{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:F5DQBU4QKNFNNC5WR4YZJVMOVT","short_pith_number":"pith:F5DQBU4Q","canonical_record":{"source":{"id":"2605.27244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-05-26T16:25:02Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"f6395861ec96f7cd81fbe9fd70fe5db0671d20a279981bf4ec1dae254a16f3f7","abstract_canon_sha256":"2d3e877129b14c35af0089919dfe062e97987a082c7f1f783f732c31d20aadd7"},"schema_version":"1.0"},"canonical_sha256":"2f4700d390534ad68bb68f3194d58eaccb1f0b8f5694970948c0e6c70d77a358","source":{"kind":"arxiv","id":"2605.27244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27244","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27244v1","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27244","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"F5DQBU4QKNFN","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"F5DQBU4QKNFNNC5W","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"F5DQBU4Q","created_at":"2026-05-27T02:06:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:F5DQBU4QKNFNNC5WR4YZJVMOVT","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-05-26T16:25:02Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"f6395861ec96f7cd81fbe9fd70fe5db0671d20a279981bf4ec1dae254a16f3f7","abstract_canon_sha256":"2d3e877129b14c35af0089919dfe062e97987a082c7f1f783f732c31d20aadd7"},"schema_version":"1.0"},"canonical_sha256":"2f4700d390534ad68bb68f3194d58eaccb1f0b8f5694970948c0e6c70d77a358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:06:07.406167Z","signature_b64":"8tJ+nT5RK+RkYQlh0P28K0hwfpyFEwuTw40HWxTY1/hHmm4lTjrlc6TZuDXfnJgrg8xaoz5eBBwvhQ2yYqGxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f4700d390534ad68bb68f3194d58eaccb1f0b8f5694970948c0e6c70d77a358","last_reissued_at":"2026-05-27T02:06:07.405548Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:06:07.405548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27244","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":"2026-05-27T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3g6JLRmOAn85Zg/4aQJJohLHg8ghdIug3GLeX17vEzus3qZW0sV+WG7Mmc5a7sIB6ocKvJjHhGeWE9SDs/oHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:05:08.422717Z"},"content_sha256":"ebd93ebcb4dbc54d8e311149a7ba9c9d4b2d3a19b762d6036853c570d8cda784","schema_version":"1.0","event_id":"sha256:ebd93ebcb4dbc54d8e311149a7ba9c9d4b2d3a19b762d6036853c570d8cda784"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:F5DQBU4QKNFNNC5WR4YZJVMOVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Residual regularity in tensor triangular geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CT","authors_text":"Emmy Van Rooy","submitted_at":"2026-05-26T16:25:02Z","abstract_excerpt":"We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived category of permutation modules is residually regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27244","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/2605.27244/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":"2026-05-27T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HltEJBkQZrPA4Cdl6ToNxHf49NHl5Ymfe044TgxxbAxqfGi1xkjh3mF13+eO6v8kQ+2fVAni3E4hbSfGJFuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:05:08.423677Z"},"content_sha256":"5190faf32556dc6cdd70b6e209df531d9720b172fa65386c658e6dea38e394f9","schema_version":"1.0","event_id":"sha256:5190faf32556dc6cdd70b6e209df531d9720b172fa65386c658e6dea38e394f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT/bundle.json","state_url":"https://pith.science/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT/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":"2026-08-13T01:05:08Z","links":{"resolver":"https://pith.science/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT","bundle":"https://pith.science/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT/bundle.json","state":"https://pith.science/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5DQBU4QKNFNNC5WR4YZJVMOVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F5DQBU4QKNFNNC5WR4YZJVMOVT","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":"2d3e877129b14c35af0089919dfe062e97987a082c7f1f783f732c31d20aadd7","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-05-26T16:25:02Z","title_canon_sha256":"f6395861ec96f7cd81fbe9fd70fe5db0671d20a279981bf4ec1dae254a16f3f7"},"schema_version":"1.0","source":{"id":"2605.27244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27244","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27244v1","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27244","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"F5DQBU4QKNFN","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"F5DQBU4QKNFNNC5W","created_at":"2026-05-27T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"F5DQBU4Q","created_at":"2026-05-27T02:06:07Z"}],"graph_snapshots":[{"event_id":"sha256:5190faf32556dc6cdd70b6e209df531d9720b172fa65386c658e6dea38e394f9","target":"graph","created_at":"2026-05-27T02:06:07Z","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/2605.27244/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived category of permutation modules is residually regular.","authors_text":"Emmy Van Rooy","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-05-26T16:25:02Z","title":"Residual regularity in tensor triangular geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27244","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:ebd93ebcb4dbc54d8e311149a7ba9c9d4b2d3a19b762d6036853c570d8cda784","target":"record","created_at":"2026-05-27T02:06:07Z","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":"2d3e877129b14c35af0089919dfe062e97987a082c7f1f783f732c31d20aadd7","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-05-26T16:25:02Z","title_canon_sha256":"f6395861ec96f7cd81fbe9fd70fe5db0671d20a279981bf4ec1dae254a16f3f7"},"schema_version":"1.0","source":{"id":"2605.27244","kind":"arxiv","version":1}},"canonical_sha256":"2f4700d390534ad68bb68f3194d58eaccb1f0b8f5694970948c0e6c70d77a358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f4700d390534ad68bb68f3194d58eaccb1f0b8f5694970948c0e6c70d77a358","first_computed_at":"2026-05-27T02:06:07.405548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:07.405548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8tJ+nT5RK+RkYQlh0P28K0hwfpyFEwuTw40HWxTY1/hHmm4lTjrlc6TZuDXfnJgrg8xaoz5eBBwvhQ2yYqGxBg==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:07.406167Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebd93ebcb4dbc54d8e311149a7ba9c9d4b2d3a19b762d6036853c570d8cda784","sha256:5190faf32556dc6cdd70b6e209df531d9720b172fa65386c658e6dea38e394f9"],"state_sha256":"034d3c36eec42a6287b733e89d22abd92a87b575375d9f1ea25e8b40801e952d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFS9yIxA9nevGpD7eXXYsRuuES6j8l24KGjCr/3dIteJG7iJgDX3bIh+8/M8GsGC7MDIeLnwDGGciDB8kU0MDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:05:08.520912Z","bundle_sha256":"7e1dcdac6a27a211c12f777d5906b42d63b9ec5d69a44d0b8a4d32110c26e8bd"}}