{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7CJASXLEHTQEBMRNQYCAUG5FSG","short_pith_number":"pith:7CJASXLE","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"},"canonical_sha256":"f892095d643ce040b22d86040a1ba59196f3c73138cd07a96307426dd12368ea","source":{"kind":"arxiv","id":"1004.3130","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3130","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3130v2","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3130","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"7CJASXLEHTQE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7CJASXLEHTQEBMRN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7CJASXLE","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7CJASXLEHTQEBMRNQYCAUG5FSG","target":"record","payload":{"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"},"canonical_sha256":"f892095d643ce040b22d86040a1ba59196f3c73138cd07a96307426dd12368ea","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"},"source_kind":"arxiv","source_id":"1004.3130","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":"2026-05-18T04:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufrM5qBNCgHKmegFfA891iP/qf72EdSHcZ2cPQi681ACSS+IJ/v2J4rJ1oPDTlauk5svO5FzCYQ6ydA7txp8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:02:02.954559Z"},"content_sha256":"58458c5ad36c03e8e4a92e208bc05899beb7921811cf2303ee8b1ba79210962d","schema_version":"1.0","event_id":"sha256:58458c5ad36c03e8e4a92e208bc05899beb7921811cf2303ee8b1ba79210962d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7CJASXLEHTQEBMRNQYCAUG5FSG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lwlf6WgoHZ8kodwxJ/SVjRYyNqlWL7YzMcOlRqVxw8HV0q8S9SmEt8OBCizc4dlUArTvxfvxhLpifzirNdswBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:02:02.954952Z"},"content_sha256":"e8dff369dbcf3315c3d2ccd41ca7a06e95ab80114ffc914e30da7ea0e9a037db","schema_version":"1.0","event_id":"sha256:e8dff369dbcf3315c3d2ccd41ca7a06e95ab80114ffc914e30da7ea0e9a037db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/bundle.json","state_url":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/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":"2026-06-26T13:02:02Z","links":{"resolver":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG","bundle":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/bundle.json","state":"https://pith.science/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CJASXLEHTQEBMRNQYCAUG5FSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7CJASXLEHTQEBMRNQYCAUG5FSG","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":"5bdc0520775c7ab151d70e58935b541c0a92468fd2eb93b5f234fa6daa6ec370","cross_cats_sorted":["math.AG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-19T09:13:27Z","title_canon_sha256":"9f80f80b0ff5a7fb4ef639bd7ed32b3cfa11c0630de4997eafbf1c7472655d63"},"schema_version":"1.0","source":{"id":"1004.3130","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3130","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3130v2","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3130","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"7CJASXLEHTQE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7CJASXLEHTQEBMRN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7CJASXLE","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:e8dff369dbcf3315c3d2ccd41ca7a06e95ab80114ffc914e30da7ea0e9a037db","target":"graph","created_at":"2026-05-18T04:33:49Z","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":"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.","authors_text":"Bruno Klingler (IMJ, IAS), Julien Maubon (IECN), Vincent Koziarz (IECN)","cross_cats":["math.AG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-19T09:13:27Z","title":"On the second cohomology of K\\\"ahler groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3130","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":"sha256:58458c5ad36c03e8e4a92e208bc05899beb7921811cf2303ee8b1ba79210962d","target":"record","created_at":"2026-05-18T04:33:49Z","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":"5bdc0520775c7ab151d70e58935b541c0a92468fd2eb93b5f234fa6daa6ec370","cross_cats_sorted":["math.AG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-19T09:13:27Z","title_canon_sha256":"9f80f80b0ff5a7fb4ef639bd7ed32b3cfa11c0630de4997eafbf1c7472655d63"},"schema_version":"1.0","source":{"id":"1004.3130","kind":"arxiv","version":2}},"canonical_sha256":"f892095d643ce040b22d86040a1ba59196f3c73138cd07a96307426dd12368ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f892095d643ce040b22d86040a1ba59196f3c73138cd07a96307426dd12368ea","first_computed_at":"2026-05-18T04:33:49.739178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:49.739178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z9gvAJ+gQ7S7rCuyPZEIt/LiixFvpQgiTeUFNMkDISONxFsnoiGYgF/F0B/6kMFuChmJGfQ81lOiKvoUQDXvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:49.739677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3130","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58458c5ad36c03e8e4a92e208bc05899beb7921811cf2303ee8b1ba79210962d","sha256:e8dff369dbcf3315c3d2ccd41ca7a06e95ab80114ffc914e30da7ea0e9a037db"],"state_sha256":"3e03e72f2727d4f58f46fdca0bdc8abae8300a99cd18c460a98de979d6e07f34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cwM4MdDG3wakaRHAslTXwpgYSGkYCpf8DPSgI8itPUe3Od6rOpxhcQEThOMnO/7WHT4gTHoTmXj/w/kZjhcYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:02:02.957497Z","bundle_sha256":"aa840246e055ceb65124f8dff58920e089dcd2235cb681c3e09d5e669fb536ce"}}