{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A6MHFJWW47OLP26YSE5NS7ABDO","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":"87bb86669ebe081231e0fd3b90ea3f038b01d5ec2341d883a6f615a63ddcd45a","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-21T15:19:58Z","title_canon_sha256":"df3703d9c0ebf6ab7b41f820672971569bfb94e61a08093de8457ad9f2c6c203"},"schema_version":"1.0","source":{"id":"1601.05673","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05673","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05673v2","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05673","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"A6MHFJWW47OL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A6MHFJWW47OLP26Y","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A6MHFJWW","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:bdd31c3d662bb7e05f21eda2734265294ee97a542b8af0fa34a850647e3123a1","target":"graph","created_at":"2026-05-18T01:15:32Z","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":"Given two torus invariant Weil divisors $D$ and $D'$ on a two-dimensional cyclic quotient singularity $X$, the groups $\\mathop{Ext}\\nolimits^i_{X}(\\mathcal{O}(D),\\mathcal{O}(D'))$, $i>0$, are naturally $\\mathbb{Z}^2$-graded. We interpret these groups via certain combinatorial objects using methods from toric geometry. In particular, it is enough to give a combinatorial description of the $\\mathop{Ext}\\nolimits^1$-groups in the polyhedra of global sections of the Weil divisors involved. Higher $\\mathop{Ext}\\nolimits^i$-groups are then reduced to the case of $\\mathop{Ext}\\nolimits^1$ via a quive","authors_text":"Lars Kastner","cross_cats":["math.AC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-21T15:19:58Z","title":"Ext and Tor on two-dimensional cyclic quotient singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05673","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:e452e9ed8658a7d17940ac634eceb0e9fe2b479ef8ac7d64940ca7840779185e","target":"record","created_at":"2026-05-18T01:15:32Z","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":"87bb86669ebe081231e0fd3b90ea3f038b01d5ec2341d883a6f615a63ddcd45a","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-21T15:19:58Z","title_canon_sha256":"df3703d9c0ebf6ab7b41f820672971569bfb94e61a08093de8457ad9f2c6c203"},"schema_version":"1.0","source":{"id":"1601.05673","kind":"arxiv","version":2}},"canonical_sha256":"079872a6d6e7dcb7ebd8913ad97c011ba64ccd2736a9904994b286ae62b2dd3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"079872a6d6e7dcb7ebd8913ad97c011ba64ccd2736a9904994b286ae62b2dd3a","first_computed_at":"2026-05-18T01:15:32.081494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:32.081494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b5TWxX4klpzZ3u7114XP/djPzoynNjMMuWocGZjh3yZDWJR/SVkwQu6KYjXHgI7Su5+kjX9kOYsMGJWSI1N7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:32.082198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05673","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e452e9ed8658a7d17940ac634eceb0e9fe2b479ef8ac7d64940ca7840779185e","sha256:bdd31c3d662bb7e05f21eda2734265294ee97a542b8af0fa34a850647e3123a1"],"state_sha256":"c17949e79a2c80b6886d4dde128714d65b398ceaa1612c3b34c0a096c2034681"}