{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JMD4XWS6YLGPCSAAW4KAEOCBFD","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":"d1fd9036a07c3cbfc9bde60aaebf65c9dd7e0704239c2c244f208decc6086ac8","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-28T09:20:24Z","title_canon_sha256":"0f0aa92793d06ecad844cf21e227c5c66a8a00271c6801276864b2e53748b752"},"schema_version":"1.0","source":{"id":"1711.10194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10194","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10194v1","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10194","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"JMD4XWS6YLGP","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JMD4XWS6YLGPCSAA","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JMD4XWS6","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:aa076b11e1d6fdc762151a26ac69e45a9f319f5638899935fe23e4fa998915e0","target":"graph","created_at":"2026-05-18T00:29:22Z","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":"Hall algebras and related constructions have had diverse applications in mathematics and physics, ranging from representation theory and quantum groups to Donaldson-Thomas theory and the algebra of BPS states. The theory of $2$-Segal spaces was introduced independently by Dyckerhoff-Kapranov and G\\'alvez-Carrillo-Kock-Tonks as a unifying framework for Hall algebras: every $2$-Space defines an algebra in the $\\infty$-category of spans, and different Hall algebras correspond to different linearisations of this universal Hall algebra.\n  A recurring theme is that Hall algebras can often be equippe","authors_text":"Mark D Penney","cross_cats":["math.AG","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-28T09:20:24Z","title":"The universal Hall bialgebra of a double 2-Segal space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10194","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:f47ca8104a8de1d9cc9ca19a41d87923e04cd51129cf71809af3fde97c1d0a2a","target":"record","created_at":"2026-05-18T00:29:22Z","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":"d1fd9036a07c3cbfc9bde60aaebf65c9dd7e0704239c2c244f208decc6086ac8","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-28T09:20:24Z","title_canon_sha256":"0f0aa92793d06ecad844cf21e227c5c66a8a00271c6801276864b2e53748b752"},"schema_version":"1.0","source":{"id":"1711.10194","kind":"arxiv","version":1}},"canonical_sha256":"4b07cbda5ec2ccf14800b71402384128f7977ab10a072285ab1d1e4a7b12a088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b07cbda5ec2ccf14800b71402384128f7977ab10a072285ab1d1e4a7b12a088","first_computed_at":"2026-05-18T00:29:22.986359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:22.986359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uW5RavStGOTmX+MHPMd1qP/VX7K7E+5pVdKCS1OjrSpvTVUu1fEE3u6EqMKkHRt4RJm1YXpniEntcfEmIgUzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:22.986934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f47ca8104a8de1d9cc9ca19a41d87923e04cd51129cf71809af3fde97c1d0a2a","sha256:aa076b11e1d6fdc762151a26ac69e45a9f319f5638899935fe23e4fa998915e0"],"state_sha256":"975bf4083ca0074271c5f0d5a0b1c484bda935ba189bc2a8d6eb6d9ca980bb96"}