Z","title_canon_sha256":"feefa7e08e6220c833e8b5cb7dc6768d712c938a93cb0f9795d27572fbbd2ce6"},"schema_version":"1.0","source":{"id":"1201.4823","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4823","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4823v2","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4823","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"3JIP7N7HYTB5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3JIP7N7HYTB53DI6","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3JIP7N7H","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9bb11e52c92ecf3dd0526f54ac944866a71d60147a51b774f28bd77085a8ba31","target":"graph","created_at":"2026-05-18T02:51:42Z","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 study oriented closed manifolds M^n possessing the following Universal Realisation of Cycles (URC) Property: For each topological space X and each integral homology class z of it, there exist a finite-sheeted covering \\hM^n of M^n and a continuous mapping f of \\hM^n to X such that f takes the fundamental class [\\hM^n] to kz for a non-zero integer k. We find wide class of examples of such manifolds M^n among so-called small covers of simple polytopes. In particular, we find 4-dimensional hyperbolic manifolds possessing the URC property. As a consequence, we prove that for each 4-dimensional ","authors_text":"Alexander A. Gaifullin","cross_cats":["math.GR","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-23T19:22:45Z","title":"Universal Realisators for Homology Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4823","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":"sha256:43c5c604a6ef5052efdf738a437e42383748d8069ba850368f888d1f26fc84c4","target":"record","created_at":"2026-05-18T02:51:42Z","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":"5eb43dfebd62017cb320973f35aa3240987ce340b05cc1063ef37f58e65345c2","cross_cats_sorted":["math.GR","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-01-23T19:22:45Z","title_canon_sha256":"feefa7e08e6220c833e8b5cb7dc6768d712c938a93cb0f9795d27572fbbd2ce6"},"schema_version":"1.0","source":{"id":"1201.4823","kind":"arxiv","version":2}},"canonical_sha256":"da50ffb7e7c4c3dd8d1e3a55618262517ce4a1c035f291a24c6a5af5f630d5a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da50ffb7e7c4c3dd8d1e3a55618262517ce4a1c035f291a24c6a5af5f630d5a3","first_computed_at":"2026-05-18T02:51:42.633446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.633446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9l9mW1G8+7eVmO2jK7acWPkwKovoEmy9wHu5+tDLb9K5sJHtab/KwDWGo/TKptwIcivQrhF7K0ZZnN9ua5FaBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.633968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4823","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43c5c604a6ef5052efdf738a437e42383748d8069ba850368f888d1f26fc84c4","sha256:9bb11e52c92ecf3dd0526f54ac944866a71d60147a51b774f28bd77085a8ba31"],"state_sha256":"504fcb8b6057c3908924c4edc5f31ba6236ecdf277cbf64e071add71c9253b83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gvDD9mVerKbibgv3H2wk52GW5b3v+Mu4OnaYz0Vx8G15wdluDKLBKOAauov3Zr5EBRHubUsrELpLxTAigPMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:39:48.138420Z","bundle_sha256":"12615a57e0edbccc938402a2fb0cf3cf39ffb4bc01ea835dcd36a2a024d46b8b"}}