{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HXZJNQDJD6MV4IRFRKFPQDH5UX","short_pith_number":"pith:HXZJNQDJ","canonical_record":{"source":{"id":"2301.13498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-01-31T09:30:05Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"43114cda74cf5d0e7ab67aa41be864f91a402936df558330711efe1fdca3230d","abstract_canon_sha256":"c15ada6dc66acd48686d856038756592989376b573a1714b5c82488fb6581e31"},"schema_version":"1.0"},"canonical_sha256":"3df296c0691f995e22258a8af80cfda5eda486f7722ad34b4b050d0aaa433110","source":{"kind":"arxiv","id":"2301.13498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.13498","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"arxiv_version","alias_value":"2301.13498v2","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.13498","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"pith_short_12","alias_value":"HXZJNQDJD6MV","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"pith_short_16","alias_value":"HXZJNQDJD6MV4IRF","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"pith_short_8","alias_value":"HXZJNQDJ","created_at":"2026-07-05T05:58:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HXZJNQDJD6MV4IRFRKFPQDH5UX","target":"record","payload":{"canonical_record":{"source":{"id":"2301.13498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-01-31T09:30:05Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"43114cda74cf5d0e7ab67aa41be864f91a402936df558330711efe1fdca3230d","abstract_canon_sha256":"c15ada6dc66acd48686d856038756592989376b573a1714b5c82488fb6581e31"},"schema_version":"1.0"},"canonical_sha256":"3df296c0691f995e22258a8af80cfda5eda486f7722ad34b4b050d0aaa433110","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:58:53.335888Z","signature_b64":"jG9jq72kVF+1gjKGIuNbx5/cWGIc0pPTYOQ5tWHWPKHTlZWTWJGt3yIU6I2KExONKAASVUuBWw+diwNUF7Q1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3df296c0691f995e22258a8af80cfda5eda486f7722ad34b4b050d0aaa433110","last_reissued_at":"2026-07-05T05:58:53.335413Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:58:53.335413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.13498","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":"2026-07-05T05:58:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf+XmHfb7AS/lByG6sCIqgxu5+9XIf4ywYvCeXI2o7BX4sT1NuEjMaKwwlzxFNfWEdsc6HZ/OlKtTb0q+6F5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:12:25.139004Z"},"content_sha256":"1063a56557a02852a3f9ecf5b19275cda48b77b3e6162d8f927ca7ed876d7d4e","schema_version":"1.0","event_id":"sha256:1063a56557a02852a3f9ecf5b19275cda48b77b3e6162d8f927ca7ed876d7d4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HXZJNQDJD6MV4IRFRKFPQDH5UX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal self-orthogonal modules and a new generalization of tilting modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Haruhisa Enomoto","submitted_at":"2023-01-31T09:30:05Z","abstract_excerpt":"We introduce a generalization of tilting modules of finite projective dimension, projectively Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ext-perpendicular categories. Under a certain finiteness condition, we prove that the following modules coincide: projectively Wakamatsu tilting, Wakamatsu tilting, maximal self-orthogonal, and self-orthogonal modules with the same rank as the algebra. This provides another proof of the weak Gorensteinness of representation-finite algebras. To prove this, we introduce Bongartz completion of self-orthogonal modules and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13498","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/2301.13498/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":"2026-07-05T05:58:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2i1AwpD1mgHBnqGYIXy16kmsPguVAK8dBgKBM9fl6lx+jTC10tKEfzIgamV/zwHQNRMIXcP2X7+sy1EZs9AjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:12:25.139500Z"},"content_sha256":"7a3df3e8ffac2cc14a8d676d4ecd02c99f073c1ec8bbdce1f457f735213c75b8","schema_version":"1.0","event_id":"sha256:7a3df3e8ffac2cc14a8d676d4ecd02c99f073c1ec8bbdce1f457f735213c75b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX/bundle.json","state_url":"https://pith.science/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX/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":"2026-08-14T14:12:25Z","links":{"resolver":"https://pith.science/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX","bundle":"https://pith.science/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX/bundle.json","state":"https://pith.science/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXZJNQDJD6MV4IRFRKFPQDH5UX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HXZJNQDJD6MV4IRFRKFPQDH5UX","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":"c15ada6dc66acd48686d856038756592989376b573a1714b5c82488fb6581e31","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-01-31T09:30:05Z","title_canon_sha256":"43114cda74cf5d0e7ab67aa41be864f91a402936df558330711efe1fdca3230d"},"schema_version":"1.0","source":{"id":"2301.13498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.13498","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"arxiv_version","alias_value":"2301.13498v2","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.13498","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"pith_short_12","alias_value":"HXZJNQDJD6MV","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"pith_short_16","alias_value":"HXZJNQDJD6MV4IRF","created_at":"2026-07-05T05:58:53Z"},{"alias_kind":"pith_short_8","alias_value":"HXZJNQDJ","created_at":"2026-07-05T05:58:53Z"}],"graph_snapshots":[{"event_id":"sha256:7a3df3e8ffac2cc14a8d676d4ecd02c99f073c1ec8bbdce1f457f735213c75b8","target":"graph","created_at":"2026-07-05T05:58:53Z","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/2301.13498/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a generalization of tilting modules of finite projective dimension, projectively Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ext-perpendicular categories. Under a certain finiteness condition, we prove that the following modules coincide: projectively Wakamatsu tilting, Wakamatsu tilting, maximal self-orthogonal, and self-orthogonal modules with the same rank as the algebra. This provides another proof of the weak Gorensteinness of representation-finite algebras. To prove this, we introduce Bongartz completion of self-orthogonal modules and ","authors_text":"Haruhisa Enomoto","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-01-31T09:30:05Z","title":"Maximal self-orthogonal modules and a new generalization of tilting modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13498","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":"sha256:1063a56557a02852a3f9ecf5b19275cda48b77b3e6162d8f927ca7ed876d7d4e","target":"record","created_at":"2026-07-05T05:58:53Z","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":"c15ada6dc66acd48686d856038756592989376b573a1714b5c82488fb6581e31","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-01-31T09:30:05Z","title_canon_sha256":"43114cda74cf5d0e7ab67aa41be864f91a402936df558330711efe1fdca3230d"},"schema_version":"1.0","source":{"id":"2301.13498","kind":"arxiv","version":2}},"canonical_sha256":"3df296c0691f995e22258a8af80cfda5eda486f7722ad34b4b050d0aaa433110","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3df296c0691f995e22258a8af80cfda5eda486f7722ad34b4b050d0aaa433110","first_computed_at":"2026-07-05T05:58:53.335413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:58:53.335413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jG9jq72kVF+1gjKGIuNbx5/cWGIc0pPTYOQ5tWHWPKHTlZWTWJGt3yIU6I2KExONKAASVUuBWw+diwNUF7Q1AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:58:53.335888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.13498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1063a56557a02852a3f9ecf5b19275cda48b77b3e6162d8f927ca7ed876d7d4e","sha256:7a3df3e8ffac2cc14a8d676d4ecd02c99f073c1ec8bbdce1f457f735213c75b8"],"state_sha256":"6605dfce705e564c484cd7ac10af6cbd9637f5d0392fd926a1ea592ed7969458"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3FnuAHR1eoXZeEJO5edZnXy31QEACI21wTgl++kxzj5TTF2nUXC80dobAq4qoi6DIUrCOtuuBrHJb5RjUX2KDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T14:12:25.143393Z","bundle_sha256":"621fb1a574ec0650b92eb75dc842e7095201e5baafa488c7f4590bf27be5300e"}}