{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ROIS7EUSU6LXZGL4NG5QCOMFVL","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":"01501f837d91e9b0a465cc68a34695d1213ec75753741322102e8be0212f63c8","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-20T18:22:09Z","title_canon_sha256":"6373ae4ba89c9b80ef87fea668fb29981e128ca1698f293b4dd08283b66fb184"},"schema_version":"1.0","source":{"id":"2412.16128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16128","created_at":"2026-07-05T09:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16128v1","created_at":"2026-07-05T09:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16128","created_at":"2026-07-05T09:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"ROIS7EUSU6LX","created_at":"2026-07-05T09:52:35Z"},{"alias_kind":"pith_short_16","alias_value":"ROIS7EUSU6LXZGL4","created_at":"2026-07-05T09:52:35Z"},{"alias_kind":"pith_short_8","alias_value":"ROIS7EUS","created_at":"2026-07-05T09:52:35Z"}],"graph_snapshots":[{"event_id":"sha256:b8ac385684beacf0e51de0793398f71fe0086c1725bec06753bc574bcad1af67","target":"graph","created_at":"2026-07-05T09:52:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.16128/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study rationality properties of irreducible characters of finite groups. We show that the continuity of $2$-rationality is a phenomenon that can be detected in the principal $2$-block, thus refining a recent result of N. N. Hung. We also propose a conjectural group theoretical criterion for the continuity gap at level $1$ for all primes","authors_text":"Carolina Vallejo, Gunter Malle, J. Miquel Mart\\'inez","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-20T18:22:09Z","title":"The continuity of $p$-rationality of characters and the principal block"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16128","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":"sha256:3d8f0e5a8ca3aeb0cafc2cee7d83c3b2e75346aec5d1bc21d3c9a1bd7b70d140","target":"record","created_at":"2026-07-05T09:52:35Z","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":"01501f837d91e9b0a465cc68a34695d1213ec75753741322102e8be0212f63c8","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-20T18:22:09Z","title_canon_sha256":"6373ae4ba89c9b80ef87fea668fb29981e128ca1698f293b4dd08283b66fb184"},"schema_version":"1.0","source":{"id":"2412.16128","kind":"arxiv","version":1}},"canonical_sha256":"8b912f9292a7977c997c69bb013985aadb41b088e920a2ee418014097e6cf1e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b912f9292a7977c997c69bb013985aadb41b088e920a2ee418014097e6cf1e4","first_computed_at":"2026-07-05T09:52:35.576580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:35.576580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVOhoeroCyFWGlGoOuPVg8TmISDiWd3RrOvwO7js/Y7tHtrmjwH6DjL/+l03Bb5ZlRVNt9F+7QQJJO1jj6V4CA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:35.577106Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d8f0e5a8ca3aeb0cafc2cee7d83c3b2e75346aec5d1bc21d3c9a1bd7b70d140","sha256:b8ac385684beacf0e51de0793398f71fe0086c1725bec06753bc574bcad1af67"],"state_sha256":"0dcb8143bb284ccabd02267fb550ccabb68eb97456fe8ff5d2f142b04fcc0e91"}