{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:46UNE2SLJKVVSZ5CHJN5BVIRPB","short_pith_number":"pith:46UNE2SL","canonical_record":{"source":{"id":"1310.6501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-10-24T07:05:02Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"265ef0b943cb426e0d7a700956d9176a3c41b2dae3ff03079144d9f0bfd91984","abstract_canon_sha256":"e19af62dcdae1d0b72d55c989c43248e8026f6727c4a69cc0e9ea24936bd258b"},"schema_version":"1.0"},"canonical_sha256":"e7a8d26a4b4aab5967a23a5bd0d511787591e46658fdc455ddd4b02d2918e6fa","source":{"kind":"arxiv","id":"1310.6501","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6501","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6501v1","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6501","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"46UNE2SLJKVV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"46UNE2SLJKVVSZ5C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"46UNE2SL","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:46UNE2SLJKVVSZ5CHJN5BVIRPB","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-10-24T07:05:02Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"265ef0b943cb426e0d7a700956d9176a3c41b2dae3ff03079144d9f0bfd91984","abstract_canon_sha256":"e19af62dcdae1d0b72d55c989c43248e8026f6727c4a69cc0e9ea24936bd258b"},"schema_version":"1.0"},"canonical_sha256":"e7a8d26a4b4aab5967a23a5bd0d511787591e46658fdc455ddd4b02d2918e6fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:48.510737Z","signature_b64":"YIVcJOBEVwdlEhIh3BjFBSfgsW/CYKAW3fqGy+akwO7E9RWo6fffeEUH5yFL6LFOwEdOoCeQvWQmOLDIxPUXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7a8d26a4b4aab5967a23a5bd0d511787591e46658fdc455ddd4b02d2918e6fa","last_reissued_at":"2026-05-18T02:51:48.510253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:48.510253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6501","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":"2026-05-18T02:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Atcc3CMepjr8INPGGCQ1C1e/DWPuRWmM4UulBb49u7YnTsBTKusijwwaJ4sOCf8QeeCHbjdiOIvHCecKTB5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:45:34.567769Z"},"content_sha256":"a04186046a99737b0e89ecd589d7c216d177cad53581503705a6c6530b4091a6","schema_version":"1.0","event_id":"sha256:a04186046a99737b0e89ecd589d7c216d177cad53581503705a6c6530b4091a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:46UNE2SLJKVVSZ5CHJN5BVIRPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quiver Bialgebras and Monoidal Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.QA","authors_text":"Blas Torrecillas, Hua-Lin Huang","submitted_at":"2013-10-24T07:05:02Z","abstract_excerpt":"We study the bialgebra structures on quiver coalgebras and the monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural bialgebra structures. This endows the category of locally nilpotent and locally finite representations of an arbitrary quiver with natural monoidal structures from bialgebras. We also obtain theorems of Gabriel type for pointed bialgebras and hereditary finite pointed monoidal categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6501","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":"2026-05-18T02:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kz072qr9KlXJKw674XxFv/3XERVe8wkUYHqFrZI1gIPXOE9dCq8xgE0zorpXucYMxdipyg4RMQ9XukAT/FOmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:45:34.568114Z"},"content_sha256":"7e9498bbe9183d51f75d7268ff91e8669b9bafbbc7aed82a237c3004f52942fa","schema_version":"1.0","event_id":"sha256:7e9498bbe9183d51f75d7268ff91e8669b9bafbbc7aed82a237c3004f52942fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB/bundle.json","state_url":"https://pith.science/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB/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":"2026-06-21T21:45:34Z","links":{"resolver":"https://pith.science/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB","bundle":"https://pith.science/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB/bundle.json","state":"https://pith.science/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46UNE2SLJKVVSZ5CHJN5BVIRPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:46UNE2SLJKVVSZ5CHJN5BVIRPB","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":"e19af62dcdae1d0b72d55c989c43248e8026f6727c4a69cc0e9ea24936bd258b","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-10-24T07:05:02Z","title_canon_sha256":"265ef0b943cb426e0d7a700956d9176a3c41b2dae3ff03079144d9f0bfd91984"},"schema_version":"1.0","source":{"id":"1310.6501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6501","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6501v1","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6501","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"46UNE2SLJKVV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"46UNE2SLJKVVSZ5C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"46UNE2SL","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:7e9498bbe9183d51f75d7268ff91e8669b9bafbbc7aed82a237c3004f52942fa","target":"graph","created_at":"2026-05-18T02:51:48Z","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 bialgebra structures on quiver coalgebras and the monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural bialgebra structures. This endows the category of locally nilpotent and locally finite representations of an arbitrary quiver with natural monoidal structures from bialgebras. We also obtain theorems of Gabriel type for pointed bialgebras and hereditary finite pointed monoidal categories.","authors_text":"Blas Torrecillas, Hua-Lin Huang","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-10-24T07:05:02Z","title":"Quiver Bialgebras and Monoidal Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6501","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:a04186046a99737b0e89ecd589d7c216d177cad53581503705a6c6530b4091a6","target":"record","created_at":"2026-05-18T02:51:48Z","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":"e19af62dcdae1d0b72d55c989c43248e8026f6727c4a69cc0e9ea24936bd258b","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-10-24T07:05:02Z","title_canon_sha256":"265ef0b943cb426e0d7a700956d9176a3c41b2dae3ff03079144d9f0bfd91984"},"schema_version":"1.0","source":{"id":"1310.6501","kind":"arxiv","version":1}},"canonical_sha256":"e7a8d26a4b4aab5967a23a5bd0d511787591e46658fdc455ddd4b02d2918e6fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7a8d26a4b4aab5967a23a5bd0d511787591e46658fdc455ddd4b02d2918e6fa","first_computed_at":"2026-05-18T02:51:48.510253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:48.510253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YIVcJOBEVwdlEhIh3BjFBSfgsW/CYKAW3fqGy+akwO7E9RWo6fffeEUH5yFL6LFOwEdOoCeQvWQmOLDIxPUXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:48.510737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a04186046a99737b0e89ecd589d7c216d177cad53581503705a6c6530b4091a6","sha256:7e9498bbe9183d51f75d7268ff91e8669b9bafbbc7aed82a237c3004f52942fa"],"state_sha256":"dfb892597afd14eaecb70ec357138ae351192c4ca45eaddc2f80d17e6c4c402e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMY4tlT3+EHMSfcezh16tZqIWuGNqnJVTyp92uib7Y1QEgu9lTJqK6MAJxmrhJCgiHRVCZbQXHFNi1U73WdUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:45:34.570099Z","bundle_sha256":"0e67f361e5281bc56f0becefa3e0913426069f875f1fec500e7a2db1f6567026"}}