{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7CJASXLEHTQEBMRNQYCAUG5FSG","short_pith_number":"pith:7CJASXLE","schema_version":"1.0","canonical_sha256":"f892095d643ce040b22d86040a1ba59196f3c73138cd07a96307426dd12368ea","source":{"kind":"arxiv","id":"1004.3130","version":2},"attestation_state":"computed","paper":{"title":"On the second cohomology of K\\\"ahler groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.DG","authors_text":"Bruno Klingler (IMJ, IAS), Julien Maubon (IECN), Vincent Koziarz (IECN)","submitted_at":"2010-04-19T09:13:27Z","abstract_excerpt":"Carlson and Toledo conjectured that any infinite fundamental group $\\Gamma$ of a compact K\\\"ahler manifold satisfies $H^2(\\Gamma,\\R)\\not =0$. We assume that $\\Gamma$ admits an unbounded reductive rigid linear representation. This representation necessarily comes from a complex variation of Hodge structure ($\\C$-VHS) on the K\\\"ahler manifold. We prove the conjecture under some assumption on the $\\C$-VHS. We also study some related geometric/topological properties of period domains associated to such $\\C$-VHS."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1004.3130","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-19T09:13:27Z","cross_cats_sorted":["math.AG","math.GT"],"title_canon_sha256":"9f80f80b0ff5a7fb4ef639bd7ed32b3cfa11c0630de4997eafbf1c7472655d63","abstract_canon_sha256":"5bdc0520775c7ab151d70e58935b541c0a92468fd2eb93b5f234fa6daa6ec370"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:49.739677Z","signature_b64":"z9gvAJ+gQ7S7rCuyPZEIt/LiixFvpQgiTeUFNMkDISONxFsnoiGYgF/F0B/6kMFuChmJGfQ81lOiKvoUQDXvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f892095d643ce040b22d86040a1ba59196f3c73138cd07a96307426dd12368ea","last_reissued_at":"2026-05-18T04:33:49.739178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:49.739178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the second cohomology of K\\\"ahler groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.DG","authors_text":"Bruno Klingler (IMJ, IAS), Julien Maubon (IECN), Vincent Koziarz (IECN)","submitted_at":"2010-04-19T09:13:27Z","abstract_excerpt":"Carlson and Toledo conjectured that any infinite fundamental group $\\Gamma$ of a compact K\\\"ahler manifold satisfies $H^2(\\Gamma,\\R)\\not =0$. We assume that $\\Gamma$ admits an unbounded reductive rigid linear representation. This representation necessarily comes from a complex variation of Hodge structure ($\\C$-VHS) on the K\\\"ahler manifold. We prove the conjecture under some assumption on the $\\C$-VHS. We also study some related geometric/topological properties of period domains associated to such $\\C$-VHS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3130","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1004.3130","created_at":"2026-05-18T04:33:49.739260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.3130v2","created_at":"2026-05-18T04:33:49.739260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3130","created_at":"2026-05-18T04:33:49.739260+00:00"},{"alias_kind":"pith_short_12","alias_value":"7CJASXLEHTQE","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"7CJASXLEHTQEBMRN","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"7CJASXLE","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG","json":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG.json","graph_json":"https://pith.science/api/pith-number/7CJASXLEHTQEBMRNQYCAUG5FSG/graph.json","events_json":"https://pith.science/api/pith-number/7CJASXLEHTQEBMRNQYCAUG5FSG/events.json","paper":"https://pith.science/paper/7CJASXLE"},"agent_actions":{"view_html":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG","download_json":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG.json","view_paper":"https://pith.science/paper/7CJASXLE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.3130&json=true","fetch_graph":"https://pith.science/api/pith-number/7CJASXLEHTQEBMRNQYCAUG5FSG/graph.json","fetch_events":"https://pith.science/api/pith-number/7CJASXLEHTQEBMRNQYCAUG5FSG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/action/storage_attestation","attest_author":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/action/author_attestation","sign_citation":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/action/citation_signature","submit_replication":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/action/replication_record"}},"created_at":"2026-05-18T04:33:49.739260+00:00","updated_at":"2026-05-18T04:33:49.739260+00:00"}