{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PYRBKDFU44OTMB34WF54XKEJSB","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":"5d41f80bcbd8e9d6144fd432c6970ad70896e568db8ca2281a1ba59f0c8e9991","cross_cats_sorted":["math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-28T16:43:28Z","title_canon_sha256":"0654a2b50ce5672f9d1be824deb318d3864b63311f59b1e5f1f940f947b8c30d"},"schema_version":"1.0","source":{"id":"1611.09234","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09234","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09234v2","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09234","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"PYRBKDFU44OT","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYRBKDFU44OTMB34","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYRBKDFU","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:0c8c489d605c1599598606dfd6258ad70f03a542dd158d27c1b347d76b956ae2","target":"graph","created_at":"2026-05-18T00:20:56Z","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 introduce a relative version of the $2$-Segal simplicial spaces defined by Dyckerhoff and Kapranov and G\\'{a}lvez-Carrillo, Kock and Tonks. Examples of relative $2$-Segal spaces include the categorified unoriented cyclic nerve, real pseudoholomorphic polygons in almost complex manifolds and the $\\mathcal{R}_{\\bullet}$-construction from Grothendieck-Witt theory. We show that a relative $2$-Segal space defines a categorical representation of the Hall algebra associated to the base $2$-Segal space. In this way, after decategorification we recover a number of known constructions of Hall algebra","authors_text":"Matthew B. Young","cross_cats":["math.CT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-28T16:43:28Z","title":"Relative $2$-Segal spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09234","kind":"arxiv","version":2},"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":"sha256:30704ec436aa822600c9bb01648a0c981d600d74852d7b430153cb812cf4052f","target":"record","created_at":"2026-05-18T00:20:56Z","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":"5d41f80bcbd8e9d6144fd432c6970ad70896e568db8ca2281a1ba59f0c8e9991","cross_cats_sorted":["math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-28T16:43:28Z","title_canon_sha256":"0654a2b50ce5672f9d1be824deb318d3864b63311f59b1e5f1f940f947b8c30d"},"schema_version":"1.0","source":{"id":"1611.09234","kind":"arxiv","version":2}},"canonical_sha256":"7e22150cb4e71d36077cb17bcba889907edee40815129d69197d1e076f230c2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e22150cb4e71d36077cb17bcba889907edee40815129d69197d1e076f230c2a","first_computed_at":"2026-05-18T00:20:56.939555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:56.939555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4f7KvTYqS8xpSYDKztxRlEI/BZN3fcK2n5x4P5ueKZUo8YpExsPbXW6eDSGGs4FEUb+m0VKGqeh4If/8dO5OAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:56.940099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09234","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30704ec436aa822600c9bb01648a0c981d600d74852d7b430153cb812cf4052f","sha256:0c8c489d605c1599598606dfd6258ad70f03a542dd158d27c1b347d76b956ae2"],"state_sha256":"3c14eaf37ee80674858389d0e0dc61e5790e5ef2c861f87bbc0325f79f13f757"}