{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KKGUR62K2XNBT77XMURRHOF4H2","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":"ae7327040431a38ae41d764652e870d50a7542fbd9b4b26dec3cfa53d4b454d1","cross_cats_sorted":["math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-09T16:31:38Z","title_canon_sha256":"8a0f1d01ddde23cb2a14c4cf5a60244536cec6a2d7a55d2ac569b293778f5316"},"schema_version":"1.0","source":{"id":"1609.02853","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02853","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02853v3","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02853","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"pith_short_12","alias_value":"KKGUR62K2XNB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KKGUR62K2XNBT77X","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KKGUR62K","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:7a82d2119dad1adcf5de35bdd86596af30056d7d14fd4ec67f469029432e0076","target":"graph","created_at":"2026-05-18T00:45:06Z","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":"It is known by results of Dyckerhoff-Kapranov and of G\\'alvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction has a unital 2-Segal structure. Here, we prove that a certain S.-functor defines an equivalence between the category of augmented stable double categories and the category of unital 2-Segal sets. The inverse equivalence is described explicitly by a path construction. We illustrate the equivalence for the known examples of partial monoids, cobordism categories with genus constraints and graph coalgebras.","authors_text":"Ang\\'elica M. Osorno, Claudia I. Scheimbauer, Julia E. Bergner, Martina Rovelli, Viktoriya Ozornova","cross_cats":["math.CT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-09T16:31:38Z","title":"2-Segal sets and the Waldhausen construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02853","kind":"arxiv","version":3},"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":"sha256:16f1a1ee6b816617d02b41352927a89980f612dc5af99d998dc02544d9dba860","target":"record","created_at":"2026-05-18T00:45:06Z","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":"ae7327040431a38ae41d764652e870d50a7542fbd9b4b26dec3cfa53d4b454d1","cross_cats_sorted":["math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-09T16:31:38Z","title_canon_sha256":"8a0f1d01ddde23cb2a14c4cf5a60244536cec6a2d7a55d2ac569b293778f5316"},"schema_version":"1.0","source":{"id":"1609.02853","kind":"arxiv","version":3}},"canonical_sha256":"528d48fb4ad5da19fff7652313b8bc3e8431bc6f32245e65a3bf07eaba7f0e36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"528d48fb4ad5da19fff7652313b8bc3e8431bc6f32245e65a3bf07eaba7f0e36","first_computed_at":"2026-05-18T00:45:06.393675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:06.393675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hDqFKOkLU/W3xLT21Hn5EXq66wxnslo9AX4XSr4DD6Y1LY1ZeD5ipBt2McyEOpgDLt+dQKeBh6RUD6oYDrimAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:06.394101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02853","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16f1a1ee6b816617d02b41352927a89980f612dc5af99d998dc02544d9dba860","sha256:7a82d2119dad1adcf5de35bdd86596af30056d7d14fd4ec67f469029432e0076"],"state_sha256":"96cdb75714079af916a46c837031457ced85623b54f64ca26d9740046dbada07"}