{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CGADAX6D7YCFJAR7XFENX5WI27","short_pith_number":"pith:CGADAX6D","canonical_record":{"source":{"id":"1704.03359","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-11T15:34:13Z","cross_cats_sorted":[],"title_canon_sha256":"a93e81937b3ab78521e4ca2feb5d8b731ca11bd6495efba3c7507e5c3663d863","abstract_canon_sha256":"19b8cf5d2e3a0d5727b02bb20a48bf3e08adcf4109047d53367d23e7689cf43b"},"schema_version":"1.0"},"canonical_sha256":"1180305fc3fe0454823fb948dbf6c8d7f858eece010d1dc9ffca4a59ab457d82","source":{"kind":"arxiv","id":"1704.03359","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03359","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03359v2","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03359","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"CGADAX6D7YCF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CGADAX6D7YCFJAR7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CGADAX6D","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CGADAX6D7YCFJAR7XFENX5WI27","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03359","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-11T15:34:13Z","cross_cats_sorted":[],"title_canon_sha256":"a93e81937b3ab78521e4ca2feb5d8b731ca11bd6495efba3c7507e5c3663d863","abstract_canon_sha256":"19b8cf5d2e3a0d5727b02bb20a48bf3e08adcf4109047d53367d23e7689cf43b"},"schema_version":"1.0"},"canonical_sha256":"1180305fc3fe0454823fb948dbf6c8d7f858eece010d1dc9ffca4a59ab457d82","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:44.561267Z","signature_b64":"HMslctPVOF5YAL2hXl0f853/IqXPEggl3Eoa86wAo9FP5Yh6jgnKWpmy7zD/kmDP19ACxGErSnGO3Xcqj0yWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1180305fc3fe0454823fb948dbf6c8d7f858eece010d1dc9ffca4a59ab457d82","last_reissued_at":"2026-05-17T23:51:44.560712Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:44.560712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03359","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Pkm1Tlp6C3o1t4EcdifHJBAazmaSa1CAjEIEvI43eoW/5WMoDeLKkslg0aalP3kSSZJsFU+jgXTSWVqdYPqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:47:32.844308Z"},"content_sha256":"4c36908b6d4120fa599cecd71ca234cea42ea6366588b0dd0ed45b636192e904","schema_version":"1.0","event_id":"sha256:4c36908b6d4120fa599cecd71ca234cea42ea6366588b0dd0ed45b636192e904"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CGADAX6D7YCFJAR7XFENX5WI27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Piecewise Hereditary algebras of Dynkin and extended Dynkin type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eduardo N. Marcos, Marcelo Moreira","submitted_at":"2017-04-11T15:34:13Z","abstract_excerpt":"We present a study on the description of incidence algebras that are piecewise hereditary, which we denominate Phia algebras. We describe the quiver with relations of the Phia algebras of Dynkin type and introduce a new family of Phia algebras of extended Dynkin type, which we call ANS family, in reference to Assem, Nehring, and Skowro\\'nski. In this description, the important method was the one of cutting sets on trivial extensions, inspired by this we made of a computer program which shows exactly the cutting sets on the given trivial extension that result on incidence algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03359","kind":"arxiv","version":2},"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":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XcusCsKxoWaf1wtJDfnucqNDEc+UQyl5VgPL5miqjXMFOG0mtdy/ALpmOsQIcOgWMTo5RA2Q+OzCf80YScQIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:47:32.845196Z"},"content_sha256":"87ea30e61cf87ff8ee9bf8bf22ca9cbc34466d08e3a664d1ba0e49cc39d1e7d2","schema_version":"1.0","event_id":"sha256:87ea30e61cf87ff8ee9bf8bf22ca9cbc34466d08e3a664d1ba0e49cc39d1e7d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGADAX6D7YCFJAR7XFENX5WI27/bundle.json","state_url":"https://pith.science/pith/CGADAX6D7YCFJAR7XFENX5WI27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGADAX6D7YCFJAR7XFENX5WI27/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":"2026-06-09T23:47:32Z","links":{"resolver":"https://pith.science/pith/CGADAX6D7YCFJAR7XFENX5WI27","bundle":"https://pith.science/pith/CGADAX6D7YCFJAR7XFENX5WI27/bundle.json","state":"https://pith.science/pith/CGADAX6D7YCFJAR7XFENX5WI27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGADAX6D7YCFJAR7XFENX5WI27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CGADAX6D7YCFJAR7XFENX5WI27","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":"19b8cf5d2e3a0d5727b02bb20a48bf3e08adcf4109047d53367d23e7689cf43b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-11T15:34:13Z","title_canon_sha256":"a93e81937b3ab78521e4ca2feb5d8b731ca11bd6495efba3c7507e5c3663d863"},"schema_version":"1.0","source":{"id":"1704.03359","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03359","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03359v2","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03359","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"CGADAX6D7YCF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CGADAX6D7YCFJAR7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CGADAX6D","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:87ea30e61cf87ff8ee9bf8bf22ca9cbc34466d08e3a664d1ba0e49cc39d1e7d2","target":"graph","created_at":"2026-05-17T23:51:44Z","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 present a study on the description of incidence algebras that are piecewise hereditary, which we denominate Phia algebras. We describe the quiver with relations of the Phia algebras of Dynkin type and introduce a new family of Phia algebras of extended Dynkin type, which we call ANS family, in reference to Assem, Nehring, and Skowro\\'nski. In this description, the important method was the one of cutting sets on trivial extensions, inspired by this we made of a computer program which shows exactly the cutting sets on the given trivial extension that result on incidence algebras.","authors_text":"Eduardo N. Marcos, Marcelo Moreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-11T15:34:13Z","title":"Piecewise Hereditary algebras of Dynkin and extended Dynkin type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03359","kind":"arxiv","version":2},"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":"sha256:4c36908b6d4120fa599cecd71ca234cea42ea6366588b0dd0ed45b636192e904","target":"record","created_at":"2026-05-17T23:51:44Z","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":"19b8cf5d2e3a0d5727b02bb20a48bf3e08adcf4109047d53367d23e7689cf43b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-11T15:34:13Z","title_canon_sha256":"a93e81937b3ab78521e4ca2feb5d8b731ca11bd6495efba3c7507e5c3663d863"},"schema_version":"1.0","source":{"id":"1704.03359","kind":"arxiv","version":2}},"canonical_sha256":"1180305fc3fe0454823fb948dbf6c8d7f858eece010d1dc9ffca4a59ab457d82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1180305fc3fe0454823fb948dbf6c8d7f858eece010d1dc9ffca4a59ab457d82","first_computed_at":"2026-05-17T23:51:44.560712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:44.560712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HMslctPVOF5YAL2hXl0f853/IqXPEggl3Eoa86wAo9FP5Yh6jgnKWpmy7zD/kmDP19ACxGErSnGO3Xcqj0yWBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:44.561267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03359","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c36908b6d4120fa599cecd71ca234cea42ea6366588b0dd0ed45b636192e904","sha256:87ea30e61cf87ff8ee9bf8bf22ca9cbc34466d08e3a664d1ba0e49cc39d1e7d2"],"state_sha256":"6a5cd59068117d9c4c3d4ea6fd188c633db80163539854dbe66ddcd1b04269d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKkxUWB8Ccrtx0QPdN97/V/1gRIdrdWwiv0Lruv3GFDU8cyfGfLC9LZZw9z126TSxBOXgejyD8N+j8NYHrQIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T23:47:32.849139Z","bundle_sha256":"2583bb3daa04cfac8b9100caeb4c886132e0dc41aaa0524b48c6a28bc42cfffe"}}