{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4GJRAD353XNU5EXDD6FCAV5TER","short_pith_number":"pith:4GJRAD35","canonical_record":{"source":{"id":"2601.04053","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-01-07T16:17:36Z","cross_cats_sorted":["math.AC","math.CT"],"title_canon_sha256":"350228a18bcc221ffa2798bcd837f214c2f44506b6c964e966f48924e1d376ba","abstract_canon_sha256":"e34a3bc57f934f2bc8a1cfd5d2ccf3e21898a9133c3eaf920b6796a146f4010d"},"schema_version":"1.0"},"canonical_sha256":"e193100f7ddddb4e92e31f8a2057b3246e6080a62082edf678ab455dba94268c","source":{"kind":"arxiv","id":"2601.04053","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.04053","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"2601.04053v4","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.04053","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"4GJRAD353XNU","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"pith_short_16","alias_value":"4GJRAD353XNU5EXD","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"pith_short_8","alias_value":"4GJRAD35","created_at":"2026-07-17T01:21:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4GJRAD353XNU5EXDD6FCAV5TER","target":"record","payload":{"canonical_record":{"source":{"id":"2601.04053","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-01-07T16:17:36Z","cross_cats_sorted":["math.AC","math.CT"],"title_canon_sha256":"350228a18bcc221ffa2798bcd837f214c2f44506b6c964e966f48924e1d376ba","abstract_canon_sha256":"e34a3bc57f934f2bc8a1cfd5d2ccf3e21898a9133c3eaf920b6796a146f4010d"},"schema_version":"1.0"},"canonical_sha256":"e193100f7ddddb4e92e31f8a2057b3246e6080a62082edf678ab455dba94268c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:45.230522Z","signature_b64":"XgfE120O6dzoJ3s+LRQxO7ihOX81fLNcqn3nnW3l+HhX9Im/8T7WbAkNk5TP/voB2SJPySI7JuacL33sHM82Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e193100f7ddddb4e92e31f8a2057b3246e6080a62082edf678ab455dba94268c","last_reissued_at":"2026-07-17T01:21:45.229480Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:45.229480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.04053","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-17T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqTcOI8bUW3oPHyn/HfoyLRS40U7BwOHwo8wLINso0dCm4bJdsS6gqhLKC9c5hvGgWwXqWjJUskbT14/6gN9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:36:33.480820Z"},"content_sha256":"1c561e8fe15f06f001450358c0f4c5e0a913b99b5c16ab06aa929706c9310389","schema_version":"1.0","event_id":"sha256:1c561e8fe15f06f001450358c0f4c5e0a913b99b5c16ab06aa929706c9310389"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4GJRAD353XNU5EXDD6FCAV5TER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect generation for regular algebraic stacks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.CT"],"primary_cat":"math.AG","authors_text":"Pat Lank","submitted_at":"2026-01-07T16:17:36Z","abstract_excerpt":"We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect complex. In the concentrated case, the category is singly compactly generated. Key ingredients in the proofs include gluing generators along recollement and the use of suitable filtrations and presentations of the algebraic stack."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04053","kind":"arxiv","version":4},"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/2601.04053/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":"2026-07-17T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOU/zdrRNyBFCr/4jODIdL+WfHzce6XC+bMsuQentT9v5WPP9yoayBj5XyUf+7ah4wk+wi4AA/imiOGFHDNUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:36:33.481413Z"},"content_sha256":"7aaba2e66bca44ebb53050f1c43e315228e22da2801d124230f94bd21ddd0437","schema_version":"1.0","event_id":"sha256:7aaba2e66bca44ebb53050f1c43e315228e22da2801d124230f94bd21ddd0437"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GJRAD353XNU5EXDD6FCAV5TER/bundle.json","state_url":"https://pith.science/pith/4GJRAD353XNU5EXDD6FCAV5TER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GJRAD353XNU5EXDD6FCAV5TER/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":"2026-08-09T20:36:33Z","links":{"resolver":"https://pith.science/pith/4GJRAD353XNU5EXDD6FCAV5TER","bundle":"https://pith.science/pith/4GJRAD353XNU5EXDD6FCAV5TER/bundle.json","state":"https://pith.science/pith/4GJRAD353XNU5EXDD6FCAV5TER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GJRAD353XNU5EXDD6FCAV5TER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4GJRAD353XNU5EXDD6FCAV5TER","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":"e34a3bc57f934f2bc8a1cfd5d2ccf3e21898a9133c3eaf920b6796a146f4010d","cross_cats_sorted":["math.AC","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-01-07T16:17:36Z","title_canon_sha256":"350228a18bcc221ffa2798bcd837f214c2f44506b6c964e966f48924e1d376ba"},"schema_version":"1.0","source":{"id":"2601.04053","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.04053","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"2601.04053v4","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.04053","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"4GJRAD353XNU","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"pith_short_16","alias_value":"4GJRAD353XNU5EXD","created_at":"2026-07-17T01:21:45Z"},{"alias_kind":"pith_short_8","alias_value":"4GJRAD35","created_at":"2026-07-17T01:21:45Z"}],"graph_snapshots":[{"event_id":"sha256:7aaba2e66bca44ebb53050f1c43e315228e22da2801d124230f94bd21ddd0437","target":"graph","created_at":"2026-07-17T01:21:45Z","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/2601.04053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect complex. In the concentrated case, the category is singly compactly generated. Key ingredients in the proofs include gluing generators along recollement and the use of suitable filtrations and presentations of the algebraic stack.","authors_text":"Pat Lank","cross_cats":["math.AC","math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-01-07T16:17:36Z","title":"Perfect generation for regular algebraic stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04053","kind":"arxiv","version":4},"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":"sha256:1c561e8fe15f06f001450358c0f4c5e0a913b99b5c16ab06aa929706c9310389","target":"record","created_at":"2026-07-17T01:21:45Z","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":"e34a3bc57f934f2bc8a1cfd5d2ccf3e21898a9133c3eaf920b6796a146f4010d","cross_cats_sorted":["math.AC","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-01-07T16:17:36Z","title_canon_sha256":"350228a18bcc221ffa2798bcd837f214c2f44506b6c964e966f48924e1d376ba"},"schema_version":"1.0","source":{"id":"2601.04053","kind":"arxiv","version":4}},"canonical_sha256":"e193100f7ddddb4e92e31f8a2057b3246e6080a62082edf678ab455dba94268c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e193100f7ddddb4e92e31f8a2057b3246e6080a62082edf678ab455dba94268c","first_computed_at":"2026-07-17T01:21:45.229480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:21:45.229480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XgfE120O6dzoJ3s+LRQxO7ihOX81fLNcqn3nnW3l+HhX9Im/8T7WbAkNk5TP/voB2SJPySI7JuacL33sHM82Dw==","signature_status":"signed_v1","signed_at":"2026-07-17T01:21:45.230522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.04053","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c561e8fe15f06f001450358c0f4c5e0a913b99b5c16ab06aa929706c9310389","sha256:7aaba2e66bca44ebb53050f1c43e315228e22da2801d124230f94bd21ddd0437"],"state_sha256":"d1da1822df1753501d029ac55e536b6abca0914bb0d2622629bd417f71e97630"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PbQY4Rm9Tc1X4UtCfxe/PvVPK2xDdGBHP9OByDyzbGBm8X9coPjiMhd61egCF2AUPyTjleBXQrGCnznSvCrCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:36:33.486039Z","bundle_sha256":"22267b3bc882577627fa7c19404d965d60878f1b6b0422890bd01f3558cc8be6"}}