{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OUVRN72Z55F4LL6LZN6HTAAZPA","short_pith_number":"pith:OUVRN72Z","canonical_record":{"source":{"id":"1304.4263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-15T20:51:23Z","cross_cats_sorted":[],"title_canon_sha256":"4d423695e5f0968979d7e848c56c192759c8cdb83a0ad3018020156a036f011d","abstract_canon_sha256":"e5c70b2e9a5b2175c5b7219ab7c1672c1f0377feb1fc3fbf6df1e9aaabbbb431"},"schema_version":"1.0"},"canonical_sha256":"752b16ff59ef4bc5afcbcb7c798019781c94c1618357a1a9e9412f29f009fdd4","source":{"kind":"arxiv","id":"1304.4263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4263","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4263v2","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4263","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"OUVRN72Z55F4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OUVRN72Z55F4LL6L","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OUVRN72Z","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OUVRN72Z55F4LL6LZN6HTAAZPA","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-15T20:51:23Z","cross_cats_sorted":[],"title_canon_sha256":"4d423695e5f0968979d7e848c56c192759c8cdb83a0ad3018020156a036f011d","abstract_canon_sha256":"e5c70b2e9a5b2175c5b7219ab7c1672c1f0377feb1fc3fbf6df1e9aaabbbb431"},"schema_version":"1.0"},"canonical_sha256":"752b16ff59ef4bc5afcbcb7c798019781c94c1618357a1a9e9412f29f009fdd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.140658Z","signature_b64":"uJayHGIpWD7UhUt9sIVnPzrk1/Qbb8mj9Dhx1MszF50dr9A08PUzuIm8y60ttQi8sJ09EEhOP7udSjG07rDjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"752b16ff59ef4bc5afcbcb7c798019781c94c1618357a1a9e9412f29f009fdd4","last_reissued_at":"2026-05-18T01:36:21.140149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.140149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4263","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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ithrRNZlZAQxV/haCslay6VRfU0M3osnQ5ZrGuE85TCaj+u2ntyNpfnvYrYds5K7KvUu232wuBrMiy7hsrwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:28:58.740136Z"},"content_sha256":"bad95f4b0c0e72e2cf698482425365a3ebaac81befb5bfeca48faf2118f605b0","schema_version":"1.0","event_id":"sha256:bad95f4b0c0e72e2cf698482425365a3ebaac81befb5bfeca48faf2118f605b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OUVRN72Z55F4LL6LZN6HTAAZPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the K-theory of groups with Finite Decomposition Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Daniel Kasprowski","submitted_at":"2013-04-15T20:51:23Z","abstract_excerpt":"It is proved that the assembly map in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups $\\Gamma$ with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tesser and Yu) that admit a finite dimensional model for $\\underbar E\\Gamma$ and have an upper bound on the order of their finite subgroups. In particular this applies to finitely generated linear groups over fields with characteristic zero with a finite dimensional model for $\\underbar E\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4263","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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7wiNFIVVETvad0/09zXcOuCcF3pmBAmSnR3s/01L65rEfwRBKqOkqROtz0IVHHyisqVFU4+l8quH7aTmcSGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:28:58.740518Z"},"content_sha256":"8d3a1a57193db6fbfe676242b6e46ba336fc059033571369588c654f29f78d51","schema_version":"1.0","event_id":"sha256:8d3a1a57193db6fbfe676242b6e46ba336fc059033571369588c654f29f78d51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUVRN72Z55F4LL6LZN6HTAAZPA/bundle.json","state_url":"https://pith.science/pith/OUVRN72Z55F4LL6LZN6HTAAZPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUVRN72Z55F4LL6LZN6HTAAZPA/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":"2026-06-04T03:28:58Z","links":{"resolver":"https://pith.science/pith/OUVRN72Z55F4LL6LZN6HTAAZPA","bundle":"https://pith.science/pith/OUVRN72Z55F4LL6LZN6HTAAZPA/bundle.json","state":"https://pith.science/pith/OUVRN72Z55F4LL6LZN6HTAAZPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUVRN72Z55F4LL6LZN6HTAAZPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OUVRN72Z55F4LL6LZN6HTAAZPA","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":"e5c70b2e9a5b2175c5b7219ab7c1672c1f0377feb1fc3fbf6df1e9aaabbbb431","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-15T20:51:23Z","title_canon_sha256":"4d423695e5f0968979d7e848c56c192759c8cdb83a0ad3018020156a036f011d"},"schema_version":"1.0","source":{"id":"1304.4263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4263","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4263v2","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4263","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"OUVRN72Z55F4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OUVRN72Z55F4LL6L","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OUVRN72Z","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:8d3a1a57193db6fbfe676242b6e46ba336fc059033571369588c654f29f78d51","target":"graph","created_at":"2026-05-18T01:36:21Z","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":"It is proved that the assembly map in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups $\\Gamma$ with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tesser and Yu) that admit a finite dimensional model for $\\underbar E\\Gamma$ and have an upper bound on the order of their finite subgroups. In particular this applies to finitely generated linear groups over fields with characteristic zero with a finite dimensional model for $\\underbar E\\Gamma$.","authors_text":"Daniel Kasprowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-15T20:51:23Z","title":"On the K-theory of groups with Finite Decomposition Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4263","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:bad95f4b0c0e72e2cf698482425365a3ebaac81befb5bfeca48faf2118f605b0","target":"record","created_at":"2026-05-18T01:36:21Z","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":"e5c70b2e9a5b2175c5b7219ab7c1672c1f0377feb1fc3fbf6df1e9aaabbbb431","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-15T20:51:23Z","title_canon_sha256":"4d423695e5f0968979d7e848c56c192759c8cdb83a0ad3018020156a036f011d"},"schema_version":"1.0","source":{"id":"1304.4263","kind":"arxiv","version":2}},"canonical_sha256":"752b16ff59ef4bc5afcbcb7c798019781c94c1618357a1a9e9412f29f009fdd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"752b16ff59ef4bc5afcbcb7c798019781c94c1618357a1a9e9412f29f009fdd4","first_computed_at":"2026-05-18T01:36:21.140149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.140149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uJayHGIpWD7UhUt9sIVnPzrk1/Qbb8mj9Dhx1MszF50dr9A08PUzuIm8y60ttQi8sJ09EEhOP7udSjG07rDjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.140658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bad95f4b0c0e72e2cf698482425365a3ebaac81befb5bfeca48faf2118f605b0","sha256:8d3a1a57193db6fbfe676242b6e46ba336fc059033571369588c654f29f78d51"],"state_sha256":"31b36cd1696f82f4ab1d0478a42557518c3821803de6935567f012d665dab2cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKWDTH4HlrvyFiY4mzsboOQ/Oghq6W3Ju2M+ahwfrBWeff4nTyUdwruPFR131inf+yjacPlIjn64S0gTdEAOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:28:58.742624Z","bundle_sha256":"55f4eb9ce8013172fa113141ab789247a6bb4556fbb012136064d1c88a0f4875"}}