{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VTO62XNIHURQHIZTQOJNXBCCM4","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":"f44a37bb3916a8f3af39d95ab54bddb1ebae7cc11e1f32434a26a65d8fa73e1c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-12-22T20:13:37Z","title_canon_sha256":"5b36a2ca731f8d71c61704bba42ffdc243124f2322bc29dd882941b0db89bf8e"},"schema_version":"1.0","source":{"id":"2112.12209","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.12209","created_at":"2026-07-05T09:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"2112.12209v2","created_at":"2026-07-05T09:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.12209","created_at":"2026-07-05T09:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"VTO62XNIHURQ","created_at":"2026-07-05T09:21:34Z"},{"alias_kind":"pith_short_16","alias_value":"VTO62XNIHURQHIZT","created_at":"2026-07-05T09:21:34Z"},{"alias_kind":"pith_short_8","alias_value":"VTO62XNI","created_at":"2026-07-05T09:21:34Z"}],"graph_snapshots":[{"event_id":"sha256:3f6da1e71264d85826fdbbb03dbce40b2ca4ad81c7c637c7101aa9e99655bf07","target":"graph","created_at":"2026-07-05T09:21:34Z","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/2112.12209/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we define local dimensions of points in a poset and show that these numbers for realisations behave in a similar way as they do for upper semilattices. Furthermore, similarly to upper semilattices, realisations have well-behaved discrete approximations which are suitable for capturing homological properties of functors indexed by them. These discretisations are convenient and effective for describing tameness of functors.","authors_text":"Alvin Jin, Francesca Tombari, Wojciech Chacholski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-12-22T20:13:37Z","title":"Realisations of posets and tameness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.12209","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":"sha256:50325304407e46287e002bf82f20a91aae4b41e7738a1f70a4c631dbbc9bc975","target":"record","created_at":"2026-07-05T09:21:34Z","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":"f44a37bb3916a8f3af39d95ab54bddb1ebae7cc11e1f32434a26a65d8fa73e1c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2021-12-22T20:13:37Z","title_canon_sha256":"5b36a2ca731f8d71c61704bba42ffdc243124f2322bc29dd882941b0db89bf8e"},"schema_version":"1.0","source":{"id":"2112.12209","kind":"arxiv","version":2}},"canonical_sha256":"acdded5da83d2303a3338392db84426717523ef904a20f2aee134705cd90e5af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acdded5da83d2303a3338392db84426717523ef904a20f2aee134705cd90e5af","first_computed_at":"2026-07-05T09:21:34.726422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:34.726422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QYCp4+OsF1EqMfLmcBwYA2dmQMI1XuzWZakdyfyYvu6AwPEi57mZc6//nTRH5Xb+zBWoojCCC9kAb0TNXYT6Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:34.726904Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.12209","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50325304407e46287e002bf82f20a91aae4b41e7738a1f70a4c631dbbc9bc975","sha256:3f6da1e71264d85826fdbbb03dbce40b2ca4ad81c7c637c7101aa9e99655bf07"],"state_sha256":"4ce3409315a658dd48e91b45ca1c182ed3e8356d942db57b205d6c94c09cf7a5"}