{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:E3XPL5EOCYPGLJCJXDEDIYY2Z6","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":"9416f4169a3106793a74b5518d9cf7a7701ae7bae007778fb253947fc99a7527","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-05-19T14:23:33Z","title_canon_sha256":"b6350f03e13a8bd27ae5aaec52ce18324fed8f781e18c81a7988e8455ee2bc82"},"schema_version":"1.0","source":{"id":"2405.11561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.11561","created_at":"2026-07-05T08:20:41Z"},{"alias_kind":"arxiv_version","alias_value":"2405.11561v1","created_at":"2026-07-05T08:20:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11561","created_at":"2026-07-05T08:20:41Z"},{"alias_kind":"pith_short_12","alias_value":"E3XPL5EOCYPG","created_at":"2026-07-05T08:20:41Z"},{"alias_kind":"pith_short_16","alias_value":"E3XPL5EOCYPGLJCJ","created_at":"2026-07-05T08:20:41Z"},{"alias_kind":"pith_short_8","alias_value":"E3XPL5EO","created_at":"2026-07-05T08:20:41Z"}],"graph_snapshots":[{"event_id":"sha256:3977339316c946b52f1bfdf549e4aa13740b4e383bd1c7b3118e721c3bc5f7c4","target":"graph","created_at":"2026-07-05T08:20:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.11561/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Waldhausen's $S_\\bullet$-construction gives a way to define the algebraic $K$-theory space of a category with cofibrations. Specifically, the $K$-theory space of a category with cofibrations $\\mathcal{C}$ can be defined as the loop space of the realization of the simplicial topological space $|iS_\\bullet \\mathcal{C} |$. Dyckerhoff and Kapranov observed that if $\\mathcal{C}$ is chosen to be a proto-exact category, then this simplicial topological space is 2-Segal. A natural question is then what variants of this $S_\\bullet$-construction give 2-Segal spaces. We find that for $|iS_\\bullet \\mathca","authors_text":"Tanner Nathan Carawan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-05-19T14:23:33Z","title":"2-Segal maps associated to a category with cofibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11561","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":"sha256:734c20438d195d6fd91ba7215e658647ba57c105a666813cb305ab560d96da1d","target":"record","created_at":"2026-07-05T08:20:41Z","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":"9416f4169a3106793a74b5518d9cf7a7701ae7bae007778fb253947fc99a7527","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-05-19T14:23:33Z","title_canon_sha256":"b6350f03e13a8bd27ae5aaec52ce18324fed8f781e18c81a7988e8455ee2bc82"},"schema_version":"1.0","source":{"id":"2405.11561","kind":"arxiv","version":1}},"canonical_sha256":"26eef5f48e161e65a449b8c834631acf84454f67acc6ad6a646618e010775089","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26eef5f48e161e65a449b8c834631acf84454f67acc6ad6a646618e010775089","first_computed_at":"2026-07-05T08:20:41.653127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:20:41.653127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nk4bgbg7WuuvUrrrDSS21mdDFr7mP59qky03mOXlNfUgoZGDWdau2/1YLepJaHzlVDfZtZiKCYuIwIE6TicADw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:20:41.653598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.11561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734c20438d195d6fd91ba7215e658647ba57c105a666813cb305ab560d96da1d","sha256:3977339316c946b52f1bfdf549e4aa13740b4e383bd1c7b3118e721c3bc5f7c4"],"state_sha256":"f14937734abc872be50ca8c5ab6e71138a7d5ee190436d42c2edfb8def848619"}