{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WVT5BEA6UXTJVBGR7LS53BGW3L","short_pith_number":"pith:WVT5BEA6","canonical_record":{"source":{"id":"1404.5011","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-20T04:49:10Z","cross_cats_sorted":["math.CT","math.RT"],"title_canon_sha256":"b772e085cb388f2acaee647a058219a3327d664ce9ab1126bf7237161320303e","abstract_canon_sha256":"7f118fa5a48af07a5d266a3a0e847073d10923dab53ffee239e26956586fad2d"},"schema_version":"1.0"},"canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","source":{"kind":"arxiv","id":"1404.5011","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5011","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5011v6","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5011","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"WVT5BEA6UXTJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WVT5BEA6UXTJVBGR","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WVT5BEA6","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WVT5BEA6UXTJVBGR7LS53BGW3L","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5011","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-20T04:49:10Z","cross_cats_sorted":["math.CT","math.RT"],"title_canon_sha256":"b772e085cb388f2acaee647a058219a3327d664ce9ab1126bf7237161320303e","abstract_canon_sha256":"7f118fa5a48af07a5d266a3a0e847073d10923dab53ffee239e26956586fad2d"},"schema_version":"1.0"},"canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:10.963113Z","signature_b64":"umONmCujccjewholhaR54jlSHlbcUgkyvfIlo1yzpTKw21RzL49BPlt0fwYLyx4ktehxqhvYV1nhxCua6gBvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","last_reissued_at":"2026-05-18T00:01:10.962333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:10.962333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5011","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zbsc88dowdn69ok19oF7jkdpERtnQvsz2TPSiRZdvQMY552G5NKWGkaK3DKXaI11vJOsWO6L+HT00oTkgakEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T08:20:51.830368Z"},"content_sha256":"86d6a223d6343238c88cbbc53769c4a89cf0f8aba1e1bc8c8b68b0dd4ff7e8d7","schema_version":"1.0","event_id":"sha256:86d6a223d6343238c88cbbc53769c4a89cf0f8aba1e1bc8c8b68b0dd4ff7e8d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WVT5BEA6UXTJVBGR7LS53BGW3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical Bockstein sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.KT","authors_text":"Leonid Positselski","submitted_at":"2014-04-20T04:49:10Z","abstract_excerpt":"We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to recover the abelian/exact category of modular representations of a finite group from the exact category of its l-adic representations. The construction uses matrix factorizations in a nontraditional way. We obtain the Bockstein long exact sequences for the Ext groups in the exact categories produced by reduction. Our motivation comes from the theory of Artin-T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5011","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"toqVyM994LbMWl5B/ndZX4YCBL4V7NguD1XHbC5xtDzS4Trwpo50OVw16RzgWjQc4K5aHQglGOJBcQxd65bqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T08:20:51.830730Z"},"content_sha256":"f673c892c7a9798e5f47c8e471fd1197e42e1da0bf13e67f0817ff6a2edeacbe","schema_version":"1.0","event_id":"sha256:f673c892c7a9798e5f47c8e471fd1197e42e1da0bf13e67f0817ff6a2edeacbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/bundle.json","state_url":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/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":"2026-05-20T08:20:51Z","links":{"resolver":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L","bundle":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/bundle.json","state":"https://pith.science/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVT5BEA6UXTJVBGR7LS53BGW3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WVT5BEA6UXTJVBGR7LS53BGW3L","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":"7f118fa5a48af07a5d266a3a0e847073d10923dab53ffee239e26956586fad2d","cross_cats_sorted":["math.CT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-20T04:49:10Z","title_canon_sha256":"b772e085cb388f2acaee647a058219a3327d664ce9ab1126bf7237161320303e"},"schema_version":"1.0","source":{"id":"1404.5011","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5011","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5011v6","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5011","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"WVT5BEA6UXTJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WVT5BEA6UXTJVBGR","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WVT5BEA6","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:f673c892c7a9798e5f47c8e471fd1197e42e1da0bf13e67f0817ff6a2edeacbe","target":"graph","created_at":"2026-05-18T00:01:10Z","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"},"paper":{"abstract_excerpt":"We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to recover the abelian/exact category of modular representations of a finite group from the exact category of its l-adic representations. The construction uses matrix factorizations in a nontraditional way. We obtain the Bockstein long exact sequences for the Ext groups in the exact categories produced by reduction. Our motivation comes from the theory of Artin-T","authors_text":"Leonid Positselski","cross_cats":["math.CT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-20T04:49:10Z","title":"Categorical Bockstein sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5011","kind":"arxiv","version":6},"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":"sha256:86d6a223d6343238c88cbbc53769c4a89cf0f8aba1e1bc8c8b68b0dd4ff7e8d7","target":"record","created_at":"2026-05-18T00:01:10Z","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":"7f118fa5a48af07a5d266a3a0e847073d10923dab53ffee239e26956586fad2d","cross_cats_sorted":["math.CT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2014-04-20T04:49:10Z","title_canon_sha256":"b772e085cb388f2acaee647a058219a3327d664ce9ab1126bf7237161320303e"},"schema_version":"1.0","source":{"id":"1404.5011","kind":"arxiv","version":6}},"canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b567d0901ea5e69a84d1fae5dd84d6dadc27080402b36c4a0ab4ba6e6b02b183","first_computed_at":"2026-05-18T00:01:10.962333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:10.962333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umONmCujccjewholhaR54jlSHlbcUgkyvfIlo1yzpTKw21RzL49BPlt0fwYLyx4ktehxqhvYV1nhxCua6gBvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:10.963113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5011","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86d6a223d6343238c88cbbc53769c4a89cf0f8aba1e1bc8c8b68b0dd4ff7e8d7","sha256:f673c892c7a9798e5f47c8e471fd1197e42e1da0bf13e67f0817ff6a2edeacbe"],"state_sha256":"77b49562d233394492ef4992afa84c7c93823ecdccabd7bf08848611e56823a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3LPfZDNWYjnPrPzr0ociUwdRkeA6m3TFjxlaS+7kd4WYKog1YvCM9c8BSOW9NnGbgUHZB8hcH482vSdZ3WRKCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T08:20:51.832810Z","bundle_sha256":"3663f24c0769ceafed481318c57fe3e061243585cfdc2a514d9febb932212c7d"}}