{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:M3UEWEDQ4M6L7PRP5YFQUEZC2D","short_pith_number":"pith:M3UEWEDQ","canonical_record":{"source":{"id":"1308.0022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-07-31T20:05:27Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9ba9171b3db1dc57cee3608486bb2ac17a89db68335124d11ef6001fe85d243c","abstract_canon_sha256":"6a3947ac36aca0904c08bdc0546e03468fa5eb3440448e1dc594f19e3b53b270"},"schema_version":"1.0"},"canonical_sha256":"66e84b1070e33cbfbe2fee0b0a1322d0eee6d699e35673023b6220bd2a528233","source":{"kind":"arxiv","id":"1308.0022","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0022","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0022v2","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0022","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"pith_short_12","alias_value":"M3UEWEDQ4M6L","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M3UEWEDQ4M6L7PRP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M3UEWEDQ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:M3UEWEDQ4M6L7PRP5YFQUEZC2D","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-07-31T20:05:27Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9ba9171b3db1dc57cee3608486bb2ac17a89db68335124d11ef6001fe85d243c","abstract_canon_sha256":"6a3947ac36aca0904c08bdc0546e03468fa5eb3440448e1dc594f19e3b53b270"},"schema_version":"1.0"},"canonical_sha256":"66e84b1070e33cbfbe2fee0b0a1322d0eee6d699e35673023b6220bd2a528233","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:20.375753Z","signature_b64":"5xbHAMHNvalb5lc/DdqhpsMX7NtNLquD9vs2c3JWcb8ih4qtt3OUqxVrZoc5gvMdtiiDmPu7GV9/4aELY3MxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66e84b1070e33cbfbe2fee0b0a1322d0eee6d699e35673023b6220bd2a528233","last_reissued_at":"2026-05-18T03:15:20.374944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:20.374944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0022","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a0FUhDdsUvWerqp26d8/nYbJpHNQ9rlrmjp0p8bUdLNUWt819OaNhsJxHVAZaXRSurBvb9beksptJEZMxqorDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:07:13.795251Z"},"content_sha256":"150f968411235e1b0325eb88d8018d8d3b0446f476d0faf41504517690e387ca","schema_version":"1.0","event_id":"sha256:150f968411235e1b0325eb88d8018d8d3b0446f476d0faf41504517690e387ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:M3UEWEDQ4M6L7PRP5YFQUEZC2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A classification of homogeneous K\\\"{a}hler manifolds with discrete isotropy and top nonvanishing homology in codimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"S. Ruhallah Ahmadi","submitted_at":"2013-07-31T20:05:27Z","abstract_excerpt":"Suppose $G$ is a connected complex Lie group and $\\Gamma$ is a discrete subgroup such that $X := G/\\Gamma$ is K\\\"ahler and the codimension of the top non--vanishing homology group of $X$ with coefficients in $\\mathbb Z_2$ is less than or equal to two. We show that $G$ is solvable and a finite covering of $X$ is biholomorphic to a product $C\\times A$, where $C$ is a Cousin group and $A$ is $\\{e \\}$, $\\mathbb C$, $\\mathbb C^*$, or $\\mathbb C^*\\times\\mathbb C^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0022","kind":"arxiv","version":2},"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":"2026-05-18T03:15:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WME8pgKV2e35Dr3o4iVp219YU0rjKQbzWekfXLm3YCQFRFQi8uSNATyfgx7x3DWpynOjD2W64kSxs3ol78GeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:07:13.795614Z"},"content_sha256":"897f7f7cc1caa99561f531644fd1241d0e68d49456088ec29c9d25fd29724358","schema_version":"1.0","event_id":"sha256:897f7f7cc1caa99561f531644fd1241d0e68d49456088ec29c9d25fd29724358"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D/bundle.json","state_url":"https://pith.science/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D/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":"2026-06-11T02:07:13Z","links":{"resolver":"https://pith.science/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D","bundle":"https://pith.science/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D/bundle.json","state":"https://pith.science/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3UEWEDQ4M6L7PRP5YFQUEZC2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M3UEWEDQ4M6L7PRP5YFQUEZC2D","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":"6a3947ac36aca0904c08bdc0546e03468fa5eb3440448e1dc594f19e3b53b270","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-07-31T20:05:27Z","title_canon_sha256":"9ba9171b3db1dc57cee3608486bb2ac17a89db68335124d11ef6001fe85d243c"},"schema_version":"1.0","source":{"id":"1308.0022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0022","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0022v2","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0022","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"pith_short_12","alias_value":"M3UEWEDQ4M6L","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M3UEWEDQ4M6L7PRP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M3UEWEDQ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:897f7f7cc1caa99561f531644fd1241d0e68d49456088ec29c9d25fd29724358","target":"graph","created_at":"2026-05-18T03:15:20Z","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":"Suppose $G$ is a connected complex Lie group and $\\Gamma$ is a discrete subgroup such that $X := G/\\Gamma$ is K\\\"ahler and the codimension of the top non--vanishing homology group of $X$ with coefficients in $\\mathbb Z_2$ is less than or equal to two. We show that $G$ is solvable and a finite covering of $X$ is biholomorphic to a product $C\\times A$, where $C$ is a Cousin group and $A$ is $\\{e \\}$, $\\mathbb C$, $\\mathbb C^*$, or $\\mathbb C^*\\times\\mathbb C^*$.","authors_text":"S. Ruhallah Ahmadi","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-07-31T20:05:27Z","title":"A classification of homogeneous K\\\"{a}hler manifolds with discrete isotropy and top nonvanishing homology in codimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0022","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":"sha256:150f968411235e1b0325eb88d8018d8d3b0446f476d0faf41504517690e387ca","target":"record","created_at":"2026-05-18T03:15:20Z","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":"6a3947ac36aca0904c08bdc0546e03468fa5eb3440448e1dc594f19e3b53b270","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-07-31T20:05:27Z","title_canon_sha256":"9ba9171b3db1dc57cee3608486bb2ac17a89db68335124d11ef6001fe85d243c"},"schema_version":"1.0","source":{"id":"1308.0022","kind":"arxiv","version":2}},"canonical_sha256":"66e84b1070e33cbfbe2fee0b0a1322d0eee6d699e35673023b6220bd2a528233","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66e84b1070e33cbfbe2fee0b0a1322d0eee6d699e35673023b6220bd2a528233","first_computed_at":"2026-05-18T03:15:20.374944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:20.374944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xbHAMHNvalb5lc/DdqhpsMX7NtNLquD9vs2c3JWcb8ih4qtt3OUqxVrZoc5gvMdtiiDmPu7GV9/4aELY3MxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:20.375753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:150f968411235e1b0325eb88d8018d8d3b0446f476d0faf41504517690e387ca","sha256:897f7f7cc1caa99561f531644fd1241d0e68d49456088ec29c9d25fd29724358"],"state_sha256":"024d546e0896fbb8e33d7bfd065e0e7f3b106c414bae6c7598a78f87375f01ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URTA8PIck3xvYgKtPqSkPqgHU+B+YoqLok6OIUSo27mJ4M2o/wyvxFyF0BBQ9KM72P43Zz6dWgE82oWyBfGECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:07:13.797979Z","bundle_sha256":"29eb099626ba88a6db13eb50dca4d350b06bd68e00a18601ea01e71fb2326644"}}