{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZUEFSZVSHZNGTIIUBQFO3EX46N","short_pith_number":"pith:ZUEFSZVS","canonical_record":{"source":{"id":"1902.07878","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-21T06:16:09Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"85ab1fd9f8f5b7c559b9bd32428ce3e1188f00dbf2af8efef4fbb5cd5538655b","abstract_canon_sha256":"95b627e91dd19b87e14014c95af89ad8ab8a708d2da6a097097ca871ed05bee0"},"schema_version":"1.0"},"canonical_sha256":"cd085966b23e5a69a1140c0aed92fcf36280567daa0efaedf78aab609dff1519","source":{"kind":"arxiv","id":"1902.07878","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07878","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07878v3","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07878","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZUEFSZVSHZNG","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"pith_short_16","alias_value":"ZUEFSZVSHZNGTIIU","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"pith_short_8","alias_value":"ZUEFSZVS","created_at":"2026-07-05T02:12:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZUEFSZVSHZNGTIIUBQFO3EX46N","target":"record","payload":{"canonical_record":{"source":{"id":"1902.07878","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-21T06:16:09Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"85ab1fd9f8f5b7c559b9bd32428ce3e1188f00dbf2af8efef4fbb5cd5538655b","abstract_canon_sha256":"95b627e91dd19b87e14014c95af89ad8ab8a708d2da6a097097ca871ed05bee0"},"schema_version":"1.0"},"canonical_sha256":"cd085966b23e5a69a1140c0aed92fcf36280567daa0efaedf78aab609dff1519","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:12:22.319836Z","signature_b64":"/uC68fNvJORrBBJhMVaUksqYMJwelLosx68bqEl259Go4vYjFFuWAzMpV5XQSU1KU4h2VIiy4WMjXniVWqhICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd085966b23e5a69a1140c0aed92fcf36280567daa0efaedf78aab609dff1519","last_reissued_at":"2026-07-05T02:12:22.319304Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:12:22.319304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.07878","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CykactcnevR+33n08SIEVhlSZaSnHtTzw4cGE5PMuO55N+sLDU/Ahmn7yaTNXAdBS7oUrZkvQXKBMRJY9360CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:34:49.120895Z"},"content_sha256":"7ed0c92016d3b7a17990699e98a415b43913f5b154e9491aae4c0436c559853c","schema_version":"1.0","event_id":"sha256:7ed0c92016d3b7a17990699e98a415b43913f5b154e9491aae4c0436c559853c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZUEFSZVSHZNGTIIUBQFO3EX46N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher preprojective algebras, Koszul algebras, and superpotentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Joseph Grant, Osamu Iyama","submitted_at":"2019-02-21T06:16:09Z","abstract_excerpt":"In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained by adding arrows to the quiver of the original algebra, and these arrows can be read off from the last term of the bimodule resolution of the original algebra. In the Koszul case we are able to obtain the new relations of the higher preprojective algebra by differentiating a superpotential and we show that when our original algebra is $d$-hereditary all the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07878","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.07878/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tvXZpQ3n+5q83fteKUv+4sg4h6oRPAzJxpwdods0H5FPrtj5uITea2pmO3s3hif9mNxT8Kcnvp8HTMYdoDFwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:34:49.121422Z"},"content_sha256":"254d98acd7eb878629382ac528fbf5a1a7177561108af2b4d45e6cc00f499625","schema_version":"1.0","event_id":"sha256:254d98acd7eb878629382ac528fbf5a1a7177561108af2b4d45e6cc00f499625"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N/bundle.json","state_url":"https://pith.science/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N/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":"2026-08-15T00:34:49Z","links":{"resolver":"https://pith.science/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N","bundle":"https://pith.science/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N/bundle.json","state":"https://pith.science/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZUEFSZVSHZNGTIIUBQFO3EX46N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZUEFSZVSHZNGTIIUBQFO3EX46N","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":"95b627e91dd19b87e14014c95af89ad8ab8a708d2da6a097097ca871ed05bee0","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-21T06:16:09Z","title_canon_sha256":"85ab1fd9f8f5b7c559b9bd32428ce3e1188f00dbf2af8efef4fbb5cd5538655b"},"schema_version":"1.0","source":{"id":"1902.07878","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07878","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07878v3","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07878","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZUEFSZVSHZNG","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"pith_short_16","alias_value":"ZUEFSZVSHZNGTIIU","created_at":"2026-07-05T02:12:22Z"},{"alias_kind":"pith_short_8","alias_value":"ZUEFSZVS","created_at":"2026-07-05T02:12:22Z"}],"graph_snapshots":[{"event_id":"sha256:254d98acd7eb878629382ac528fbf5a1a7177561108af2b4d45e6cc00f499625","target":"graph","created_at":"2026-07-05T02:12:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.07878/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained by adding arrows to the quiver of the original algebra, and these arrows can be read off from the last term of the bimodule resolution of the original algebra. In the Koszul case we are able to obtain the new relations of the higher preprojective algebra by differentiating a superpotential and we show that when our original algebra is $d$-hereditary all the r","authors_text":"Joseph Grant, Osamu Iyama","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-21T06:16:09Z","title":"Higher preprojective algebras, Koszul algebras, and superpotentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07878","kind":"arxiv","version":3},"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":"sha256:7ed0c92016d3b7a17990699e98a415b43913f5b154e9491aae4c0436c559853c","target":"record","created_at":"2026-07-05T02:12:22Z","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":"95b627e91dd19b87e14014c95af89ad8ab8a708d2da6a097097ca871ed05bee0","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-21T06:16:09Z","title_canon_sha256":"85ab1fd9f8f5b7c559b9bd32428ce3e1188f00dbf2af8efef4fbb5cd5538655b"},"schema_version":"1.0","source":{"id":"1902.07878","kind":"arxiv","version":3}},"canonical_sha256":"cd085966b23e5a69a1140c0aed92fcf36280567daa0efaedf78aab609dff1519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd085966b23e5a69a1140c0aed92fcf36280567daa0efaedf78aab609dff1519","first_computed_at":"2026-07-05T02:12:22.319304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:12:22.319304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/uC68fNvJORrBBJhMVaUksqYMJwelLosx68bqEl259Go4vYjFFuWAzMpV5XQSU1KU4h2VIiy4WMjXniVWqhICA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:12:22.319836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.07878","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ed0c92016d3b7a17990699e98a415b43913f5b154e9491aae4c0436c559853c","sha256:254d98acd7eb878629382ac528fbf5a1a7177561108af2b4d45e6cc00f499625"],"state_sha256":"d44af8ac257fad297339bf8f48ead6e69c1272bd4bb3d76ebf5ee409a8e64a6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QU/8G2fKoEdwXlWT1hWAFrzYNr9WCYKkEoibrxF1sylUTLpxev/e4lKBl5oNBx84ZkNyMtRIVFQ3ObJWOoODBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T00:34:49.124927Z","bundle_sha256":"21ae07702e796aff9c3b42f21e9960a70e207eb9fff3f989904c310cac9c2564"}}