{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HKXSLBPLTNLBHLWD5GX3SLHEBB","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":"8843eb1b331c962cfd0095b9cd57c894be8431576438b2dea9ca8344f52416ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-06T13:32:12Z","title_canon_sha256":"2edc6ccf15fcb0325ec257e3b4d5467ef5a674914240646fccb3754afeb7594e"},"schema_version":"1.0","source":{"id":"1810.04015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04015","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04015v1","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04015","created_at":"2026-05-18T00:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"HKXSLBPLTNLB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HKXSLBPLTNLBHLWD","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HKXSLBPL","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:f77c372427216c162a62d77cfbe0f46465d3e7494faf6429f06bc01db911a2bb","target":"graph","created_at":"2026-05-18T00:03:44Z","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":"The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\\dots p_{n}$, where $p_{i}$'s are primes, there always exists a subnormal series: $\\langle {e} \\rangle = G_{o} < G_{1} < \\dots < G_{n} = G$ such that $G_{i}/G_{i-1}$ is isomorphic to a cyclic group of order $p_{i}$, $i = 1,2,\\dots,n$. Associated with this series, there exists a system of generators consisting $n$ elements $x_{1}, x_{2}, \\dots, x_{n}$ (say), such that $G_{i} = \\langle x_{1}, x_{2}","authors_text":"Soham Swadhin Pradhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-06T13:32:12Z","title":"Algorithmic construction of representations of finite solvable groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04015","kind":"arxiv","version":1},"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:efe23cd0acdd37d3af0623240432ea67dabd713849240e7634a8ecd77bfe7a9c","target":"record","created_at":"2026-05-18T00:03:44Z","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":"8843eb1b331c962cfd0095b9cd57c894be8431576438b2dea9ca8344f52416ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-06T13:32:12Z","title_canon_sha256":"2edc6ccf15fcb0325ec257e3b4d5467ef5a674914240646fccb3754afeb7594e"},"schema_version":"1.0","source":{"id":"1810.04015","kind":"arxiv","version":1}},"canonical_sha256":"3aaf2585eb9b5613aec3e9afb92ce408600dc66d3338d056574f4b69b9fbffa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aaf2585eb9b5613aec3e9afb92ce408600dc66d3338d056574f4b69b9fbffa8","first_computed_at":"2026-05-18T00:03:44.093246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:44.093246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DwZW1ShSI6GMmJ07Vg3L6u/Prkg6U5m3v+UIu5xsbWfltCmHxRe5a2bPySOBw9dqO33488U5shBa1aK1m/xaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:44.093696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efe23cd0acdd37d3af0623240432ea67dabd713849240e7634a8ecd77bfe7a9c","sha256:f77c372427216c162a62d77cfbe0f46465d3e7494faf6429f06bc01db911a2bb"],"state_sha256":"569d9f03ef448954d04e3e9fc77e0030d9900aed2c9b56c56afadeb2b3623cfd"}