{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CYX5JD6MXNIRPGGHWTMH5RKUT7","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":"7b4f2f11f1e82cd7248480c5ea33ecbffb464105f8d34b22996f860695087ffc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-04-25T17:48:35Z","title_canon_sha256":"55c523c2f0527e94db49f7e8bb66ad24a01ab2f7711dfd03423eb0b40f58ba7e"},"schema_version":"1.0","source":{"id":"1304.6970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6970","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6970v1","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6970","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"CYX5JD6MXNIR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CYX5JD6MXNIRPGGH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CYX5JD6M","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:6fb2a5ee03cb06c825a96f21840c42729a4a1d24676ad29002c573f589839f96","target":"graph","created_at":"2026-05-18T03:27:10Z","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 structure of the Hall algebra of two-periodic complexes recently introduced by Bridgeland. We introduce coproduct on Bridgeland's Hall algebra, and show that in the hereditary case the resulting bialgebra structure coincides with that on Drinfeld double of the ordinary Hall algebra","authors_text":"Shintarou Yanagida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-04-25T17:48:35Z","title":"Bialgebra structure on Bridgeland's Hall algebra of two-periodic complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6970","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:fc94239c6c1d4464c8a3c0d6e2da2395ebbbaad7eb9fcfd0504e23914be4598d","target":"record","created_at":"2026-05-18T03:27:10Z","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":"7b4f2f11f1e82cd7248480c5ea33ecbffb464105f8d34b22996f860695087ffc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-04-25T17:48:35Z","title_canon_sha256":"55c523c2f0527e94db49f7e8bb66ad24a01ab2f7711dfd03423eb0b40f58ba7e"},"schema_version":"1.0","source":{"id":"1304.6970","kind":"arxiv","version":1}},"canonical_sha256":"162fd48fccbb511798c7b4d87ec5549fe80b6466b070ea0ed0e1fe70cd3291a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"162fd48fccbb511798c7b4d87ec5549fe80b6466b070ea0ed0e1fe70cd3291a2","first_computed_at":"2026-05-18T03:27:10.686268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:10.686268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+hj2Quj+AcijuGrmWA0rmncgb2+Ci95FYO1ZKgPXgUM8A7SIPlVzQAJVA3Yfxjk7zZy7OBEngOxiNdXzwZX6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:10.687115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc94239c6c1d4464c8a3c0d6e2da2395ebbbaad7eb9fcfd0504e23914be4598d","sha256:6fb2a5ee03cb06c825a96f21840c42729a4a1d24676ad29002c573f589839f96"],"state_sha256":"d43bfdb8761e90c23ac6f44172a4d7943ab2178b5c5618343bac399d96829a29"}