{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:U6IOAQ3VDUPRSY6JQNABHV7Y3E","short_pith_number":"pith:U6IOAQ3V","canonical_record":{"source":{"id":"1204.6278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-27T17:37:21Z","cross_cats_sorted":["math.AG","math.CV","math.GT"],"title_canon_sha256":"74643067c1ee722ca1f784513402131850febd7a183d9ed9c6b43f749967df7b","abstract_canon_sha256":"1bd03ed96e7765d2492b2b99e35df5351c54900ce4e71d386015b3908969aec4"},"schema_version":"1.0"},"canonical_sha256":"a790e043751d1f1963c9834013d7f8d931593cebfc3ef488375fb8dc089f8f61","source":{"kind":"arxiv","id":"1204.6278","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6278","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6278v3","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6278","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"U6IOAQ3VDUPR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U6IOAQ3VDUPRSY6J","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U6IOAQ3V","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:U6IOAQ3VDUPRSY6JQNABHV7Y3E","target":"record","payload":{"canonical_record":{"source":{"id":"1204.6278","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-27T17:37:21Z","cross_cats_sorted":["math.AG","math.CV","math.GT"],"title_canon_sha256":"74643067c1ee722ca1f784513402131850febd7a183d9ed9c6b43f749967df7b","abstract_canon_sha256":"1bd03ed96e7765d2492b2b99e35df5351c54900ce4e71d386015b3908969aec4"},"schema_version":"1.0"},"canonical_sha256":"a790e043751d1f1963c9834013d7f8d931593cebfc3ef488375fb8dc089f8f61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:05.212738Z","signature_b64":"EZWQUJhNEnfrM72tk6ZxYz3ACIqcP1ZFaSCrcEftuwKE8Ex1jEaqfEpHu5cUQ55AAC41uX8W7x+E2858nbOOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a790e043751d1f1963c9834013d7f8d931593cebfc3ef488375fb8dc089f8f61","last_reissued_at":"2026-05-18T03:46:05.212267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:05.212267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.6278","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gqH5edntMhX+SwkUt1CT/i5PbCD4h6LOlxwTL1A4MUK5qJsLVc40ihwyCEOJ44Gt61lxr6mKBf7whQSpZY1nDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:00:44.777778Z"},"content_sha256":"33ff10c0561706462a4b1a3dd82719800d7b9246df8e36d13cb669a1f9e8f4fd","schema_version":"1.0","event_id":"sha256:33ff10c0561706462a4b1a3dd82719800d7b9246df8e36d13cb669a1f9e8f4fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:U6IOAQ3VDUPRSY6JQNABHV7Y3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The deficiencies of Kaehler groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.GT"],"primary_cat":"math.GR","authors_text":"D. Kotschick","submitted_at":"2012-04-27T17:37:21Z","abstract_excerpt":"Generalizing the theorem of Green--Lazarsfeld and Gromov, we classify Kaehler groups of deficiency at least two. As a consequence we see that there are no Kaehler groups of even and strictly positive deficiency. With the same arguments we prove that Kaehler groups that are non-Abelian and are limit groups in the sense of Sela are surface groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6278","kind":"arxiv","version":3},"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":"2026-05-18T03:46:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q/9AAONkV0JWlwCc/tygM6P6Tj6OErJ4Zio54YWUWQtMSV8HwUa531FTDqsq4kdknwsU0j+oET9Iv7mHVP8RCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:00:44.778113Z"},"content_sha256":"192a6f1dabc5e3995935fb4ade4e061ca06206f559571f345030319447a83823","schema_version":"1.0","event_id":"sha256:192a6f1dabc5e3995935fb4ade4e061ca06206f559571f345030319447a83823"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E/bundle.json","state_url":"https://pith.science/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E/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":"2026-06-27T03:00:44Z","links":{"resolver":"https://pith.science/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E","bundle":"https://pith.science/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E/bundle.json","state":"https://pith.science/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6IOAQ3VDUPRSY6JQNABHV7Y3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U6IOAQ3VDUPRSY6JQNABHV7Y3E","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":"1bd03ed96e7765d2492b2b99e35df5351c54900ce4e71d386015b3908969aec4","cross_cats_sorted":["math.AG","math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-27T17:37:21Z","title_canon_sha256":"74643067c1ee722ca1f784513402131850febd7a183d9ed9c6b43f749967df7b"},"schema_version":"1.0","source":{"id":"1204.6278","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6278","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6278v3","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6278","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"U6IOAQ3VDUPR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U6IOAQ3VDUPRSY6J","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U6IOAQ3V","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:192a6f1dabc5e3995935fb4ade4e061ca06206f559571f345030319447a83823","target":"graph","created_at":"2026-05-18T03:46:05Z","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":"Generalizing the theorem of Green--Lazarsfeld and Gromov, we classify Kaehler groups of deficiency at least two. As a consequence we see that there are no Kaehler groups of even and strictly positive deficiency. With the same arguments we prove that Kaehler groups that are non-Abelian and are limit groups in the sense of Sela are surface groups.","authors_text":"D. Kotschick","cross_cats":["math.AG","math.CV","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-27T17:37:21Z","title":"The deficiencies of Kaehler groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6278","kind":"arxiv","version":3},"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":"sha256:33ff10c0561706462a4b1a3dd82719800d7b9246df8e36d13cb669a1f9e8f4fd","target":"record","created_at":"2026-05-18T03:46:05Z","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":"1bd03ed96e7765d2492b2b99e35df5351c54900ce4e71d386015b3908969aec4","cross_cats_sorted":["math.AG","math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-27T17:37:21Z","title_canon_sha256":"74643067c1ee722ca1f784513402131850febd7a183d9ed9c6b43f749967df7b"},"schema_version":"1.0","source":{"id":"1204.6278","kind":"arxiv","version":3}},"canonical_sha256":"a790e043751d1f1963c9834013d7f8d931593cebfc3ef488375fb8dc089f8f61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a790e043751d1f1963c9834013d7f8d931593cebfc3ef488375fb8dc089f8f61","first_computed_at":"2026-05-18T03:46:05.212267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:05.212267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZWQUJhNEnfrM72tk6ZxYz3ACIqcP1ZFaSCrcEftuwKE8Ex1jEaqfEpHu5cUQ55AAC41uX8W7x+E2858nbOOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:05.212738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6278","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33ff10c0561706462a4b1a3dd82719800d7b9246df8e36d13cb669a1f9e8f4fd","sha256:192a6f1dabc5e3995935fb4ade4e061ca06206f559571f345030319447a83823"],"state_sha256":"191561c02518d40dbf59b658dd538ee9dbf8253ebcbf079ec9a9801afd849c4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AAxO11U8F2Ct4TcpW2RmuqtkK5JOkhnAg/amgA4/gCvnnFCAO1FutYzP9mFtivJ/qAVqvMalstLbVxc8Ir20Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:00:44.779878Z","bundle_sha256":"91d51cb1d8a54fa3e7a05e44ceade6cd9d82361c779d192d97071a94b4eb4dad"}}