{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BQ2G4XVUGRLVJHSO3PETTWM6JJ","short_pith_number":"pith:BQ2G4XVU","canonical_record":{"source":{"id":"1907.07194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-16T18:00:22Z","cross_cats_sorted":[],"title_canon_sha256":"0474f03cecc55c2d37af605b8de2d9203c67737362b1c2a142da90fbfcc2cba0","abstract_canon_sha256":"12b0569a02e51e3481349fe1a8e0378c5a2807e32a0e3e1ac2711458b3d7af49"},"schema_version":"1.0"},"canonical_sha256":"0c346e5eb43457549e4edbc939d99e4a430aec79d598cc5f0dbaa816935db9a1","source":{"kind":"arxiv","id":"1907.07194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07194","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07194v1","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07194","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"BQ2G4XVUGRLV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BQ2G4XVUGRLVJHSO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BQ2G4XVU","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BQ2G4XVUGRLVJHSO3PETTWM6JJ","target":"record","payload":{"canonical_record":{"source":{"id":"1907.07194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-16T18:00:22Z","cross_cats_sorted":[],"title_canon_sha256":"0474f03cecc55c2d37af605b8de2d9203c67737362b1c2a142da90fbfcc2cba0","abstract_canon_sha256":"12b0569a02e51e3481349fe1a8e0378c5a2807e32a0e3e1ac2711458b3d7af49"},"schema_version":"1.0"},"canonical_sha256":"0c346e5eb43457549e4edbc939d99e4a430aec79d598cc5f0dbaa816935db9a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:27.465841Z","signature_b64":"zXEGTM1nTynpRCDFvka8hC72LFYDctb48As7u4d6dU9CKYDja9u0Ix4lOQgXHZBXTbKTjZhAgeBoZlJqfpxCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c346e5eb43457549e4edbc939d99e4a430aec79d598cc5f0dbaa816935db9a1","last_reissued_at":"2026-05-17T23:40:27.465071Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:27.465071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.07194","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":"2026-05-17T23:40:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Wf9q7yCauJ8iRLNATSfuGyeq4P0y1k9WIUaOKdrFW2+whIHHH8uZ92BnmT/BeCnWGMX15b2IvmmzNH3FVmbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:18:42.738145Z"},"content_sha256":"ebbed8e0cdc3f9a9b09c2a6d60dd0a839a55c67ac66666810aa445df2b3a785f","schema_version":"1.0","event_id":"sha256:ebbed8e0cdc3f9a9b09c2a6d60dd0a839a55c67ac66666810aa445df2b3a785f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BQ2G4XVUGRLVJHSO3PETTWM6JJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recollements and Ladders for weighted projective lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shiquan Ruan","submitted_at":"2019-07-16T18:00:22Z","abstract_excerpt":"In this paper, we construct recollements and ladders for exceptional curves by using reduction/insertion functors due to $p$-cycle construction. As applications to weighted projective lines, we classify recollements for the category of coherent sheaves over a weighted projective line, and give an explicit description of ladders in two different levels: the bounded derived category of coherent sheaves and the stable category of vector bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07194","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":"2026-05-17T23:40:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCvzFpO7hjcYvw0B1BsQoZWZbwcMK2ZtLgt/Jt9/wt2ZIVQKIewM6d0E8gvB98D4gwqPPlVfNeEZMB0mCE5tBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:18:42.738863Z"},"content_sha256":"1867c58cd55b31f3d63869fc982000d8a4c60fedeaa6cb4490ed24bcf1b85b98","schema_version":"1.0","event_id":"sha256:1867c58cd55b31f3d63869fc982000d8a4c60fedeaa6cb4490ed24bcf1b85b98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ/bundle.json","state_url":"https://pith.science/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ/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":"2026-06-11T17:18:42Z","links":{"resolver":"https://pith.science/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ","bundle":"https://pith.science/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ/bundle.json","state":"https://pith.science/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQ2G4XVUGRLVJHSO3PETTWM6JJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BQ2G4XVUGRLVJHSO3PETTWM6JJ","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":"12b0569a02e51e3481349fe1a8e0378c5a2807e32a0e3e1ac2711458b3d7af49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-16T18:00:22Z","title_canon_sha256":"0474f03cecc55c2d37af605b8de2d9203c67737362b1c2a142da90fbfcc2cba0"},"schema_version":"1.0","source":{"id":"1907.07194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07194","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07194v1","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07194","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"BQ2G4XVUGRLV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BQ2G4XVUGRLVJHSO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BQ2G4XVU","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:1867c58cd55b31f3d63869fc982000d8a4c60fedeaa6cb4490ed24bcf1b85b98","target":"graph","created_at":"2026-05-17T23:40:27Z","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 construct recollements and ladders for exceptional curves by using reduction/insertion functors due to $p$-cycle construction. As applications to weighted projective lines, we classify recollements for the category of coherent sheaves over a weighted projective line, and give an explicit description of ladders in two different levels: the bounded derived category of coherent sheaves and the stable category of vector bundles.","authors_text":"Shiquan Ruan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-16T18:00:22Z","title":"Recollements and Ladders for weighted projective lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07194","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:ebbed8e0cdc3f9a9b09c2a6d60dd0a839a55c67ac66666810aa445df2b3a785f","target":"record","created_at":"2026-05-17T23:40:27Z","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":"12b0569a02e51e3481349fe1a8e0378c5a2807e32a0e3e1ac2711458b3d7af49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-16T18:00:22Z","title_canon_sha256":"0474f03cecc55c2d37af605b8de2d9203c67737362b1c2a142da90fbfcc2cba0"},"schema_version":"1.0","source":{"id":"1907.07194","kind":"arxiv","version":1}},"canonical_sha256":"0c346e5eb43457549e4edbc939d99e4a430aec79d598cc5f0dbaa816935db9a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c346e5eb43457549e4edbc939d99e4a430aec79d598cc5f0dbaa816935db9a1","first_computed_at":"2026-05-17T23:40:27.465071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:27.465071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXEGTM1nTynpRCDFvka8hC72LFYDctb48As7u4d6dU9CKYDja9u0Ix4lOQgXHZBXTbKTjZhAgeBoZlJqfpxCBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:27.465841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbed8e0cdc3f9a9b09c2a6d60dd0a839a55c67ac66666810aa445df2b3a785f","sha256:1867c58cd55b31f3d63869fc982000d8a4c60fedeaa6cb4490ed24bcf1b85b98"],"state_sha256":"237e08c73532e406a0bd71593b81055619af47a6b8b47fe3fc64e0205a3b3d09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0I4FUX/oRUc6ewIwE8EVM7B3hkXqOd9uburS1e8W4YtFqdrdeESUOgAQQH3eW+TfJ7gtrwlFRfhPwVlPd4q1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:18:42.742897Z","bundle_sha256":"345e8a06c74163b4a43696c3b8758fb59e604d4ee0bbb52459077d1435c734ac"}}