{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HH75BNNFRP6SLJJWFMDPPCGCF4","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":"fdcf41b7ecdafb4c5a014147abcdd4e35b2ded9940817dc873ed88abd17d8092","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-10T14:38:31Z","title_canon_sha256":"51750d1afa19eeaa510ff755345113919986ede5753474afaf8b30869682145e"},"schema_version":"1.0","source":{"id":"1807.03677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03677","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03677v2","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03677","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"HH75BNNFRP6S","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HH75BNNFRP6SLJJW","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HH75BNNF","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:bfbf203b75fe7c23f9a937f3434ddc39f4832fc7bb2592d7a3d021a64a270da6","target":"graph","created_at":"2026-05-17T23:43:56Z","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":"We address the problem of which functions can arise as Dehn functions of K\\\"ahler groups. We explain why there are examples of K\\\"ahler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a K\\\"ahler group which has Dehn function bounded below by a cubic function and above by $n^6$. As a consequence we obtain that for a compact K\\\"ahler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.","authors_text":"Claudio Llosa Isenrich, Romain Tessera","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-10T14:38:31Z","title":"On the Dehn functions of K\\\"ahler groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03677","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":"sha256:8aa00bdd42ce4238e02a2687f7a3664a7146a05b357c4d214553418286d47a59","target":"record","created_at":"2026-05-17T23:43:56Z","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":"fdcf41b7ecdafb4c5a014147abcdd4e35b2ded9940817dc873ed88abd17d8092","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-10T14:38:31Z","title_canon_sha256":"51750d1afa19eeaa510ff755345113919986ede5753474afaf8b30869682145e"},"schema_version":"1.0","source":{"id":"1807.03677","kind":"arxiv","version":2}},"canonical_sha256":"39ffd0b5a58bfd25a5362b06f788c22f1a9188c195e1f57833a211f679ce0b84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39ffd0b5a58bfd25a5362b06f788c22f1a9188c195e1f57833a211f679ce0b84","first_computed_at":"2026-05-17T23:43:56.632432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:56.632432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mHp6n6H16eK0Y4wCcLEuHnaeBVLdDJ3ziyoEbGKKHdJ/GZTu1P8347U+5dDYyGPLNmKCF2gnF+ZyO3EfrJoKCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:56.633063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8aa00bdd42ce4238e02a2687f7a3664a7146a05b357c4d214553418286d47a59","sha256:bfbf203b75fe7c23f9a937f3434ddc39f4832fc7bb2592d7a3d021a64a270da6"],"state_sha256":"dde1866d89f4dd0782545897df073aee1abf71e90e9abbd0541fdfb1243af8f4"}