{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:UCDFXU6DTOX4APUTWBZJSVYKCP","short_pith_number":"pith:UCDFXU6D","schema_version":"1.0","canonical_sha256":"a0865bd3c39bafc03e93b07299570a13e56579eba12b74175dce9ec6a9ce4890","source":{"kind":"arxiv","id":"math/0312387","version":1},"attestation_state":"computed","paper":{"title":"Free and semi-inert cell attachments","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Peter Bubenik","submitted_at":"2003-12-19T17:48:08Z","abstract_excerpt":"Let $Y$ be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex.\n  We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously studied inert condition. Under these conditions we determine $H_*(\\Omega Y;R)$ as an $R$-module and as an $R$-algebra respectively. Under a further condition we show that $H_*(\\Omega Y;R)$ is generated by Hurewicz images.\n  As an example we study an infinite family of spaces constructed using only semi-inert cell attachments."},"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":"math/0312387","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2003-12-19T17:48:08Z","cross_cats_sorted":[],"title_canon_sha256":"4e155e7f0249a1231b26cdb4872b6a5a3145c20615db3dd057d4557822b83cd7","abstract_canon_sha256":"26948c7c646ce9de6204167d4a7bdfb1344654ef8481adc533176c1cace2730b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:22.072140Z","signature_b64":"lfokrxgLi7jfMMS2SyBx2JKjzMDcii+yzy38CAGnjP40VekWWcnAHq3qfQ0z2OtQY2I8MYMD8ELcDpWLN5fMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0865bd3c39bafc03e93b07299570a13e56579eba12b74175dce9ec6a9ce4890","last_reissued_at":"2026-05-18T01:16:22.071614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:22.071614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Free and semi-inert cell attachments","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Peter Bubenik","submitted_at":"2003-12-19T17:48:08Z","abstract_excerpt":"Let $Y$ be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex.\n  We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously studied inert condition. Under these conditions we determine $H_*(\\Omega Y;R)$ as an $R$-module and as an $R$-algebra respectively. Under a further condition we show that $H_*(\\Omega Y;R)$ is generated by Hurewicz images.\n  As an example we study an infinite family of spaces constructed using only semi-inert cell attachments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312387","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":"math/0312387","created_at":"2026-05-18T01:16:22.071693+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0312387v1","created_at":"2026-05-18T01:16:22.071693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312387","created_at":"2026-05-18T01:16:22.071693+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCDFXU6DTOX4","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCDFXU6DTOX4APUT","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCDFXU6D","created_at":"2026-05-18T12:25:52.051335+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/UCDFXU6DTOX4APUTWBZJSVYKCP","json":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP.json","graph_json":"https://pith.science/api/pith-number/UCDFXU6DTOX4APUTWBZJSVYKCP/graph.json","events_json":"https://pith.science/api/pith-number/UCDFXU6DTOX4APUTWBZJSVYKCP/events.json","paper":"https://pith.science/paper/UCDFXU6D"},"agent_actions":{"view_html":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP","download_json":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP.json","view_paper":"https://pith.science/paper/UCDFXU6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0312387&json=true","fetch_graph":"https://pith.science/api/pith-number/UCDFXU6DTOX4APUTWBZJSVYKCP/graph.json","fetch_events":"https://pith.science/api/pith-number/UCDFXU6DTOX4APUTWBZJSVYKCP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP/action/storage_attestation","attest_author":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP/action/author_attestation","sign_citation":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP/action/citation_signature","submit_replication":"https://pith.science/pith/UCDFXU6DTOX4APUTWBZJSVYKCP/action/replication_record"}},"created_at":"2026-05-18T01:16:22.071693+00:00","updated_at":"2026-05-18T01:16:22.071693+00:00"}