{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7HRJPBGH7YYQL6ZC7RBFLY55V4","short_pith_number":"pith:7HRJPBGH","schema_version":"1.0","canonical_sha256":"f9e29784c7fe3105fb22fc4255e3bdaf01f56d09231d93e62c6c81d70b0d57e8","source":{"kind":"arxiv","id":"2412.12345","version":1},"attestation_state":"computed","paper":{"title":"Critical groups and partitions of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Daniela Bubboloni, Nicolas Pinzauti","submitted_at":"2024-12-16T20:39:39Z","abstract_excerpt":"We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups."},"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":"2412.12345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-12-16T20:39:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"318e70a61516afba1dc88ff6a60030060f715a85f41b359aa63b3b1c91e4e265","abstract_canon_sha256":"db31269f33bf33def0109d8d912a879c9914ac56403d8d981eba90cf30f99fac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:19.556935Z","signature_b64":"Al6pAaijwNOZtNeNU6O2NNUPpklii9jh316WTWB8Rwj8J/OF22eRPdmoidNKTi4U1LivOiV9Ulrysn6i8G8pAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9e29784c7fe3105fb22fc4255e3bdaf01f56d09231d93e62c6c81d70b0d57e8","last_reissued_at":"2026-07-05T09:52:19.556490Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:19.556490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical groups and partitions of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Daniela Bubboloni, Nicolas Pinzauti","submitted_at":"2024-12-16T20:39:39Z","abstract_excerpt":"We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12345","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.12345/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.12345","created_at":"2026-07-05T09:52:19.556540+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.12345v1","created_at":"2026-07-05T09:52:19.556540+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.12345","created_at":"2026-07-05T09:52:19.556540+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HRJPBGH7YYQ","created_at":"2026-07-05T09:52:19.556540+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HRJPBGH7YYQL6ZC","created_at":"2026-07-05T09:52:19.556540+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HRJPBGH","created_at":"2026-07-05T09:52:19.556540+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/7HRJPBGH7YYQL6ZC7RBFLY55V4","json":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4.json","graph_json":"https://pith.science/api/pith-number/7HRJPBGH7YYQL6ZC7RBFLY55V4/graph.json","events_json":"https://pith.science/api/pith-number/7HRJPBGH7YYQL6ZC7RBFLY55V4/events.json","paper":"https://pith.science/paper/7HRJPBGH"},"agent_actions":{"view_html":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4","download_json":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4.json","view_paper":"https://pith.science/paper/7HRJPBGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.12345&json=true","fetch_graph":"https://pith.science/api/pith-number/7HRJPBGH7YYQL6ZC7RBFLY55V4/graph.json","fetch_events":"https://pith.science/api/pith-number/7HRJPBGH7YYQL6ZC7RBFLY55V4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4/action/storage_attestation","attest_author":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4/action/author_attestation","sign_citation":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4/action/citation_signature","submit_replication":"https://pith.science/pith/7HRJPBGH7YYQL6ZC7RBFLY55V4/action/replication_record"}},"created_at":"2026-07-05T09:52:19.556540+00:00","updated_at":"2026-07-05T09:52:19.556540+00:00"}