{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YOEZYY6DCBJ22KOCYC2P6WRS23","short_pith_number":"pith:YOEZYY6D","canonical_record":{"source":{"id":"1610.06808","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-10-21T14:43:19Z","cross_cats_sorted":["math.NT","math.OA"],"title_canon_sha256":"d58105b6bfab575a50a9398c68e86d74421e7b9247a3e97ed6b1ca0d81388dac","abstract_canon_sha256":"6dbccfa13104bb47a170054398f939ef295c71b08083b1b0b39c754b612a0948"},"schema_version":"1.0"},"canonical_sha256":"c3899c63c31053ad29c2c0b4ff5a32d6f290b041eee317a18e8122e3d1caac98","source":{"kind":"arxiv","id":"1610.06808","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06808","created_at":"2026-05-18T00:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06808v2","created_at":"2026-05-18T00:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06808","created_at":"2026-05-18T00:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"YOEZYY6DCBJ2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YOEZYY6DCBJ22KOC","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YOEZYY6D","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YOEZYY6DCBJ22KOCYC2P6WRS23","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06808","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-10-21T14:43:19Z","cross_cats_sorted":["math.NT","math.OA"],"title_canon_sha256":"d58105b6bfab575a50a9398c68e86d74421e7b9247a3e97ed6b1ca0d81388dac","abstract_canon_sha256":"6dbccfa13104bb47a170054398f939ef295c71b08083b1b0b39c754b612a0948"},"schema_version":"1.0"},"canonical_sha256":"c3899c63c31053ad29c2c0b4ff5a32d6f290b041eee317a18e8122e3d1caac98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:05.122634Z","signature_b64":"7xbLkBpJYZYW64JOR4dZ5ayfD2saj+XrMq/muZdzUmJ2AoJ9WKIl7jFnKz9mxzmzsRCwXnKgipVk0vQPTbqmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3899c63c31053ad29c2c0b4ff5a32d6f290b041eee317a18e8122e3d1caac98","last_reissued_at":"2026-05-18T00:35:05.121912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:05.121912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06808","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":"2026-05-18T00:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWFMryUAkmmCiaU6/YrK6F3fhcsUY7o8fpCMxUvWWjBaycMadApeM0Eey/FMVuwfINbfKEV+uOZkvjQZ69ZvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:47:58.212636Z"},"content_sha256":"ca9eb46f4960ebe706f31b7352ca9cdf6ea0701de3eacbcad257f26324c9918e","schema_version":"1.0","event_id":"sha256:ca9eb46f4960ebe706f31b7352ca9cdf6ea0701de3eacbcad257f26324c9918e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YOEZYY6DCBJ22KOCYC2P6WRS23","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hecke operators in KK-theory and the K-homology of Bianchi groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.OA"],"primary_cat":"math.KT","authors_text":"Bram Mesland, Mehmet Haluk Sengun","submitted_at":"2016-10-21T14:43:19Z","abstract_excerpt":"Let $\\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\\Gamma$ act on the geodesic boundary $\\partial X$ of $X$. Via general constructions in KK-theory, we endow the K-groups of the arithmetic manifold $X/\\Gamma$, of the reduced group C*-algebra of $\\Gamma$ and of the boundary crossed product algebra associated to the action of $\\Gamma$ on $\\partial X$, with Hecke operators. The K-theory and K-homology groups of these C*-algebras are related by a Gysin six-term exact sequence. In the case when $\\Gamma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06808","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":"2026-05-18T00:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gehWpYODqEz3McrHnyWSMNJ6upX5mw5nXghN+EeC4XU/P/m4p4pjHrGANJ3SirR11qYFk+CUbRRVPyDleOuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:47:58.213004Z"},"content_sha256":"a28e9149b48d1501742425cb5951ad20751869a73207ab069762eaf043a39cf2","schema_version":"1.0","event_id":"sha256:a28e9149b48d1501742425cb5951ad20751869a73207ab069762eaf043a39cf2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOEZYY6DCBJ22KOCYC2P6WRS23/bundle.json","state_url":"https://pith.science/pith/YOEZYY6DCBJ22KOCYC2P6WRS23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOEZYY6DCBJ22KOCYC2P6WRS23/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":"2026-05-26T08:47:58Z","links":{"resolver":"https://pith.science/pith/YOEZYY6DCBJ22KOCYC2P6WRS23","bundle":"https://pith.science/pith/YOEZYY6DCBJ22KOCYC2P6WRS23/bundle.json","state":"https://pith.science/pith/YOEZYY6DCBJ22KOCYC2P6WRS23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOEZYY6DCBJ22KOCYC2P6WRS23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YOEZYY6DCBJ22KOCYC2P6WRS23","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":"6dbccfa13104bb47a170054398f939ef295c71b08083b1b0b39c754b612a0948","cross_cats_sorted":["math.NT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-10-21T14:43:19Z","title_canon_sha256":"d58105b6bfab575a50a9398c68e86d74421e7b9247a3e97ed6b1ca0d81388dac"},"schema_version":"1.0","source":{"id":"1610.06808","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06808","created_at":"2026-05-18T00:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06808v2","created_at":"2026-05-18T00:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06808","created_at":"2026-05-18T00:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"YOEZYY6DCBJ2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YOEZYY6DCBJ22KOC","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YOEZYY6D","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:a28e9149b48d1501742425cb5951ad20751869a73207ab069762eaf043a39cf2","target":"graph","created_at":"2026-05-18T00:35:05Z","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":"Let $\\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\\Gamma$ act on the geodesic boundary $\\partial X$ of $X$. Via general constructions in KK-theory, we endow the K-groups of the arithmetic manifold $X/\\Gamma$, of the reduced group C*-algebra of $\\Gamma$ and of the boundary crossed product algebra associated to the action of $\\Gamma$ on $\\partial X$, with Hecke operators. The K-theory and K-homology groups of these C*-algebras are related by a Gysin six-term exact sequence. In the case when $\\Gamma","authors_text":"Bram Mesland, Mehmet Haluk Sengun","cross_cats":["math.NT","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-10-21T14:43:19Z","title":"Hecke operators in KK-theory and the K-homology of Bianchi groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06808","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:ca9eb46f4960ebe706f31b7352ca9cdf6ea0701de3eacbcad257f26324c9918e","target":"record","created_at":"2026-05-18T00:35:05Z","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":"6dbccfa13104bb47a170054398f939ef295c71b08083b1b0b39c754b612a0948","cross_cats_sorted":["math.NT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-10-21T14:43:19Z","title_canon_sha256":"d58105b6bfab575a50a9398c68e86d74421e7b9247a3e97ed6b1ca0d81388dac"},"schema_version":"1.0","source":{"id":"1610.06808","kind":"arxiv","version":2}},"canonical_sha256":"c3899c63c31053ad29c2c0b4ff5a32d6f290b041eee317a18e8122e3d1caac98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3899c63c31053ad29c2c0b4ff5a32d6f290b041eee317a18e8122e3d1caac98","first_computed_at":"2026-05-18T00:35:05.121912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:05.121912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7xbLkBpJYZYW64JOR4dZ5ayfD2saj+XrMq/muZdzUmJ2AoJ9WKIl7jFnKz9mxzmzsRCwXnKgipVk0vQPTbqmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:05.122634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06808","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca9eb46f4960ebe706f31b7352ca9cdf6ea0701de3eacbcad257f26324c9918e","sha256:a28e9149b48d1501742425cb5951ad20751869a73207ab069762eaf043a39cf2"],"state_sha256":"ed1d8083923d6166ec79432f1286cfc92692bcedd0a460050c18d283fb9f5693"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p8e8SxESuxR/vi01UXBNyki1sPPCx+GOTegjBoVQbIarL+RT3eME00TGv8gylQfNuTWA2Mht9CBoFlNA+8JwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:47:58.215954Z","bundle_sha256":"01b480e44294a0720e1edb5540d3109e1e144a6960d70676078954f2936ad448"}}