{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RPSC67B3PZPMIF64IZVHOB5HTO","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":"46d71d9e6de35a5b687cc04b7c59a1f7cde6a81b42bbcf6115f98a3c72fe022a","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-07-22T16:37:37Z","title_canon_sha256":"97e424c34fe2ee5448db207a7c61ca0b03a1ab09e3566dd466c8695e1e43c861"},"schema_version":"1.0","source":{"id":"1907.09412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09412","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09412v1","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09412","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"RPSC67B3PZPM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RPSC67B3PZPMIF64","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RPSC67B3","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:f066d3e5517d7d2e051ec0152032588c7d4d8fbc3c6ce49e45713e9934e3f8c3","target":"graph","created_at":"2026-05-17T23:39:59Z","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 prove that certain triangulated categories are (weakly) approximable in the sense of A. Neeman. We prove that a triangulated $C$ that is compactly generated by a single object $G$ is weakly approximable if $C(G,G[i])=0$ for $i>1$ (we say that $G$ is weakly negative if this assumption is fulfilled; the case where the equality $C(G,G[1])=0$ is fulfilled as well was mentioned by Neeman himself). Moreover, if $G\\cong \\bigoplus_{0\\le i\\le n}G_i$ and $C(G_i,G_j[1])=0$ whenever $i\\le j$ then $C$ is also approximable.\n  The latter result can be useful since (under a few more additional assumptions)","authors_text":"Mikhail V. Bondarko, Sergei V. Vostokov","cross_cats":["math.AG","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-07-22T16:37:37Z","title":"On weakly negative subcategories, weight structures, and (weakly) approximable triangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09412","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":"sha256:21b5ce76268324383fdaff94d7285bda44475e3a3e38b2e215e5d92526fdd0f8","target":"record","created_at":"2026-05-17T23:39:59Z","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":"46d71d9e6de35a5b687cc04b7c59a1f7cde6a81b42bbcf6115f98a3c72fe022a","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2019-07-22T16:37:37Z","title_canon_sha256":"97e424c34fe2ee5448db207a7c61ca0b03a1ab09e3566dd466c8695e1e43c861"},"schema_version":"1.0","source":{"id":"1907.09412","kind":"arxiv","version":1}},"canonical_sha256":"8be42f7c3b7e5ec417dc466a7707a79b8aaf27e0570ab2784f360a3264269373","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8be42f7c3b7e5ec417dc466a7707a79b8aaf27e0570ab2784f360a3264269373","first_computed_at":"2026-05-17T23:39:59.263263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:59.263263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fO1muVg/BtvzZthq+iZBDJL+qvEaFsCAd7PgJ6WkI+UksYgFG8PLBHChgLLKhMyLW1vtZ9NL5YyJTZSZTkjzCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:59.263853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21b5ce76268324383fdaff94d7285bda44475e3a3e38b2e215e5d92526fdd0f8","sha256:f066d3e5517d7d2e051ec0152032588c7d4d8fbc3c6ce49e45713e9934e3f8c3"],"state_sha256":"edfcaa3887e7da82520d091b4ef103cdc25f919123b9573162dd80a9deb6ffc9"}