{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:OIPGUHOFYWZZCOG5KKHD6IA5UV","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":"afb5af6c4ccb398f12f9791dd2bf6faeddd798f83deaba0c83b9b9556943bab4","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.KT","submitted_at":"2006-06-19T19:16:13Z","title_canon_sha256":"5266a0424a816e36032f5129120a48607059588c2922ce0e7f614bcbf47a4db8"},"schema_version":"1.0","source":{"id":"math/0606473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606473","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606473v1","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606473","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"OIPGUHOFYWZZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"OIPGUHOFYWZZCOG5","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"OIPGUHOF","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:07edf1baab39626288c51e215a79f948f546513ec6b690bd8b6bb7ab838e505c","target":"graph","created_at":"2026-05-18T04:08:53Z","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":"For $\\Gamma$ a relatively hyperbolic group, we construct a model for the universal space among $\\Gamma$-spaces with isotropy on the family VC of virtually cyclic subgroups of $\\Gamma$. We provide a recipe for identifying the maximal infinite virtually cyclic subgroups of Coxeter groups which are lattices in $O^+(n,1)= \\iso(\\mathbb H^n)$. We use the information we obtain to explicitly compute the lower algebraic K-theory of the Coxeter group $\\gt$ (a non-uniform lattice in $O^+(3,1)$). Part of this computation involves calculating certain Waldhausen Nil-groups for $\\mathbb Z[D_2]$, $\\mathbb Z[D","authors_text":"I. J. Ortiz, J.-F. Lafont","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.KT","submitted_at":"2006-06-19T19:16:13Z","title":"Relative hyperbolicity, classifying spaces, and lower algebraic K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606473","kind":"arxiv","version":1},"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":"sha256:865bf37ccc4f97bf288a603ab5792833000abbf3c2743ad8ec4e719959409f35","target":"record","created_at":"2026-05-18T04:08:53Z","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":"afb5af6c4ccb398f12f9791dd2bf6faeddd798f83deaba0c83b9b9556943bab4","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.KT","submitted_at":"2006-06-19T19:16:13Z","title_canon_sha256":"5266a0424a816e36032f5129120a48607059588c2922ce0e7f614bcbf47a4db8"},"schema_version":"1.0","source":{"id":"math/0606473","kind":"arxiv","version":1}},"canonical_sha256":"721e6a1dc5c5b39138dd528e3f201da572bf9350af480fd7096aa6643fd2b2fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"721e6a1dc5c5b39138dd528e3f201da572bf9350af480fd7096aa6643fd2b2fb","first_computed_at":"2026-05-18T04:08:53.420696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.420696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2fdE+O+CDcPsLklfXRucD5ES6Q/xt2x/bqHOOpadkzbeZWIRLvn0RFrbWzuHHRG9XRMd8cWlchCvQqRjZ0x8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.421279Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:865bf37ccc4f97bf288a603ab5792833000abbf3c2743ad8ec4e719959409f35","sha256:07edf1baab39626288c51e215a79f948f546513ec6b690bd8b6bb7ab838e505c"],"state_sha256":"af54bca104195c4693f40a095f7989834db6ad40e7d2a007bb37eb52a90c9f29"}