{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FM6SHC6SSYGL3WBPL7ZS4FFNBO","short_pith_number":"pith:FM6SHC6S","canonical_record":{"source":{"id":"1908.04738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-13T16:59:16Z","cross_cats_sorted":[],"title_canon_sha256":"bbf2fa7f2fe6946d1167721aa3a9d87b98fcc626ab68d72abf19b0a55677b310","abstract_canon_sha256":"32d584a440a6cff8e2c3ed128c4a8efc28e67059ba9d06eb901a7198ccd06411"},"schema_version":"1.0"},"canonical_sha256":"2b3d238bd2960cbdd82f5ff32e14ad0bb55bef88d0d2763e8c33f0bee6f02a86","source":{"kind":"arxiv","id":"1908.04738","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04738","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04738v2","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04738","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"FM6SHC6SSYGL","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"FM6SHC6SSYGL3WBP","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"FM6SHC6S","created_at":"2026-07-05T07:05:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FM6SHC6SSYGL3WBPL7ZS4FFNBO","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-13T16:59:16Z","cross_cats_sorted":[],"title_canon_sha256":"bbf2fa7f2fe6946d1167721aa3a9d87b98fcc626ab68d72abf19b0a55677b310","abstract_canon_sha256":"32d584a440a6cff8e2c3ed128c4a8efc28e67059ba9d06eb901a7198ccd06411"},"schema_version":"1.0"},"canonical_sha256":"2b3d238bd2960cbdd82f5ff32e14ad0bb55bef88d0d2763e8c33f0bee6f02a86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:05:37.601256Z","signature_b64":"busGVax5DaN20Qz3uiPTNADudylDYNzzajjrNLAjMQ1beNuf1VFh6k8z6ESR8RuAZxcFxmB/HLlyXuA0UAwlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b3d238bd2960cbdd82f5ff32e14ad0bb55bef88d0d2763e8c33f0bee6f02a86","last_reissued_at":"2026-07-05T07:05:37.600769Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:05:37.600769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04738","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":"2026-07-05T07:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yienPmz+/4PQ0+eQpOcOatmfyYn6XoMnzA0CoUjg8Gli16wg+sOFovnYb+tZ4mwCLGh6Em5KrPGgNBha3ScXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:43:13.274852Z"},"content_sha256":"afaf5c8cb4388ea65eeebc4c5426e4723c7ad39d835fbad5ce2affee8b8fc42c","schema_version":"1.0","event_id":"sha256:afaf5c8cb4388ea65eeebc4c5426e4723c7ad39d835fbad5ce2affee8b8fc42c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FM6SHC6SSYGL3WBPL7ZS4FFNBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On weakly Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Rene Marczinzik","submitted_at":"2019-08-13T16:59:16Z","abstract_excerpt":"We prove that algebras are left weakly Gorenstein in case the subcategory $^{\\perp}A \\cap \\Omega^n(A)$ is representation-finite. This applies in particular to all monomial algebras and endomorphism algebras of modules over representation-finite algebras. We also give a proof of the Auslander-Reiten conjecture for such algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04738","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04738/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":"2026-07-05T07:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LszLbo58GTZxoT7Ra/vrJvUeFxWxT0RgXY/DCIQdnPMn5RggVt65Ootyy8seKruHnA8ZH98qqBOX1SXfczjQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:43:13.275323Z"},"content_sha256":"99bd84c825c11484995c0be16159f114385d377ff53ea7e674bd85742d8c5b58","schema_version":"1.0","event_id":"sha256:99bd84c825c11484995c0be16159f114385d377ff53ea7e674bd85742d8c5b58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO/bundle.json","state_url":"https://pith.science/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO/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":"2026-08-16T05:43:13Z","links":{"resolver":"https://pith.science/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO","bundle":"https://pith.science/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO/bundle.json","state":"https://pith.science/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FM6SHC6SSYGL3WBPL7ZS4FFNBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FM6SHC6SSYGL3WBPL7ZS4FFNBO","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":"32d584a440a6cff8e2c3ed128c4a8efc28e67059ba9d06eb901a7198ccd06411","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-13T16:59:16Z","title_canon_sha256":"bbf2fa7f2fe6946d1167721aa3a9d87b98fcc626ab68d72abf19b0a55677b310"},"schema_version":"1.0","source":{"id":"1908.04738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04738","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04738v2","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04738","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"FM6SHC6SSYGL","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"FM6SHC6SSYGL3WBP","created_at":"2026-07-05T07:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"FM6SHC6S","created_at":"2026-07-05T07:05:37Z"}],"graph_snapshots":[{"event_id":"sha256:99bd84c825c11484995c0be16159f114385d377ff53ea7e674bd85742d8c5b58","target":"graph","created_at":"2026-07-05T07:05:37Z","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/1908.04738/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that algebras are left weakly Gorenstein in case the subcategory $^{\\perp}A \\cap \\Omega^n(A)$ is representation-finite. This applies in particular to all monomial algebras and endomorphism algebras of modules over representation-finite algebras. We also give a proof of the Auslander-Reiten conjecture for such algebras.","authors_text":"Rene Marczinzik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-13T16:59:16Z","title":"On weakly Gorenstein algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04738","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:afaf5c8cb4388ea65eeebc4c5426e4723c7ad39d835fbad5ce2affee8b8fc42c","target":"record","created_at":"2026-07-05T07:05:37Z","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":"32d584a440a6cff8e2c3ed128c4a8efc28e67059ba9d06eb901a7198ccd06411","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-13T16:59:16Z","title_canon_sha256":"bbf2fa7f2fe6946d1167721aa3a9d87b98fcc626ab68d72abf19b0a55677b310"},"schema_version":"1.0","source":{"id":"1908.04738","kind":"arxiv","version":2}},"canonical_sha256":"2b3d238bd2960cbdd82f5ff32e14ad0bb55bef88d0d2763e8c33f0bee6f02a86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b3d238bd2960cbdd82f5ff32e14ad0bb55bef88d0d2763e8c33f0bee6f02a86","first_computed_at":"2026-07-05T07:05:37.600769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:05:37.600769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"busGVax5DaN20Qz3uiPTNADudylDYNzzajjrNLAjMQ1beNuf1VFh6k8z6ESR8RuAZxcFxmB/HLlyXuA0UAwlDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:05:37.601256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afaf5c8cb4388ea65eeebc4c5426e4723c7ad39d835fbad5ce2affee8b8fc42c","sha256:99bd84c825c11484995c0be16159f114385d377ff53ea7e674bd85742d8c5b58"],"state_sha256":"2c54e52ed1194f3858f8e4658c03a4b780b07042ada28efee71a26783afe9e8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlz/cKTBHAuBTo+Ns0UAAaoha1MUvUJcLX9vq2az1XjsFf0SaOfJS91WKj0iaya2mu1ywV269JTR6pRB8cdsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:43:13.279971Z","bundle_sha256":"408999bd7f3bc4d1e19431de89d989d05d5f6ee586410129bd53cad6d2460ca8"}}