{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:S3YSQBUUSKEV7KBAOVNRR42225","short_pith_number":"pith:S3YSQBUU","schema_version":"1.0","canonical_sha256":"96f128069492895fa820755b18f35ad77aed7229ee549608330faeb5cab44cef","source":{"kind":"arxiv","id":"1602.05759","version":1},"attestation_state":"computed","paper":{"title":"Realizing homology classes up to cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andr\\'as Sz\\H{u}cs, Mark Grant, Tam\\'as Terpai","submitted_at":"2016-02-18T11:27:57Z","abstract_excerpt":"It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod 2 homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient."},"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":"1602.05759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-02-18T11:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"21264f1945f14db14f3f52cb46567d84bede9ad02ab456e122b7b0c0206ca389","abstract_canon_sha256":"cc21c09ba729b83337c4e6333c7840aa8382a75c5e21bd649d2f9ff5e64e4154"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.272872Z","signature_b64":"0GuIBopW5WmSrx6M1+HGZ47xnib94fR80hwWdjbFaqJk3RTYOwRGLh+IPqEAHgd+Z3xISu7MKpQTUqBMNBJUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96f128069492895fa820755b18f35ad77aed7229ee549608330faeb5cab44cef","last_reissued_at":"2026-05-18T01:20:23.272379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.272379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Realizing homology classes up to cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andr\\'as Sz\\H{u}cs, Mark Grant, Tam\\'as Terpai","submitted_at":"2016-02-18T11:27:57Z","abstract_excerpt":"It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod 2 homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05759","kind":"arxiv","version":1},"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":"1602.05759","created_at":"2026-05-18T01:20:23.272453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05759v1","created_at":"2026-05-18T01:20:23.272453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05759","created_at":"2026-05-18T01:20:23.272453+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3YSQBUUSKEV","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3YSQBUUSKEV7KBA","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3YSQBUU","created_at":"2026-05-18T12:30:41.710351+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/S3YSQBUUSKEV7KBAOVNRR42225","json":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225.json","graph_json":"https://pith.science/api/pith-number/S3YSQBUUSKEV7KBAOVNRR42225/graph.json","events_json":"https://pith.science/api/pith-number/S3YSQBUUSKEV7KBAOVNRR42225/events.json","paper":"https://pith.science/paper/S3YSQBUU"},"agent_actions":{"view_html":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225","download_json":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225.json","view_paper":"https://pith.science/paper/S3YSQBUU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05759&json=true","fetch_graph":"https://pith.science/api/pith-number/S3YSQBUUSKEV7KBAOVNRR42225/graph.json","fetch_events":"https://pith.science/api/pith-number/S3YSQBUUSKEV7KBAOVNRR42225/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225/action/storage_attestation","attest_author":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225/action/author_attestation","sign_citation":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225/action/citation_signature","submit_replication":"https://pith.science/pith/S3YSQBUUSKEV7KBAOVNRR42225/action/replication_record"}},"created_at":"2026-05-18T01:20:23.272453+00:00","updated_at":"2026-05-18T01:20:23.272453+00:00"}