{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WPVVTVGOWW25WSPYOLRSG6OKYX","short_pith_number":"pith:WPVVTVGO","canonical_record":{"source":{"id":"2606.20379","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-18T15:38:06Z","cross_cats_sorted":[],"title_canon_sha256":"1461ae941a65df8937e7453cfce89e6e9db34c726bfc1cbfbd55261afadb1553","abstract_canon_sha256":"40698ca7c55232ab20e77c465a5790d621787d65f8073488047f7ee3c605d751"},"schema_version":"1.0"},"canonical_sha256":"b3eb59d4ceb5b5db49f872e32379cac5c8f3680520910972d01f9e5f31563677","source":{"kind":"arxiv","id":"2606.20379","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20379","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20379v1","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20379","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"WPVVTVGOWW25","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"pith_short_16","alias_value":"WPVVTVGOWW25WSPY","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"pith_short_8","alias_value":"WPVVTVGO","created_at":"2026-06-19T16:13:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WPVVTVGOWW25WSPYOLRSG6OKYX","target":"record","payload":{"canonical_record":{"source":{"id":"2606.20379","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-18T15:38:06Z","cross_cats_sorted":[],"title_canon_sha256":"1461ae941a65df8937e7453cfce89e6e9db34c726bfc1cbfbd55261afadb1553","abstract_canon_sha256":"40698ca7c55232ab20e77c465a5790d621787d65f8073488047f7ee3c605d751"},"schema_version":"1.0"},"canonical_sha256":"b3eb59d4ceb5b5db49f872e32379cac5c8f3680520910972d01f9e5f31563677","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:13:10.706515Z","signature_b64":"2AxFTmjq2mKCRpquCGuUdWiU5dw2gM8b4Gv/rS9bjN9UTrx9wGStseDV5DBfjvzvE3V3SMaA0K+SIVK1Jd6CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3eb59d4ceb5b5db49f872e32379cac5c8f3680520910972d01f9e5f31563677","last_reissued_at":"2026-06-19T16:13:10.706032Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:13:10.706032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.20379","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z02t9Oh/O0pQUUhSXfL3AR+W4DngGaXoochZ8SxB12WXoXBNJS951RqQjnjXlKuW1RHc0B46HtN5L4j3pMJiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:28:07.994278Z"},"content_sha256":"f0df17cbfe649c77e120a840cf85a9466b82d4b794bfedd4723043dc76a4c3a7","schema_version":"1.0","event_id":"sha256:f0df17cbfe649c77e120a840cf85a9466b82d4b794bfedd4723043dc76a4c3a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WPVVTVGOWW25WSPYOLRSG6OKYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linking conjugacy classes and minimal invariant characters of normal subgroups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Iris Gilabert, Lucia Sanus, Mar\\'ia Jos\\'e Felipe","submitted_at":"2026-06-18T15:38:06Z","abstract_excerpt":"Let $G$ be a finite group and $N$ a normal subgroup of $G$. We report on recent results concerning minimal $G$-invariant characters of $N$ (which are the sums of the characters on each orbit of the action of $G$ by conjugation on $\\text{Irr}(N)$) and their influence on the structure of $N$, as well as their relationship to the $G$-conjugacy classes of $N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20379","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/2606.20379/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrBAF92ZCPM90WRwzLI8nfCKKTTAm1iMtUh/bH2wBC0WiaodYPEFJ6jMr27BvLpa4YXSvAuYv6xSCws/qdYbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:28:07.994666Z"},"content_sha256":"6ee1f194ab750878055205f31959b81422b44d5e5e899eb7237eea6559f46d00","schema_version":"1.0","event_id":"sha256:6ee1f194ab750878055205f31959b81422b44d5e5e899eb7237eea6559f46d00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPVVTVGOWW25WSPYOLRSG6OKYX/bundle.json","state_url":"https://pith.science/pith/WPVVTVGOWW25WSPYOLRSG6OKYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPVVTVGOWW25WSPYOLRSG6OKYX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T23:28:07Z","links":{"resolver":"https://pith.science/pith/WPVVTVGOWW25WSPYOLRSG6OKYX","bundle":"https://pith.science/pith/WPVVTVGOWW25WSPYOLRSG6OKYX/bundle.json","state":"https://pith.science/pith/WPVVTVGOWW25WSPYOLRSG6OKYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPVVTVGOWW25WSPYOLRSG6OKYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WPVVTVGOWW25WSPYOLRSG6OKYX","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":"40698ca7c55232ab20e77c465a5790d621787d65f8073488047f7ee3c605d751","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-18T15:38:06Z","title_canon_sha256":"1461ae941a65df8937e7453cfce89e6e9db34c726bfc1cbfbd55261afadb1553"},"schema_version":"1.0","source":{"id":"2606.20379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20379","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20379v1","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20379","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"WPVVTVGOWW25","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"pith_short_16","alias_value":"WPVVTVGOWW25WSPY","created_at":"2026-06-19T16:13:10Z"},{"alias_kind":"pith_short_8","alias_value":"WPVVTVGO","created_at":"2026-06-19T16:13:10Z"}],"graph_snapshots":[{"event_id":"sha256:6ee1f194ab750878055205f31959b81422b44d5e5e899eb7237eea6559f46d00","target":"graph","created_at":"2026-06-19T16:13:10Z","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/2606.20379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a finite group and $N$ a normal subgroup of $G$. We report on recent results concerning minimal $G$-invariant characters of $N$ (which are the sums of the characters on each orbit of the action of $G$ by conjugation on $\\text{Irr}(N)$) and their influence on the structure of $N$, as well as their relationship to the $G$-conjugacy classes of $N$.","authors_text":"Iris Gilabert, Lucia Sanus, Mar\\'ia Jos\\'e Felipe","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-18T15:38:06Z","title":"Linking conjugacy classes and minimal invariant characters of normal subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20379","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:f0df17cbfe649c77e120a840cf85a9466b82d4b794bfedd4723043dc76a4c3a7","target":"record","created_at":"2026-06-19T16:13:10Z","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":"40698ca7c55232ab20e77c465a5790d621787d65f8073488047f7ee3c605d751","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-18T15:38:06Z","title_canon_sha256":"1461ae941a65df8937e7453cfce89e6e9db34c726bfc1cbfbd55261afadb1553"},"schema_version":"1.0","source":{"id":"2606.20379","kind":"arxiv","version":1}},"canonical_sha256":"b3eb59d4ceb5b5db49f872e32379cac5c8f3680520910972d01f9e5f31563677","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3eb59d4ceb5b5db49f872e32379cac5c8f3680520910972d01f9e5f31563677","first_computed_at":"2026-06-19T16:13:10.706032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:13:10.706032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2AxFTmjq2mKCRpquCGuUdWiU5dw2gM8b4Gv/rS9bjN9UTrx9wGStseDV5DBfjvzvE3V3SMaA0K+SIVK1Jd6CDQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:13:10.706515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0df17cbfe649c77e120a840cf85a9466b82d4b794bfedd4723043dc76a4c3a7","sha256:6ee1f194ab750878055205f31959b81422b44d5e5e899eb7237eea6559f46d00"],"state_sha256":"95ccbf2824ab71bc297f66a3c09abe59b4075199bd6440a62e95e6a90eb76700"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkx72lnnIj25a8cet8XlAMa6jUjPiny2rkBF0nau47Y5HU9AgyGkcisba7+GzaXgrlo79g4sMnjN/u2CE/PsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:28:07.996695Z","bundle_sha256":"5b0fb86e0b6e3dd7e374b7a530a318da43b04da00c0f74cafdd5529f79108078"}}