{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QCL3J4SMKKCX2J2CPROYYIQK72","short_pith_number":"pith:QCL3J4SM","schema_version":"1.0","canonical_sha256":"8097b4f24c52857d27427c5d8c220afe947bc70017358b036247933fd382e6f5","source":{"kind":"arxiv","id":"1810.05462","version":1},"attestation_state":"computed","paper":{"title":"Symbolic computation of Schur multipliers with an application to the groups of order dividing $p^6$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bettina Eick, Taleea Jalaeeyan Ghorbanzadeh","submitted_at":"2018-10-12T11:51:20Z","abstract_excerpt":"We describe an algorithm to compute the Schur multipliers of all nilpotent Lie $p$-rings in the family defined by a symbolic nilpotent Lie $p$-ring. Symbolic nilpotent Lie $p$-rings can be used to describe the isomorphism types of $p$-groups of order $p^n$ for $n \\leq 7$ and all primes $p \\geq n$. We apply our algorithm to compute the Schur multipliers of all $p$-groups of order dividing $p^6$."},"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":"1810.05462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-10-12T11:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"8c0455f4d9e9ac11cb7a23cee166915b85694f8296922d4e9d9a4f7a3a5b6105","abstract_canon_sha256":"b30737ce38478aa78acb3e205264ac1a50c3195485852f776e9c43432c514926"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:30.465029Z","signature_b64":"PClHB8oCxdz01w3W9htrGfcSkDL6fy26dP0c/sO8dVCJXPyy9mHHvxVSwzh7FaqK4Iy3zpIq2EavE5AfBeVCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8097b4f24c52857d27427c5d8c220afe947bc70017358b036247933fd382e6f5","last_reissued_at":"2026-05-18T00:03:30.464472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:30.464472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symbolic computation of Schur multipliers with an application to the groups of order dividing $p^6$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bettina Eick, Taleea Jalaeeyan Ghorbanzadeh","submitted_at":"2018-10-12T11:51:20Z","abstract_excerpt":"We describe an algorithm to compute the Schur multipliers of all nilpotent Lie $p$-rings in the family defined by a symbolic nilpotent Lie $p$-ring. Symbolic nilpotent Lie $p$-rings can be used to describe the isomorphism types of $p$-groups of order $p^n$ for $n \\leq 7$ and all primes $p \\geq n$. We apply our algorithm to compute the Schur multipliers of all $p$-groups of order dividing $p^6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05462","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":"1810.05462","created_at":"2026-05-18T00:03:30.464555+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.05462v1","created_at":"2026-05-18T00:03:30.464555+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05462","created_at":"2026-05-18T00:03:30.464555+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCL3J4SMKKCX","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCL3J4SMKKCX2J2C","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCL3J4SM","created_at":"2026-05-18T12:32:46.962924+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/QCL3J4SMKKCX2J2CPROYYIQK72","json":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72.json","graph_json":"https://pith.science/api/pith-number/QCL3J4SMKKCX2J2CPROYYIQK72/graph.json","events_json":"https://pith.science/api/pith-number/QCL3J4SMKKCX2J2CPROYYIQK72/events.json","paper":"https://pith.science/paper/QCL3J4SM"},"agent_actions":{"view_html":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72","download_json":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72.json","view_paper":"https://pith.science/paper/QCL3J4SM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.05462&json=true","fetch_graph":"https://pith.science/api/pith-number/QCL3J4SMKKCX2J2CPROYYIQK72/graph.json","fetch_events":"https://pith.science/api/pith-number/QCL3J4SMKKCX2J2CPROYYIQK72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72/action/storage_attestation","attest_author":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72/action/author_attestation","sign_citation":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72/action/citation_signature","submit_replication":"https://pith.science/pith/QCL3J4SMKKCX2J2CPROYYIQK72/action/replication_record"}},"created_at":"2026-05-18T00:03:30.464555+00:00","updated_at":"2026-05-18T00:03:30.464555+00:00"}