{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:S6OTMVE2WAE664IVBV3YLKLZKC","short_pith_number":"pith:S6OTMVE2","canonical_record":{"source":{"id":"1611.02958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-09T14:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"53e3f7a793246c4366721869b08c2b9cfe8996b5c153bb36d0611042670b1729","abstract_canon_sha256":"2723258e5b4c2ee9ee5c0c4e01327910099c03f7bed141bceda81b7afeb5814b"},"schema_version":"1.0"},"canonical_sha256":"979d36549ab009ef71150d7785a9795092d73ae6b9c92ac20a3fec04c4afdf26","source":{"kind":"arxiv","id":"1611.02958","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02958","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02958v1","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02958","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"S6OTMVE2WAE6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"S6OTMVE2WAE664IV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"S6OTMVE2","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:S6OTMVE2WAE664IVBV3YLKLZKC","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-09T14:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"53e3f7a793246c4366721869b08c2b9cfe8996b5c153bb36d0611042670b1729","abstract_canon_sha256":"2723258e5b4c2ee9ee5c0c4e01327910099c03f7bed141bceda81b7afeb5814b"},"schema_version":"1.0"},"canonical_sha256":"979d36549ab009ef71150d7785a9795092d73ae6b9c92ac20a3fec04c4afdf26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:43.002833Z","signature_b64":"GF6rE/XfKD3hzdNe7E2Z0mZ2ca/CyibrZ4LeWtg23zbatwq5BxQDxsw/zHRws7Dk7oOOU+V9tLzJNly6KrmGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"979d36549ab009ef71150d7785a9795092d73ae6b9c92ac20a3fec04c4afdf26","last_reissued_at":"2026-05-18T00:59:43.002179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:43.002179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02958","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n3DOPKkcyImTuxDsQ0yMD4+3If09XorwEJUBNeAQWsEf3FZczluRZpwngBsOJeEaj92kuBykY17p4gFjl98bBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:20:38.759975Z"},"content_sha256":"033cb732f46ecf2417df67b6a19bc68363b531b43f32772d9963c8e82c22b106","schema_version":"1.0","event_id":"sha256:033cb732f46ecf2417df67b6a19bc68363b531b43f32772d9963c8e82c22b106"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:S6OTMVE2WAE664IVBV3YLKLZKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A correspondence of good G-sets under partial geometric quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johannes Schmitt","submitted_at":"2016-11-09T14:52:50Z","abstract_excerpt":"For a complex variety $\\hat X$ with an action of a reductive group $\\hat G$ and a geometric quotient $\\pi: \\hat X \\to X$ by a closed normal subgroup $H \\subset \\hat G$, we show that open sets of $X$ admitting good quotients by $G=\\hat G / H$ correspond bijectively to open sets in $\\hat X$ with good $\\hat G$-quotients. We use this to compute GIT-chambers and their associated quotients for the diagonal action of $\\text{PGL}_2$ on $(\\mathbb{P}^1)^n$ in certain subcones of the $\\text{PGL}_2$-effective cone via a torus action on affine space. This allows us to represent these quotients as toric var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02958","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J67afrCgcK2iwbsqaCaaxsxv+wL3dLqW21FtXb17iUP6fAvYzUJ2EUB5oYfoy4DtqOmMqqgzlwOCWI+fYLjJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:20:38.760337Z"},"content_sha256":"e63d6a18927de17744edc27709a8abe776a1e23e7ca81e0cbb5c80c58d9cac12","schema_version":"1.0","event_id":"sha256:e63d6a18927de17744edc27709a8abe776a1e23e7ca81e0cbb5c80c58d9cac12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S6OTMVE2WAE664IVBV3YLKLZKC/bundle.json","state_url":"https://pith.science/pith/S6OTMVE2WAE664IVBV3YLKLZKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S6OTMVE2WAE664IVBV3YLKLZKC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T10:20:38Z","links":{"resolver":"https://pith.science/pith/S6OTMVE2WAE664IVBV3YLKLZKC","bundle":"https://pith.science/pith/S6OTMVE2WAE664IVBV3YLKLZKC/bundle.json","state":"https://pith.science/pith/S6OTMVE2WAE664IVBV3YLKLZKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S6OTMVE2WAE664IVBV3YLKLZKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S6OTMVE2WAE664IVBV3YLKLZKC","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":"2723258e5b4c2ee9ee5c0c4e01327910099c03f7bed141bceda81b7afeb5814b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-09T14:52:50Z","title_canon_sha256":"53e3f7a793246c4366721869b08c2b9cfe8996b5c153bb36d0611042670b1729"},"schema_version":"1.0","source":{"id":"1611.02958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02958","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02958v1","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02958","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"S6OTMVE2WAE6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"S6OTMVE2WAE664IV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"S6OTMVE2","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:e63d6a18927de17744edc27709a8abe776a1e23e7ca81e0cbb5c80c58d9cac12","target":"graph","created_at":"2026-05-18T00:59:43Z","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":"For a complex variety $\\hat X$ with an action of a reductive group $\\hat G$ and a geometric quotient $\\pi: \\hat X \\to X$ by a closed normal subgroup $H \\subset \\hat G$, we show that open sets of $X$ admitting good quotients by $G=\\hat G / H$ correspond bijectively to open sets in $\\hat X$ with good $\\hat G$-quotients. We use this to compute GIT-chambers and their associated quotients for the diagonal action of $\\text{PGL}_2$ on $(\\mathbb{P}^1)^n$ in certain subcones of the $\\text{PGL}_2$-effective cone via a torus action on affine space. This allows us to represent these quotients as toric var","authors_text":"Johannes Schmitt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-09T14:52:50Z","title":"A correspondence of good G-sets under partial geometric quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02958","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":"sha256:033cb732f46ecf2417df67b6a19bc68363b531b43f32772d9963c8e82c22b106","target":"record","created_at":"2026-05-18T00:59:43Z","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":"2723258e5b4c2ee9ee5c0c4e01327910099c03f7bed141bceda81b7afeb5814b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-09T14:52:50Z","title_canon_sha256":"53e3f7a793246c4366721869b08c2b9cfe8996b5c153bb36d0611042670b1729"},"schema_version":"1.0","source":{"id":"1611.02958","kind":"arxiv","version":1}},"canonical_sha256":"979d36549ab009ef71150d7785a9795092d73ae6b9c92ac20a3fec04c4afdf26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979d36549ab009ef71150d7785a9795092d73ae6b9c92ac20a3fec04c4afdf26","first_computed_at":"2026-05-18T00:59:43.002179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:43.002179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GF6rE/XfKD3hzdNe7E2Z0mZ2ca/CyibrZ4LeWtg23zbatwq5BxQDxsw/zHRws7Dk7oOOU+V9tLzJNly6KrmGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:43.002833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:033cb732f46ecf2417df67b6a19bc68363b531b43f32772d9963c8e82c22b106","sha256:e63d6a18927de17744edc27709a8abe776a1e23e7ca81e0cbb5c80c58d9cac12"],"state_sha256":"980e9c65af1b8a294f0b8a42ae8d004339d98d51a5043b0d53ea3dcf7745e603"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zHIe0rJwIgz7XT1J8M6eFZe0yw3XvwN04jDbVjlTP93uT7vhriB2ndPg0tB2ScVQUTystnJPKZculLKdsyPqDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:20:38.762273Z","bundle_sha256":"ec34a36d639ace14bfe8aa7e4ea8d9f65811fe9fa94ae96f0073d2935d16c1db"}}