{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:AP6PW3RX5JCRRPL6DE2ZQ4NEZ4","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":"6e0f8b1b42469c522bcd830a6fbc1572aa170df2b87756d7fee6fc28498365d9","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2022-09-27T16:28:17Z","title_canon_sha256":"2175b663303e4d60c1185ea04c3f4de4176c81a4ad41586e06261381313bafad"},"schema_version":"1.0","source":{"id":"2209.13510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13510","created_at":"2026-07-05T05:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13510v2","created_at":"2026-07-05T05:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13510","created_at":"2026-07-05T05:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"AP6PW3RX5JCR","created_at":"2026-07-05T05:02:14Z"},{"alias_kind":"pith_short_16","alias_value":"AP6PW3RX5JCRRPL6","created_at":"2026-07-05T05:02:14Z"},{"alias_kind":"pith_short_8","alias_value":"AP6PW3RX","created_at":"2026-07-05T05:02:14Z"}],"graph_snapshots":[{"event_id":"sha256:3bc28a940694aee3350f89d2de1c69435a9be646fcf47964908692593a0c59d4","target":"graph","created_at":"2026-07-05T05:02:14Z","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/2209.13510/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the categories PsTop and Lim of pseudotopological spaces and limit spaces, respectively, admit cofibration category structures, and that PsTop admits a model category structure, giving several ways to simultaneously study the homotopy theory of classical topological spaces, combinatorial spaces such as graphs and matroids, and metric spaces endowed with a privileged scale, in addition to spaces of maps between them. In the process, we give a sufficient condition for a topological construct which contains compactly generated Hausdorff spaces as a subcategory to admit an $I$-categor","authors_text":"Antonio Rieser","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2022-09-27T16:28:17Z","title":"Cofibration and Model Category Structures for Discrete and Continuous Homotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13510","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:a01c571743cb4ad2e7b9a17b81a516595eb22da6b176462d09723de1c2088c2f","target":"record","created_at":"2026-07-05T05:02:14Z","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":"6e0f8b1b42469c522bcd830a6fbc1572aa170df2b87756d7fee6fc28498365d9","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2022-09-27T16:28:17Z","title_canon_sha256":"2175b663303e4d60c1185ea04c3f4de4176c81a4ad41586e06261381313bafad"},"schema_version":"1.0","source":{"id":"2209.13510","kind":"arxiv","version":2}},"canonical_sha256":"03fcfb6e37ea4518bd7e19359871a4cf3cdee34149fad897c753cbce6976c922","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03fcfb6e37ea4518bd7e19359871a4cf3cdee34149fad897c753cbce6976c922","first_computed_at":"2026-07-05T05:02:14.241427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:14.241427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/LbaSPZG9gYRuFCQ4ebbtliwFkntLvtMU6Riv8tS0K0JRiqvZyknWwXLo+XmSUlIa4CCw0od2H6hpmOIWT3UBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:14.241927Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.13510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a01c571743cb4ad2e7b9a17b81a516595eb22da6b176462d09723de1c2088c2f","sha256:3bc28a940694aee3350f89d2de1c69435a9be646fcf47964908692593a0c59d4"],"state_sha256":"1149e8bf8f8a4c9cb23497663b226c804592f87eb446c43a3f4ff89c1b24ff4f"}