{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E7T2RBA47OPUOPJTJSKPFLXAPT","short_pith_number":"pith:E7T2RBA4","canonical_record":{"source":{"id":"1710.08966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T19:46:37Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"63341b25f98a8f15cc968a61d462bfc140f2949362f1ecddba5d1273ec24e29e","abstract_canon_sha256":"15303116f63cea05582c138cf262bfcaca1e6201377515b1e7394fc3ffba7071"},"schema_version":"1.0"},"canonical_sha256":"27e7a8841cfb9f473d334c94f2aee07cd17a518833e7924f34c4558440de499f","source":{"kind":"arxiv","id":"1710.08966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08966","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08966v1","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08966","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"E7T2RBA47OPU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E7T2RBA47OPUOPJT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E7T2RBA4","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E7T2RBA47OPUOPJTJSKPFLXAPT","target":"record","payload":{"canonical_record":{"source":{"id":"1710.08966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T19:46:37Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"63341b25f98a8f15cc968a61d462bfc140f2949362f1ecddba5d1273ec24e29e","abstract_canon_sha256":"15303116f63cea05582c138cf262bfcaca1e6201377515b1e7394fc3ffba7071"},"schema_version":"1.0"},"canonical_sha256":"27e7a8841cfb9f473d334c94f2aee07cd17a518833e7924f34c4558440de499f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:00.660875Z","signature_b64":"YD1BTBt4+bXbRMKWP1ec8HVkVgG2tlGpoEUHbhxkNiIlI8mzvrIMwCjuJ7XtTConxq3pc6kKTlRHYqUXkPk6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27e7a8841cfb9f473d334c94f2aee07cd17a518833e7924f34c4558440de499f","last_reissued_at":"2026-05-18T00:32:00.660344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:00.660344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.08966","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pK47tfwjpQdAXQq32IHsR734dZ8BXwantW/yUyatzX0/ITQ94qhR39pkH8TZnY9BPGkaloeF8nUEP+nNl3SGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:31:43.830470Z"},"content_sha256":"eb7f305ab1e71b22f589414a0d437f0bdfa6c851381bcf42a3b4bcc95cc87d3e","schema_version":"1.0","event_id":"sha256:eb7f305ab1e71b22f589414a0d437f0bdfa6c851381bcf42a3b4bcc95cc87d3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E7T2RBA47OPUOPJTJSKPFLXAPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functors and morphisms determined by subcategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Shijie Zhu","submitted_at":"2017-10-24T19:46:37Z","abstract_excerpt":"We study the existence and uniqueness of minimal right determiners in various categories. Particularly in a Hom-finite hereditary abelian category with enough projectives, we prove that the Auslander-Reiten-Smal{\\o}-Ringel formula of the minimal right determiner still holds. As an application, we give a formula of minimal right determiners in the category of finitely presented representations of strongly locally finite quivers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08966","kind":"arxiv","version":1},"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":"2026-05-18T00:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjhBJHDsW/uYgjqFgHn//WAT9KhySPZUs+ERnYrAnjQUkEsDjeb0hEhBrRHVESq+HWCtw0VJjtRIXiq28oznCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:31:43.831241Z"},"content_sha256":"39b826ec6ecf7f4eb74f5bfdc8603290c374bf8cc877b3c7606cfca1a398153b","schema_version":"1.0","event_id":"sha256:39b826ec6ecf7f4eb74f5bfdc8603290c374bf8cc877b3c7606cfca1a398153b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7T2RBA47OPUOPJTJSKPFLXAPT/bundle.json","state_url":"https://pith.science/pith/E7T2RBA47OPUOPJTJSKPFLXAPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7T2RBA47OPUOPJTJSKPFLXAPT/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":"2026-05-31T07:31:43Z","links":{"resolver":"https://pith.science/pith/E7T2RBA47OPUOPJTJSKPFLXAPT","bundle":"https://pith.science/pith/E7T2RBA47OPUOPJTJSKPFLXAPT/bundle.json","state":"https://pith.science/pith/E7T2RBA47OPUOPJTJSKPFLXAPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7T2RBA47OPUOPJTJSKPFLXAPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E7T2RBA47OPUOPJTJSKPFLXAPT","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":"15303116f63cea05582c138cf262bfcaca1e6201377515b1e7394fc3ffba7071","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T19:46:37Z","title_canon_sha256":"63341b25f98a8f15cc968a61d462bfc140f2949362f1ecddba5d1273ec24e29e"},"schema_version":"1.0","source":{"id":"1710.08966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08966","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08966v1","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08966","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"E7T2RBA47OPU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E7T2RBA47OPUOPJT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E7T2RBA4","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:39b826ec6ecf7f4eb74f5bfdc8603290c374bf8cc877b3c7606cfca1a398153b","target":"graph","created_at":"2026-05-18T00:32:00Z","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 study the existence and uniqueness of minimal right determiners in various categories. Particularly in a Hom-finite hereditary abelian category with enough projectives, we prove that the Auslander-Reiten-Smal{\\o}-Ringel formula of the minimal right determiner still holds. As an application, we give a formula of minimal right determiners in the category of finitely presented representations of strongly locally finite quivers.","authors_text":"Shijie Zhu","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T19:46:37Z","title":"Functors and morphisms determined by subcategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08966","kind":"arxiv","version":1},"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:eb7f305ab1e71b22f589414a0d437f0bdfa6c851381bcf42a3b4bcc95cc87d3e","target":"record","created_at":"2026-05-18T00:32:00Z","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":"15303116f63cea05582c138cf262bfcaca1e6201377515b1e7394fc3ffba7071","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T19:46:37Z","title_canon_sha256":"63341b25f98a8f15cc968a61d462bfc140f2949362f1ecddba5d1273ec24e29e"},"schema_version":"1.0","source":{"id":"1710.08966","kind":"arxiv","version":1}},"canonical_sha256":"27e7a8841cfb9f473d334c94f2aee07cd17a518833e7924f34c4558440de499f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27e7a8841cfb9f473d334c94f2aee07cd17a518833e7924f34c4558440de499f","first_computed_at":"2026-05-18T00:32:00.660344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:00.660344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YD1BTBt4+bXbRMKWP1ec8HVkVgG2tlGpoEUHbhxkNiIlI8mzvrIMwCjuJ7XtTConxq3pc6kKTlRHYqUXkPk6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:00.660875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb7f305ab1e71b22f589414a0d437f0bdfa6c851381bcf42a3b4bcc95cc87d3e","sha256:39b826ec6ecf7f4eb74f5bfdc8603290c374bf8cc877b3c7606cfca1a398153b"],"state_sha256":"ebd6afb4ab4a31ea55cd28fa1235ed6f42fa356551192c295be217df86c6f11e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QiIXUP+efgVUwRTGcDbO864C/9ZjjQvjol+WkSEZsosYIPyJaO/GYYNWEJ9RhApp8edeJ8MPjhXYqzi/4gcvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:31:43.836553Z","bundle_sha256":"d26f1e74171b78e9c8bae733d51938d685c281bab7478ed6a5690ce53c7279dd"}}