{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:O7623ZVOXRBLVIHD4GRJJO5GJ5","short_pith_number":"pith:O7623ZVO","canonical_record":{"source":{"id":"1504.04827","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-19T13:17:49Z","cross_cats_sorted":[],"title_canon_sha256":"c1610a4411376240c7d1dbe1300320b96fbb0701958d6b099a06857ca2bdc6fc","abstract_canon_sha256":"b5ec966eeffcbd48556b8db7b72da5494775fe16631f6124d98cfffaae094f12"},"schema_version":"1.0"},"canonical_sha256":"77fdade6aebc42baa0e3e1a294bba64f5b590e79870988cbf002cc0b04a2dc90","source":{"kind":"arxiv","id":"1504.04827","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04827","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04827v4","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04827","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"O7623ZVOXRBL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7623ZVOXRBLVIHD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7623ZVO","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:O7623ZVOXRBLVIHD4GRJJO5GJ5","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04827","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-19T13:17:49Z","cross_cats_sorted":[],"title_canon_sha256":"c1610a4411376240c7d1dbe1300320b96fbb0701958d6b099a06857ca2bdc6fc","abstract_canon_sha256":"b5ec966eeffcbd48556b8db7b72da5494775fe16631f6124d98cfffaae094f12"},"schema_version":"1.0"},"canonical_sha256":"77fdade6aebc42baa0e3e1a294bba64f5b590e79870988cbf002cc0b04a2dc90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:47.282061Z","signature_b64":"PsuH6rIgUzV4zS6nA2oT/sBE50Mnl0cirgkUBpNOSaQkknkRiqPOYKuJ7KLgtSQg9M4TYNgyy9aCCl44tM+aBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77fdade6aebc42baa0e3e1a294bba64f5b590e79870988cbf002cc0b04a2dc90","last_reissued_at":"2026-05-18T00:26:47.281415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:47.281415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04827","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":"2026-05-18T00:26:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cO0E98L9IRY4pvMWsPjqdmGxRSikJ4antYCGb7Ba+RmcjQFbAP39RWtLQzQhl33tick8wkphjBXIVsxtKkBFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:20:14.748733Z"},"content_sha256":"376e66809f5e855bb9df09e9cb585a7e6d96c1bf6e90546b712c28170e06b758","schema_version":"1.0","event_id":"sha256:376e66809f5e855bb9df09e9cb585a7e6d96c1bf6e90546b712c28170e06b758"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:O7623ZVOXRBLVIHD4GRJJO5GJ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of two-term tilting complexes over Brauer graph algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Aaron Chan, Takahide Adachi, Takuma Aihara","submitted_at":"2015-04-19T13:17:49Z","abstract_excerpt":"Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04827","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":""},"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":"2026-05-18T00:26:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJs/Q2aPtt4mgAM53YEfpTpHbOPE6CD1IMdfoscAVpHwUhW7ReKkpAR8IGZmtOw96rLTdvGrW7+q4r6jbMdqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:20:14.749270Z"},"content_sha256":"dad64950c041284dde5fe15e12e4ff45d3526a7dbcf574aa8dd028da7d80566d","schema_version":"1.0","event_id":"sha256:dad64950c041284dde5fe15e12e4ff45d3526a7dbcf574aa8dd028da7d80566d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5/bundle.json","state_url":"https://pith.science/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5/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":"2026-06-07T06:20:14Z","links":{"resolver":"https://pith.science/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5","bundle":"https://pith.science/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5/bundle.json","state":"https://pith.science/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7623ZVOXRBLVIHD4GRJJO5GJ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O7623ZVOXRBLVIHD4GRJJO5GJ5","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":"b5ec966eeffcbd48556b8db7b72da5494775fe16631f6124d98cfffaae094f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-19T13:17:49Z","title_canon_sha256":"c1610a4411376240c7d1dbe1300320b96fbb0701958d6b099a06857ca2bdc6fc"},"schema_version":"1.0","source":{"id":"1504.04827","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04827","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04827v4","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04827","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"O7623ZVOXRBL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7623ZVOXRBLVIHD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7623ZVO","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:dad64950c041284dde5fe15e12e4ff45d3526a7dbcf574aa8dd028da7d80566d","target":"graph","created_at":"2026-05-18T00:26:47Z","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":"Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete.","authors_text":"Aaron Chan, Takahide Adachi, Takuma Aihara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-19T13:17:49Z","title":"Classification of two-term tilting complexes over Brauer graph algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04827","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":"sha256:376e66809f5e855bb9df09e9cb585a7e6d96c1bf6e90546b712c28170e06b758","target":"record","created_at":"2026-05-18T00:26:47Z","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":"b5ec966eeffcbd48556b8db7b72da5494775fe16631f6124d98cfffaae094f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-19T13:17:49Z","title_canon_sha256":"c1610a4411376240c7d1dbe1300320b96fbb0701958d6b099a06857ca2bdc6fc"},"schema_version":"1.0","source":{"id":"1504.04827","kind":"arxiv","version":4}},"canonical_sha256":"77fdade6aebc42baa0e3e1a294bba64f5b590e79870988cbf002cc0b04a2dc90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77fdade6aebc42baa0e3e1a294bba64f5b590e79870988cbf002cc0b04a2dc90","first_computed_at":"2026-05-18T00:26:47.281415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:47.281415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsuH6rIgUzV4zS6nA2oT/sBE50Mnl0cirgkUBpNOSaQkknkRiqPOYKuJ7KLgtSQg9M4TYNgyy9aCCl44tM+aBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:47.282061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04827","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:376e66809f5e855bb9df09e9cb585a7e6d96c1bf6e90546b712c28170e06b758","sha256:dad64950c041284dde5fe15e12e4ff45d3526a7dbcf574aa8dd028da7d80566d"],"state_sha256":"65657969f51e0446a6f2f2ea5fb89363c0ffd7c876826a2a292bcc0551095e53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2h7JOdPkdKgwMBage0TrsORiFSHAG+ipq/K77vgAWqx0rdIHR9eWeF0wd1RhAlLzdfzm+sTIwjt6exFNK2IfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:20:14.751970Z","bundle_sha256":"3472b20eeba6f7d3d8c00c962a9b90d30589c3d779e936d63e2bac9d62d70c76"}}