{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:ORR4CEUIKFRSEVELY66RFCBPKX","short_pith_number":"pith:ORR4CEUI","schema_version":"1.0","canonical_sha256":"7463c11288516322548bc7bd12882f55c110cdc9d3b9ae59a4b2d8646cad1b84","source":{"kind":"arxiv","id":"math/0701686","version":2},"attestation_state":"computed","paper":{"title":"Transitive Group Actions: (IM)PRIMITIVITY and Semiregular Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Aleksander Malnic, Dragan Marusic, Istvan Kovacs, Stefko Miklavic","submitted_at":"2007-01-24T16:00:32Z","abstract_excerpt":"The following problem is considered: if $H$ is a semiregular abelian subgroup of a transitive permutation group $G$ acting on a finite set $X$, find conditions for (non) existence of $G$-invariant partitions of $X$. Conditions presented in this paper are derived by studying spectral properties of associated $G$-invariant digraphs. As an essential tool, irreducible complex characters of $H$ are used.\n  Questions of this kind arise naturally when classifying combinatorial objects which enjoy a certain degree of symmetry. As an illustration, a new and short proof of an old result of Frucht, Grave"},"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/0701686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-01-24T16:00:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ac13b5bd501d8c20b6f702ca2253978a24e125efa9a49f107f559bb7cda9be38","abstract_canon_sha256":"c5e13063de92b87fdc17a584101c46e6e432b985bac322623acbb89f93b16545"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:54.599852Z","signature_b64":"ex2Kt/NzcH8uo3qAfNHxYfGGOXHFy01mZ0C280a+NLwvvHGfVJhZXknPoXZm828qyF63Qr0SbkGbkZfFsEMhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7463c11288516322548bc7bd12882f55c110cdc9d3b9ae59a4b2d8646cad1b84","last_reissued_at":"2026-05-18T02:54:54.599303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:54.599303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transitive Group Actions: (IM)PRIMITIVITY and Semiregular Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Aleksander Malnic, Dragan Marusic, Istvan Kovacs, Stefko Miklavic","submitted_at":"2007-01-24T16:00:32Z","abstract_excerpt":"The following problem is considered: if $H$ is a semiregular abelian subgroup of a transitive permutation group $G$ acting on a finite set $X$, find conditions for (non) existence of $G$-invariant partitions of $X$. Conditions presented in this paper are derived by studying spectral properties of associated $G$-invariant digraphs. As an essential tool, irreducible complex characters of $H$ are used.\n  Questions of this kind arise naturally when classifying combinatorial objects which enjoy a certain degree of symmetry. As an illustration, a new and short proof of an old result of Frucht, Grave"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701686","kind":"arxiv","version":2},"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/0701686","created_at":"2026-05-18T02:54:54.599411+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0701686v2","created_at":"2026-05-18T02:54:54.599411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701686","created_at":"2026-05-18T02:54:54.599411+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORR4CEUIKFRS","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORR4CEUIKFRSEVEL","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORR4CEUI","created_at":"2026-05-18T12:25:55.427421+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/ORR4CEUIKFRSEVELY66RFCBPKX","json":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX.json","graph_json":"https://pith.science/api/pith-number/ORR4CEUIKFRSEVELY66RFCBPKX/graph.json","events_json":"https://pith.science/api/pith-number/ORR4CEUIKFRSEVELY66RFCBPKX/events.json","paper":"https://pith.science/paper/ORR4CEUI"},"agent_actions":{"view_html":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX","download_json":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX.json","view_paper":"https://pith.science/paper/ORR4CEUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0701686&json=true","fetch_graph":"https://pith.science/api/pith-number/ORR4CEUIKFRSEVELY66RFCBPKX/graph.json","fetch_events":"https://pith.science/api/pith-number/ORR4CEUIKFRSEVELY66RFCBPKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX/action/storage_attestation","attest_author":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX/action/author_attestation","sign_citation":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX/action/citation_signature","submit_replication":"https://pith.science/pith/ORR4CEUIKFRSEVELY66RFCBPKX/action/replication_record"}},"created_at":"2026-05-18T02:54:54.599411+00:00","updated_at":"2026-05-18T02:54:54.599411+00:00"}