{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KIE5UPFFEUZZCDCFNO2O2RHH7U","short_pith_number":"pith:KIE5UPFF","canonical_record":{"source":{"id":"2410.23941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-31T13:55:13Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"6e6cf4b3c701ef33d89240cc4bb5f8f3a519d139629c9dc2d58b88ebb05107da","abstract_canon_sha256":"76e3cb3cb3f21498a6bc8c8f57e5c0bd4b4cecbd20be26049e5408083b825446"},"schema_version":"1.0"},"canonical_sha256":"5209da3ca52533910c456bb4ed44e7fd0bb2e72af89f6648f35ab666bf7fef79","source":{"kind":"arxiv","id":"2410.23941","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23941","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23941v1","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23941","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"pith_short_12","alias_value":"KIE5UPFFEUZZ","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"KIE5UPFFEUZZCDCF","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"KIE5UPFF","created_at":"2026-07-05T09:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KIE5UPFFEUZZCDCFNO2O2RHH7U","target":"record","payload":{"canonical_record":{"source":{"id":"2410.23941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-31T13:55:13Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"6e6cf4b3c701ef33d89240cc4bb5f8f3a519d139629c9dc2d58b88ebb05107da","abstract_canon_sha256":"76e3cb3cb3f21498a6bc8c8f57e5c0bd4b4cecbd20be26049e5408083b825446"},"schema_version":"1.0"},"canonical_sha256":"5209da3ca52533910c456bb4ed44e7fd0bb2e72af89f6648f35ab666bf7fef79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:29:07.647840Z","signature_b64":"A++CCiR8gn6ereGysxF1stNyoE3h0hmQ8N79+sdK7hRAtJT5uAGeuM6WKSZyOlTQZ9bYPNlMqYldv3To/M2AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5209da3ca52533910c456bb4ed44e7fd0bb2e72af89f6648f35ab666bf7fef79","last_reissued_at":"2026-07-05T09:29:07.647301Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:29:07.647301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.23941","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":"2026-07-05T09:29:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5vA1NKxnWaCddQAS83GS0Afhfq8lIXgjY/352Y/YPUJk5FEE6zldGwFX5TLh2mHcKDvkXKwPMNzUGcYepK0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:22:00.249265Z"},"content_sha256":"ae96c51fd27d17137a5327aab61c314d2cddb0dc7d29a802d4d500765424f983","schema_version":"1.0","event_id":"sha256:ae96c51fd27d17137a5327aab61c314d2cddb0dc7d29a802d4d500765424f983"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KIE5UPFFEUZZCDCFNO2O2RHH7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"(Co)stratification of stable categories for infinite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Gregory Kendall","submitted_at":"2024-10-31T13:55:13Z","abstract_excerpt":"We classify the localising tensor ideal and colocalising hom-closed subcategories of the stable module category for $\\mathrm{LH}\\mathfrak{F}$ groups. Along the way we develop techniques to provide similar classifications for other categories of infinite groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23941","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/2410.23941/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":"2026-07-05T09:29:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4x2z7HGRK6lr7Hwt5YYnKivYOpEj7Da8TeXIZWKiuuxcKIBGiLqF9ou7ScSnUBSUzk8Tv2423L/sLyC9zr+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:22:00.249817Z"},"content_sha256":"daaf2c06ee4a9624380c29d61cd8866786f7105002340ba96f186b0500106340","schema_version":"1.0","event_id":"sha256:daaf2c06ee4a9624380c29d61cd8866786f7105002340ba96f186b0500106340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U/bundle.json","state_url":"https://pith.science/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U/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":"2026-08-17T14:22:00Z","links":{"resolver":"https://pith.science/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U","bundle":"https://pith.science/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U/bundle.json","state":"https://pith.science/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIE5UPFFEUZZCDCFNO2O2RHH7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KIE5UPFFEUZZCDCFNO2O2RHH7U","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":"76e3cb3cb3f21498a6bc8c8f57e5c0bd4b4cecbd20be26049e5408083b825446","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-31T13:55:13Z","title_canon_sha256":"6e6cf4b3c701ef33d89240cc4bb5f8f3a519d139629c9dc2d58b88ebb05107da"},"schema_version":"1.0","source":{"id":"2410.23941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23941","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23941v1","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23941","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"pith_short_12","alias_value":"KIE5UPFFEUZZ","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"KIE5UPFFEUZZCDCF","created_at":"2026-07-05T09:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"KIE5UPFF","created_at":"2026-07-05T09:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:daaf2c06ee4a9624380c29d61cd8866786f7105002340ba96f186b0500106340","target":"graph","created_at":"2026-07-05T09:29:07Z","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/2410.23941/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the localising tensor ideal and colocalising hom-closed subcategories of the stable module category for $\\mathrm{LH}\\mathfrak{F}$ groups. Along the way we develop techniques to provide similar classifications for other categories of infinite groups.","authors_text":"Gregory Kendall","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-31T13:55:13Z","title":"(Co)stratification of stable categories for infinite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23941","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:ae96c51fd27d17137a5327aab61c314d2cddb0dc7d29a802d4d500765424f983","target":"record","created_at":"2026-07-05T09:29:07Z","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":"76e3cb3cb3f21498a6bc8c8f57e5c0bd4b4cecbd20be26049e5408083b825446","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-31T13:55:13Z","title_canon_sha256":"6e6cf4b3c701ef33d89240cc4bb5f8f3a519d139629c9dc2d58b88ebb05107da"},"schema_version":"1.0","source":{"id":"2410.23941","kind":"arxiv","version":1}},"canonical_sha256":"5209da3ca52533910c456bb4ed44e7fd0bb2e72af89f6648f35ab666bf7fef79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5209da3ca52533910c456bb4ed44e7fd0bb2e72af89f6648f35ab666bf7fef79","first_computed_at":"2026-07-05T09:29:07.647301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:29:07.647301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A++CCiR8gn6ereGysxF1stNyoE3h0hmQ8N79+sdK7hRAtJT5uAGeuM6WKSZyOlTQZ9bYPNlMqYldv3To/M2AAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:29:07.647840Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.23941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae96c51fd27d17137a5327aab61c314d2cddb0dc7d29a802d4d500765424f983","sha256:daaf2c06ee4a9624380c29d61cd8866786f7105002340ba96f186b0500106340"],"state_sha256":"523da4ef42fa145e1292e46a6a4facd15f43e53e1c70b60de16dff1d94bd0c4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfaMaZUXeD7cgFGD73a0nGLhMboFx4gRvYNMo3fu7Qka/BwcNnaa59uy22vj1Fkf6U38K3myESnxNymmJ7f4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:22:00.254003Z","bundle_sha256":"04b4ca46b64cf4a0fb9b55953fc63a0c6affaea9224a27ab2fe76e8573e273cc"}}