{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UIC536GMSOBS64RCT6PBJZIBJD","short_pith_number":"pith:UIC536GM","canonical_record":{"source":{"id":"1109.1538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T19:11:14Z","cross_cats_sorted":[],"title_canon_sha256":"c745bfab2f890fcdcb4bea9ac2e7fa1b3d36a429d829eb9be81d8c0506bf57b0","abstract_canon_sha256":"60eae22de3687a42d57f55868896440d661afa5e7e46e6d4d88bb0b3d7be8e3d"},"schema_version":"1.0"},"canonical_sha256":"a205ddf8cc93832f72229f9e14e50148c2b063958eb37c02960e801b80b47450","source":{"kind":"arxiv","id":"1109.1538","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1538","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1538v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1538","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"UIC536GMSOBS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UIC536GMSOBS64RC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UIC536GM","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UIC536GMSOBS64RCT6PBJZIBJD","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T19:11:14Z","cross_cats_sorted":[],"title_canon_sha256":"c745bfab2f890fcdcb4bea9ac2e7fa1b3d36a429d829eb9be81d8c0506bf57b0","abstract_canon_sha256":"60eae22de3687a42d57f55868896440d661afa5e7e46e6d4d88bb0b3d7be8e3d"},"schema_version":"1.0"},"canonical_sha256":"a205ddf8cc93832f72229f9e14e50148c2b063958eb37c02960e801b80b47450","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:55.517581Z","signature_b64":"vPihpTvlQO/ilqkbAJYr5cx8tTZ3WhPSz47guKDKLqB6BoZ5PUjHUeDcyw3NYjufKwW7DgI9lnU6WM6pl9JTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a205ddf8cc93832f72229f9e14e50148c2b063958eb37c02960e801b80b47450","last_reissued_at":"2026-05-18T04:13:55.517100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:55.517100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1538","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":"2026-05-18T04:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w35WBMaEbrq5jeaxkqrrCwJ+sNsJTLPAFkbg3Y/lqMh1GdJAHYLYq1YveKIR5QETdS9l/v9OXuyqoFuuhtTdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:59:40.600629Z"},"content_sha256":"3051ab99a26f6939e0cdac9659c2abf446733bf5bfb4e84bdbec117b04fbbaa8","schema_version":"1.0","event_id":"sha256:3051ab99a26f6939e0cdac9659c2abf446733bf5bfb4e84bdbec117b04fbbaa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UIC536GMSOBS64RCT6PBJZIBJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence and construction of proper costratifying systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Maria In\\'es Platzeck, Melina Verdecchia, Octavio Mendoza","submitted_at":"2011-09-07T19:11:14Z","abstract_excerpt":"In this paper we further study the notion of proper costratifying systems, defined in \\cite{MPV}. We give sufficient conditions for their existence, and investigate the relation between the stratifying systems defined by K. Erdmann and C. S\\'aenz in \\cite{ES} with the proper costratifying systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1538","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":""},"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":"2026-05-18T04:13:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsAObyY6LeyCf0UI2pcLiN9PZm0OAdWzuVEgkLAkohuwXdhG+UtqVkpe0hJSwCx/kBjjElMDeF0xIBQr8ksvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:59:40.600970Z"},"content_sha256":"4a92c82566b6e7bb1c3c38fd3d471f0312d42eb772aaa0ba5baa2c86a507d577","schema_version":"1.0","event_id":"sha256:4a92c82566b6e7bb1c3c38fd3d471f0312d42eb772aaa0ba5baa2c86a507d577"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UIC536GMSOBS64RCT6PBJZIBJD/bundle.json","state_url":"https://pith.science/pith/UIC536GMSOBS64RCT6PBJZIBJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UIC536GMSOBS64RCT6PBJZIBJD/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":"2026-06-06T18:59:40Z","links":{"resolver":"https://pith.science/pith/UIC536GMSOBS64RCT6PBJZIBJD","bundle":"https://pith.science/pith/UIC536GMSOBS64RCT6PBJZIBJD/bundle.json","state":"https://pith.science/pith/UIC536GMSOBS64RCT6PBJZIBJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UIC536GMSOBS64RCT6PBJZIBJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UIC536GMSOBS64RCT6PBJZIBJD","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":"60eae22de3687a42d57f55868896440d661afa5e7e46e6d4d88bb0b3d7be8e3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T19:11:14Z","title_canon_sha256":"c745bfab2f890fcdcb4bea9ac2e7fa1b3d36a429d829eb9be81d8c0506bf57b0"},"schema_version":"1.0","source":{"id":"1109.1538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1538","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1538v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1538","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"UIC536GMSOBS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UIC536GMSOBS64RC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UIC536GM","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:4a92c82566b6e7bb1c3c38fd3d471f0312d42eb772aaa0ba5baa2c86a507d577","target":"graph","created_at":"2026-05-18T04:13:55Z","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":"In this paper we further study the notion of proper costratifying systems, defined in \\cite{MPV}. We give sufficient conditions for their existence, and investigate the relation between the stratifying systems defined by K. Erdmann and C. S\\'aenz in \\cite{ES} with the proper costratifying systems.","authors_text":"Maria In\\'es Platzeck, Melina Verdecchia, Octavio Mendoza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T19:11:14Z","title":"On the existence and construction of proper costratifying systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1538","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":"sha256:3051ab99a26f6939e0cdac9659c2abf446733bf5bfb4e84bdbec117b04fbbaa8","target":"record","created_at":"2026-05-18T04:13:55Z","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":"60eae22de3687a42d57f55868896440d661afa5e7e46e6d4d88bb0b3d7be8e3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-07T19:11:14Z","title_canon_sha256":"c745bfab2f890fcdcb4bea9ac2e7fa1b3d36a429d829eb9be81d8c0506bf57b0"},"schema_version":"1.0","source":{"id":"1109.1538","kind":"arxiv","version":1}},"canonical_sha256":"a205ddf8cc93832f72229f9e14e50148c2b063958eb37c02960e801b80b47450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a205ddf8cc93832f72229f9e14e50148c2b063958eb37c02960e801b80b47450","first_computed_at":"2026-05-18T04:13:55.517100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:55.517100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vPihpTvlQO/ilqkbAJYr5cx8tTZ3WhPSz47guKDKLqB6BoZ5PUjHUeDcyw3NYjufKwW7DgI9lnU6WM6pl9JTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:55.517581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3051ab99a26f6939e0cdac9659c2abf446733bf5bfb4e84bdbec117b04fbbaa8","sha256:4a92c82566b6e7bb1c3c38fd3d471f0312d42eb772aaa0ba5baa2c86a507d577"],"state_sha256":"d0f1fb92d0f14e19ea07f1b3b7e6915c985f45e93f439ed19b073434b50c2350"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wt1WJDpSXR3NqVA01VKmuQT8d+IKuNZdGLJarpENgS79n7r4zJgDjopEfkw+6JIdSUTYTcDSndIsxZISuDY+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:59:40.603080Z","bundle_sha256":"bba1a0b6ca43468170ec42d6118453740c0a29f4ed45a207d56318537ee1a0a2"}}