{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QWRQAUU6WHYV5EBZNCIXGUVW5D","short_pith_number":"pith:QWRQAUU6","schema_version":"1.0","canonical_sha256":"85a300529eb1f15e903968917352b6e8efc540c872afc9c4cdd77f45da57a86f","source":{"kind":"arxiv","id":"0903.5060","version":3},"attestation_state":"computed","paper":{"title":"Schreier type theorems for bicrossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2009-03-29T16:05:28Z","abstract_excerpt":"We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups $(H, G, \\alpha, \\beta)$ is deformed using a combinatorial datum $(\\sigma, v, r)$ consisting of an automorphism $\\sigma$ of $H$, a permutation $v$ of the set $G$ and a transition map $r: G\\to H$ in order to obtain a new matched pair $\\bigl(H, (G,*), \\alpha', \\beta' \\bigl)$ such that there exist an $\\sigma$-invariant isomorphism of groups $H {}_{\\alpha} \\bowtie_{\\beta} G \\cong H {}_{\\alpha'} \\bowtie_{\\beta'} (G,*)$. Moreover, if we fix the group $H$ and the automorp"},"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":"0903.5060","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-03-29T16:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"846c55083b1da4fd3a8a3cffaf2a9152f7eca8d1fd5c5442c158a37291fb27dd","abstract_canon_sha256":"884e1b574df8e823b136cc4349e621104992a711377d02adaaa20da0007b27a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:19.622830Z","signature_b64":"ExndAQzgLqsB1QxWV+I02kf0Enz72RJ4f0M+4/qDHb3XJJDZuzQ7HajFsUYA7ePp0+YbYOAzcAopBj9W8C+aAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85a300529eb1f15e903968917352b6e8efc540c872afc9c4cdd77f45da57a86f","last_reissued_at":"2026-05-18T02:56:19.622322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:19.622322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schreier type theorems for bicrossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2009-03-29T16:05:28Z","abstract_excerpt":"We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups $(H, G, \\alpha, \\beta)$ is deformed using a combinatorial datum $(\\sigma, v, r)$ consisting of an automorphism $\\sigma$ of $H$, a permutation $v$ of the set $G$ and a transition map $r: G\\to H$ in order to obtain a new matched pair $\\bigl(H, (G,*), \\alpha', \\beta' \\bigl)$ such that there exist an $\\sigma$-invariant isomorphism of groups $H {}_{\\alpha} \\bowtie_{\\beta} G \\cong H {}_{\\alpha'} \\bowtie_{\\beta'} (G,*)$. Moreover, if we fix the group $H$ and the automorp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5060","kind":"arxiv","version":3},"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":"0903.5060","created_at":"2026-05-18T02:56:19.622400+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.5060v3","created_at":"2026-05-18T02:56:19.622400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.5060","created_at":"2026-05-18T02:56:19.622400+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWRQAUU6WHYV","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWRQAUU6WHYV5EBZ","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWRQAUU6","created_at":"2026-05-18T12:26:01.383474+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/QWRQAUU6WHYV5EBZNCIXGUVW5D","json":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D.json","graph_json":"https://pith.science/api/pith-number/QWRQAUU6WHYV5EBZNCIXGUVW5D/graph.json","events_json":"https://pith.science/api/pith-number/QWRQAUU6WHYV5EBZNCIXGUVW5D/events.json","paper":"https://pith.science/paper/QWRQAUU6"},"agent_actions":{"view_html":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D","download_json":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D.json","view_paper":"https://pith.science/paper/QWRQAUU6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.5060&json=true","fetch_graph":"https://pith.science/api/pith-number/QWRQAUU6WHYV5EBZNCIXGUVW5D/graph.json","fetch_events":"https://pith.science/api/pith-number/QWRQAUU6WHYV5EBZNCIXGUVW5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D/action/storage_attestation","attest_author":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D/action/author_attestation","sign_citation":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D/action/citation_signature","submit_replication":"https://pith.science/pith/QWRQAUU6WHYV5EBZNCIXGUVW5D/action/replication_record"}},"created_at":"2026-05-18T02:56:19.622400+00:00","updated_at":"2026-05-18T02:56:19.622400+00:00"}