{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NWV43DAVBD6WT3QQFBCVKPWL2J","short_pith_number":"pith:NWV43DAV","canonical_record":{"source":{"id":"1712.00934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-04T07:24:58Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"bd750b04761e568aef2bfa29362928b0a9d6a0b06934061de417ecd4b86909bf","abstract_canon_sha256":"9f04c1b901191b1e3ed9c480c136bb08630a410b38fab8ac99315138e4683af7"},"schema_version":"1.0"},"canonical_sha256":"6dabcd8c1508fd69ee102845553ecbd27d73c42a58f2acf053f8eae0b449cfb2","source":{"kind":"arxiv","id":"1712.00934","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00934","created_at":"2026-05-18T00:28:59Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00934v1","created_at":"2026-05-18T00:28:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00934","created_at":"2026-05-18T00:28:59Z"},{"alias_kind":"pith_short_12","alias_value":"NWV43DAVBD6W","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWV43DAVBD6WT3QQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWV43DAV","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NWV43DAVBD6WT3QQFBCVKPWL2J","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-04T07:24:58Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"bd750b04761e568aef2bfa29362928b0a9d6a0b06934061de417ecd4b86909bf","abstract_canon_sha256":"9f04c1b901191b1e3ed9c480c136bb08630a410b38fab8ac99315138e4683af7"},"schema_version":"1.0"},"canonical_sha256":"6dabcd8c1508fd69ee102845553ecbd27d73c42a58f2acf053f8eae0b449cfb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:59.951984Z","signature_b64":"c7dozJNPsGDKDM1VkoX5v58in4ZkOKQ/dF/Zi49CXAmz+JtQLbUdHt4DVdPnta7YONW3MgBzNDfjE8Kj8aGvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dabcd8c1508fd69ee102845553ecbd27d73c42a58f2acf053f8eae0b449cfb2","last_reissued_at":"2026-05-18T00:28:59.951604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:59.951604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00934","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":"2026-05-18T00:28:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Mg1AZ5qnRnQXGDtNxVXhR6JSj6pGel7W3jb8+C+HPi1TOu3qJYPsM4vt98KcsW9HD/Qy6xjMdyp1pii4xwmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:37:41.235311Z"},"content_sha256":"20c93b3146806b4f40a6e57fac66c0477fcabcb9bff8f2d683bb6bbbc4963126","schema_version":"1.0","event_id":"sha256:20c93b3146806b4f40a6e57fac66c0477fcabcb9bff8f2d683bb6bbbc4963126"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NWV43DAVBD6WT3QQFBCVKPWL2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properness of moment maps for representations of quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Pradeep Das","submitted_at":"2017-12-04T07:24:58Z","abstract_excerpt":"In this note, we give a necessary and sufficient condition for the properness of moment maps for representations of quivers. We show that the moment map for the representations of a quiver is proper if and only if the quiver is acyclic, that is, it does not contain any oriented cycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00934","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":"2026-05-18T00:28:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cg30x44GHE5IbmBOPqU3uU4s5H2L3uerrTE9PQMpPvubWdmdkoYiLiBKLqiOWUjkW2WHyP87fMKQ0ekfzJ16Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:37:41.235663Z"},"content_sha256":"d12a9f6daac2f295a980a16d2dea6f274f145ec29146b6c22136afd6acd40b49","schema_version":"1.0","event_id":"sha256:d12a9f6daac2f295a980a16d2dea6f274f145ec29146b6c22136afd6acd40b49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWV43DAVBD6WT3QQFBCVKPWL2J/bundle.json","state_url":"https://pith.science/pith/NWV43DAVBD6WT3QQFBCVKPWL2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWV43DAVBD6WT3QQFBCVKPWL2J/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":"2026-07-02T22:37:41Z","links":{"resolver":"https://pith.science/pith/NWV43DAVBD6WT3QQFBCVKPWL2J","bundle":"https://pith.science/pith/NWV43DAVBD6WT3QQFBCVKPWL2J/bundle.json","state":"https://pith.science/pith/NWV43DAVBD6WT3QQFBCVKPWL2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWV43DAVBD6WT3QQFBCVKPWL2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NWV43DAVBD6WT3QQFBCVKPWL2J","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":"9f04c1b901191b1e3ed9c480c136bb08630a410b38fab8ac99315138e4683af7","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-04T07:24:58Z","title_canon_sha256":"bd750b04761e568aef2bfa29362928b0a9d6a0b06934061de417ecd4b86909bf"},"schema_version":"1.0","source":{"id":"1712.00934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00934","created_at":"2026-05-18T00:28:59Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00934v1","created_at":"2026-05-18T00:28:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00934","created_at":"2026-05-18T00:28:59Z"},{"alias_kind":"pith_short_12","alias_value":"NWV43DAVBD6W","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWV43DAVBD6WT3QQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWV43DAV","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:d12a9f6daac2f295a980a16d2dea6f274f145ec29146b6c22136afd6acd40b49","target":"graph","created_at":"2026-05-18T00:28:59Z","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":"In this note, we give a necessary and sufficient condition for the properness of moment maps for representations of quivers. We show that the moment map for the representations of a quiver is proper if and only if the quiver is acyclic, that is, it does not contain any oriented cycle.","authors_text":"Pradeep Das","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-04T07:24:58Z","title":"Properness of moment maps for representations of quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00934","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":"sha256:20c93b3146806b4f40a6e57fac66c0477fcabcb9bff8f2d683bb6bbbc4963126","target":"record","created_at":"2026-05-18T00:28:59Z","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":"9f04c1b901191b1e3ed9c480c136bb08630a410b38fab8ac99315138e4683af7","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-04T07:24:58Z","title_canon_sha256":"bd750b04761e568aef2bfa29362928b0a9d6a0b06934061de417ecd4b86909bf"},"schema_version":"1.0","source":{"id":"1712.00934","kind":"arxiv","version":1}},"canonical_sha256":"6dabcd8c1508fd69ee102845553ecbd27d73c42a58f2acf053f8eae0b449cfb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dabcd8c1508fd69ee102845553ecbd27d73c42a58f2acf053f8eae0b449cfb2","first_computed_at":"2026-05-18T00:28:59.951604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:59.951604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7dozJNPsGDKDM1VkoX5v58in4ZkOKQ/dF/Zi49CXAmz+JtQLbUdHt4DVdPnta7YONW3MgBzNDfjE8Kj8aGvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:59.951984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20c93b3146806b4f40a6e57fac66c0477fcabcb9bff8f2d683bb6bbbc4963126","sha256:d12a9f6daac2f295a980a16d2dea6f274f145ec29146b6c22136afd6acd40b49"],"state_sha256":"849ef93d22d340252a7f7b6f2e6d53a66c3a1dded4d0a194ea8d3bdd9a0fe3b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q0E4acJTYWUQEDigu4YynFfRhwznWO866nxVoxTN3vU19jBRxYoNBwO44IgoakZe96krwVuhttYXLzsSAv5WAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T22:37:41.237501Z","bundle_sha256":"5454b4c8972a87e7f9a054bbb727ce0b6302d6fa1f8b75f15f52d88437d3f294"}}