{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RZMGDMEUV5HFFKOYLMPELQ4LFB","short_pith_number":"pith:RZMGDMEU","canonical_record":{"source":{"id":"2307.16271","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-07-30T16:38:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"cf792dc000223c51cab4bb6bdde358dae65000488c5329edeae7b3cc0662fa29","abstract_canon_sha256":"8f5de4ab4eb1ccbd537def460817e63563bb5af9e55e846f4f707c53bf58e18d"},"schema_version":"1.0"},"canonical_sha256":"8e5861b094af4e52a9d85b1e45c38b2840d9341c7a20a9ecdb175e8a9a8428f6","source":{"kind":"arxiv","id":"2307.16271","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.16271","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"2307.16271v2","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.16271","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"RZMGDMEUV5HF","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"pith_short_16","alias_value":"RZMGDMEUV5HFFKOY","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"pith_short_8","alias_value":"RZMGDMEU","created_at":"2026-07-05T09:12:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RZMGDMEUV5HFFKOYLMPELQ4LFB","target":"record","payload":{"canonical_record":{"source":{"id":"2307.16271","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-07-30T16:38:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"cf792dc000223c51cab4bb6bdde358dae65000488c5329edeae7b3cc0662fa29","abstract_canon_sha256":"8f5de4ab4eb1ccbd537def460817e63563bb5af9e55e846f4f707c53bf58e18d"},"schema_version":"1.0"},"canonical_sha256":"8e5861b094af4e52a9d85b1e45c38b2840d9341c7a20a9ecdb175e8a9a8428f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:12:00.385891Z","signature_b64":"tbIZeJ7NDmwtTPavTDZCHRwSASzY4YgusdDjhi8IAHhBI03t2hq0dSrfp7xC8h8OJFuFqmtSEaPG3G1hao/AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5861b094af4e52a9d85b1e45c38b2840d9341c7a20a9ecdb175e8a9a8428f6","last_reissued_at":"2026-07-05T09:12:00.385376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:12:00.385376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.16271","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCsE9Iqmmw8C1+G6bKb6HqQ9fHxMFdQBL62MnxpjL6Vv4zPPL2Yc90UZsrKdxTvRoo9VWJWk6adxmbLimRzGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:21:09.415362Z"},"content_sha256":"56c79adbf4625624f910fa43c380041633662dd5d79a012e82047adc4d63d989","schema_version":"1.0","event_id":"sha256:56c79adbf4625624f910fa43c380041633662dd5d79a012e82047adc4d63d989"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RZMGDMEUV5HFFKOYLMPELQ4LFB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattices over finite group schemes and stratification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.RT","authors_text":"Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar, Tobias Barthel","submitted_at":"2023-07-30T16:38:22Z","abstract_excerpt":"This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full subcategory of all $G$-modules projective over $R$ generated by the lattices. The stable category of such $G$-modules is a rigidly-compactly generated, tensor triangulated category. The main result is that this stable category is stratified and costratified by the natural action of the cohomology ring of $G$. Applications include formulas for computing the suppor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.16271","kind":"arxiv","version":2},"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/2307.16271/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":"2026-07-05T09:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OsZkKJuQ30JNIisXXAd67nahsWNz9F7WkxH9LqKPQL9XwVD7rHDIu7JMCasrBgNgXb6TsTaqhGxQS3pkfsUfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:21:09.416218Z"},"content_sha256":"5c2f91d00507a2fc48f642c21b2730a12cd4cb5de48a6b855fc5f82a97351c6d","schema_version":"1.0","event_id":"sha256:5c2f91d00507a2fc48f642c21b2730a12cd4cb5de48a6b855fc5f82a97351c6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB/bundle.json","state_url":"https://pith.science/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB/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":"2026-08-09T07:21:09Z","links":{"resolver":"https://pith.science/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB","bundle":"https://pith.science/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB/bundle.json","state":"https://pith.science/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZMGDMEUV5HFFKOYLMPELQ4LFB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RZMGDMEUV5HFFKOYLMPELQ4LFB","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":"8f5de4ab4eb1ccbd537def460817e63563bb5af9e55e846f4f707c53bf58e18d","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-07-30T16:38:22Z","title_canon_sha256":"cf792dc000223c51cab4bb6bdde358dae65000488c5329edeae7b3cc0662fa29"},"schema_version":"1.0","source":{"id":"2307.16271","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.16271","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"2307.16271v2","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.16271","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"RZMGDMEUV5HF","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"pith_short_16","alias_value":"RZMGDMEUV5HFFKOY","created_at":"2026-07-05T09:12:00Z"},{"alias_kind":"pith_short_8","alias_value":"RZMGDMEU","created_at":"2026-07-05T09:12:00Z"}],"graph_snapshots":[{"event_id":"sha256:5c2f91d00507a2fc48f642c21b2730a12cd4cb5de48a6b855fc5f82a97351c6d","target":"graph","created_at":"2026-07-05T09:12:00Z","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/2307.16271/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full subcategory of all $G$-modules projective over $R$ generated by the lattices. The stable category of such $G$-modules is a rigidly-compactly generated, tensor triangulated category. The main result is that this stable category is stratified and costratified by the natural action of the cohomology ring of $G$. Applications include formulas for computing the suppor","authors_text":"Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar, Tobias Barthel","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-07-30T16:38:22Z","title":"Lattices over finite group schemes and stratification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.16271","kind":"arxiv","version":2},"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":"sha256:56c79adbf4625624f910fa43c380041633662dd5d79a012e82047adc4d63d989","target":"record","created_at":"2026-07-05T09:12:00Z","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":"8f5de4ab4eb1ccbd537def460817e63563bb5af9e55e846f4f707c53bf58e18d","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-07-30T16:38:22Z","title_canon_sha256":"cf792dc000223c51cab4bb6bdde358dae65000488c5329edeae7b3cc0662fa29"},"schema_version":"1.0","source":{"id":"2307.16271","kind":"arxiv","version":2}},"canonical_sha256":"8e5861b094af4e52a9d85b1e45c38b2840d9341c7a20a9ecdb175e8a9a8428f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e5861b094af4e52a9d85b1e45c38b2840d9341c7a20a9ecdb175e8a9a8428f6","first_computed_at":"2026-07-05T09:12:00.385376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:12:00.385376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbIZeJ7NDmwtTPavTDZCHRwSASzY4YgusdDjhi8IAHhBI03t2hq0dSrfp7xC8h8OJFuFqmtSEaPG3G1hao/AAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:12:00.385891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.16271","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56c79adbf4625624f910fa43c380041633662dd5d79a012e82047adc4d63d989","sha256:5c2f91d00507a2fc48f642c21b2730a12cd4cb5de48a6b855fc5f82a97351c6d"],"state_sha256":"c86e647051c867dab345d8911de26d42180fcb72a63d4d91c9fc2ab307658588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXAZhMkOvNQ34FiN7tFM67Qe5gmLr7/XIzQV0Wu5UQiBJp3zpopy9JvZbqv2VKX2ldM2fwUPWDOMGJ7xggOsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:21:09.421293Z","bundle_sha256":"4d6ac8c85be61ada7d01151d6e015059460fe720a6c036eaddff7cdaf16d623d"}}