{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:THKPMNZ7652RDZIBH6VRWOXY5R","short_pith_number":"pith:THKPMNZ7","canonical_record":{"source":{"id":"1212.1678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-07T18:53:34Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"11f888dc32b02010dcbc35fe19c082e299521ad3cdcda553e092abdab82d10fe","abstract_canon_sha256":"426c18884450e0ca492c0ba6f42fa770ba199df5d42f00500ce8700f170a2071"},"schema_version":"1.0"},"canonical_sha256":"99d4f6373ff77511e5013fab1b3af8ec44d5145fdb4ca46c87af85cc04b4c76a","source":{"kind":"arxiv","id":"1212.1678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1678","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1678v1","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1678","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"THKPMNZ7652R","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"THKPMNZ7652RDZIB","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"THKPMNZ7","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:THKPMNZ7652RDZIBH6VRWOXY5R","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-07T18:53:34Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"11f888dc32b02010dcbc35fe19c082e299521ad3cdcda553e092abdab82d10fe","abstract_canon_sha256":"426c18884450e0ca492c0ba6f42fa770ba199df5d42f00500ce8700f170a2071"},"schema_version":"1.0"},"canonical_sha256":"99d4f6373ff77511e5013fab1b3af8ec44d5145fdb4ca46c87af85cc04b4c76a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:56.634818Z","signature_b64":"1Kqj7Y6yNipdXJvD+ej6hdVo3h+Wm20ejgsG0Yc4/8OipFxGiYjBsB19wNT7N/vUmYf1hm5PiSAUBZ0BeEgKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99d4f6373ff77511e5013fab1b3af8ec44d5145fdb4ca46c87af85cc04b4c76a","last_reissued_at":"2026-05-18T03:38:56.634001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:56.634001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1678","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+O/Ok8/mYhx5m7ZSoovwRMBRGPqLt63c1jEMckvAIPRpz97GO7WtFSrkmrA44br/5ad/MMfsxGa1J4fYCz0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:40:52.252864Z"},"content_sha256":"5db361353c8237ae7409b022c29802315948c882a7e54bc35e5d38b0be88da33","schema_version":"1.0","event_id":"sha256:5db361353c8237ae7409b022c29802315948c882a7e54bc35e5d38b0be88da33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:THKPMNZ7652RDZIBH6VRWOXY5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subexponential group cohomology and the K-theory of Lafforgue's algebra A_{max}(pi)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"C. Ogle, R. Ji","submitted_at":"2012-12-07T18:53:34Z","abstract_excerpt":"We show that for any finitely generated group G, group cohomology classes represented by cocycles of subexponential growth are extendable over the topological K-groups of the Lafforgue algebra associated to G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1678","kind":"arxiv","version":1},"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":"2026-05-18T03:38:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uo+AOnHEFgPs3kObWEx06JpRxIyIiWXNQnOnQyX/zMl8s1IgHNBcNX7eE97pY4ReoHnJhkv8bnm0bCUqjvpVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:40:52.253304Z"},"content_sha256":"7673c6bdf7660dd657c0e472ef6d7e83b79525a0840cfee77528d0d3ab792065","schema_version":"1.0","event_id":"sha256:7673c6bdf7660dd657c0e472ef6d7e83b79525a0840cfee77528d0d3ab792065"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THKPMNZ7652RDZIBH6VRWOXY5R/bundle.json","state_url":"https://pith.science/pith/THKPMNZ7652RDZIBH6VRWOXY5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THKPMNZ7652RDZIBH6VRWOXY5R/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":"2026-06-05T22:40:52Z","links":{"resolver":"https://pith.science/pith/THKPMNZ7652RDZIBH6VRWOXY5R","bundle":"https://pith.science/pith/THKPMNZ7652RDZIBH6VRWOXY5R/bundle.json","state":"https://pith.science/pith/THKPMNZ7652RDZIBH6VRWOXY5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THKPMNZ7652RDZIBH6VRWOXY5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:THKPMNZ7652RDZIBH6VRWOXY5R","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":"426c18884450e0ca492c0ba6f42fa770ba199df5d42f00500ce8700f170a2071","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-07T18:53:34Z","title_canon_sha256":"11f888dc32b02010dcbc35fe19c082e299521ad3cdcda553e092abdab82d10fe"},"schema_version":"1.0","source":{"id":"1212.1678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1678","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1678v1","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1678","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"THKPMNZ7652R","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"THKPMNZ7652RDZIB","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"THKPMNZ7","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:7673c6bdf7660dd657c0e472ef6d7e83b79525a0840cfee77528d0d3ab792065","target":"graph","created_at":"2026-05-18T03:38:56Z","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 show that for any finitely generated group G, group cohomology classes represented by cocycles of subexponential growth are extendable over the topological K-groups of the Lafforgue algebra associated to G.","authors_text":"C. Ogle, R. Ji","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-07T18:53:34Z","title":"Subexponential group cohomology and the K-theory of Lafforgue's algebra A_{max}(pi)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1678","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":"sha256:5db361353c8237ae7409b022c29802315948c882a7e54bc35e5d38b0be88da33","target":"record","created_at":"2026-05-18T03:38:56Z","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":"426c18884450e0ca492c0ba6f42fa770ba199df5d42f00500ce8700f170a2071","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-07T18:53:34Z","title_canon_sha256":"11f888dc32b02010dcbc35fe19c082e299521ad3cdcda553e092abdab82d10fe"},"schema_version":"1.0","source":{"id":"1212.1678","kind":"arxiv","version":1}},"canonical_sha256":"99d4f6373ff77511e5013fab1b3af8ec44d5145fdb4ca46c87af85cc04b4c76a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99d4f6373ff77511e5013fab1b3af8ec44d5145fdb4ca46c87af85cc04b4c76a","first_computed_at":"2026-05-18T03:38:56.634001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:56.634001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Kqj7Y6yNipdXJvD+ej6hdVo3h+Wm20ejgsG0Yc4/8OipFxGiYjBsB19wNT7N/vUmYf1hm5PiSAUBZ0BeEgKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:56.634818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5db361353c8237ae7409b022c29802315948c882a7e54bc35e5d38b0be88da33","sha256:7673c6bdf7660dd657c0e472ef6d7e83b79525a0840cfee77528d0d3ab792065"],"state_sha256":"37317c09fceee8021c3a6dac4ab8e04a77a92f1e5bec95cf9e75bfc82ee4aaff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MbeeOCWAcvtLAcuw4V23h/ZalrvGAIe2mkaTI4BFbRndTSpkIPvrspdsNhTGDpJlwTdTDHM0j9noaQ6xhue3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:40:52.256645Z","bundle_sha256":"a377b420475547b2c7278901e6911a10a9bdbf0a702dc09e393ddc444c1f8053"}}