{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VTRK4RB46P45V2IDMIEWTEKMLT","short_pith_number":"pith:VTRK4RB4","canonical_record":{"source":{"id":"2404.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-04-10T09:06:10Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"0461109a023ae9ff25efaa18c23f126c2ea78946e4de80e851b38d4180919947","abstract_canon_sha256":"67241a14eb5baff9428dee96b92e80bc28f34219d79b32144a78eb682bcad365"},"schema_version":"1.0"},"canonical_sha256":"ace2ae443cf3f9dae903620969914c5cc238f1ebef83eff09c876dcf509b977b","source":{"kind":"arxiv","id":"2404.06840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06840","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06840v1","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06840","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"pith_short_12","alias_value":"VTRK4RB46P45","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"pith_short_16","alias_value":"VTRK4RB46P45V2ID","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"pith_short_8","alias_value":"VTRK4RB4","created_at":"2026-07-05T08:06:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VTRK4RB46P45V2IDMIEWTEKMLT","target":"record","payload":{"canonical_record":{"source":{"id":"2404.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-04-10T09:06:10Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"0461109a023ae9ff25efaa18c23f126c2ea78946e4de80e851b38d4180919947","abstract_canon_sha256":"67241a14eb5baff9428dee96b92e80bc28f34219d79b32144a78eb682bcad365"},"schema_version":"1.0"},"canonical_sha256":"ace2ae443cf3f9dae903620969914c5cc238f1ebef83eff09c876dcf509b977b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:30.903049Z","signature_b64":"aylEMGDVcQ5OKuUtatdRk2v8E3tk2bVvkiRfQX1v34aq/7eum9HFi5AOLJtOMlIcz41aiMXNP7KU0xnLAWzvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ace2ae443cf3f9dae903620969914c5cc238f1ebef83eff09c876dcf509b977b","last_reissued_at":"2026-07-05T08:06:30.902554Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:30.902554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.06840","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":"2026-07-05T08:06:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fphIPhZg6lxNSzEnzyS5uFihd/L1g1c9ouZC+ZR3P9wfJFUlIOE/GDg8QxyTa8uP+xV/0sM2R7YuegeYRQAGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:57:03.936461Z"},"content_sha256":"7ca777c1414ba0c5b6c70642ea44c47427503d083926bb1a10ec6dd0058c0048","schema_version":"1.0","event_id":"sha256:7ca777c1414ba0c5b6c70642ea44c47427503d083926bb1a10ec6dd0058c0048"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VTRK4RB46P45V2IDMIEWTEKMLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized homomorphisms and KK with extra structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"James Gabe, Joachim Cuntz","submitted_at":"2024-04-10T09:06:10Z","abstract_excerpt":"We develop the approach via quasihomomorphisms and the universal algebra $qA$ to Kasparov's $KK$-theory, so as to cover versions of $KK$ such as $KK^{nuc}$, $KK^G$ and ideal related $KK$-theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06840","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.06840/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:06:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dhp+j5XF02OrMSIrVK9iLn8OwRyMBgJ/+4pAYHHD7S/0jxp9rMVIps2+32KNGUU82pkR7CypSpuJTvyGyDBWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:57:03.937054Z"},"content_sha256":"a2817f424a3fb6fe7ca0801bc77903113a517ff59c8e374927c6c5408eb39b17","schema_version":"1.0","event_id":"sha256:a2817f424a3fb6fe7ca0801bc77903113a517ff59c8e374927c6c5408eb39b17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/bundle.json","state_url":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTRK4RB46P45V2IDMIEWTEKMLT/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":"2026-08-13T20:57:03Z","links":{"resolver":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT","bundle":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/bundle.json","state":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTRK4RB46P45V2IDMIEWTEKMLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VTRK4RB46P45V2IDMIEWTEKMLT","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":"67241a14eb5baff9428dee96b92e80bc28f34219d79b32144a78eb682bcad365","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-04-10T09:06:10Z","title_canon_sha256":"0461109a023ae9ff25efaa18c23f126c2ea78946e4de80e851b38d4180919947"},"schema_version":"1.0","source":{"id":"2404.06840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06840","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06840v1","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06840","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"pith_short_12","alias_value":"VTRK4RB46P45","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"pith_short_16","alias_value":"VTRK4RB46P45V2ID","created_at":"2026-07-05T08:06:30Z"},{"alias_kind":"pith_short_8","alias_value":"VTRK4RB4","created_at":"2026-07-05T08:06:30Z"}],"graph_snapshots":[{"event_id":"sha256:a2817f424a3fb6fe7ca0801bc77903113a517ff59c8e374927c6c5408eb39b17","target":"graph","created_at":"2026-07-05T08:06:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.06840/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the approach via quasihomomorphisms and the universal algebra $qA$ to Kasparov's $KK$-theory, so as to cover versions of $KK$ such as $KK^{nuc}$, $KK^G$ and ideal related $KK$-theory.","authors_text":"James Gabe, Joachim Cuntz","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-04-10T09:06:10Z","title":"Generalized homomorphisms and KK with extra structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06840","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":"sha256:7ca777c1414ba0c5b6c70642ea44c47427503d083926bb1a10ec6dd0058c0048","target":"record","created_at":"2026-07-05T08:06:30Z","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":"67241a14eb5baff9428dee96b92e80bc28f34219d79b32144a78eb682bcad365","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-04-10T09:06:10Z","title_canon_sha256":"0461109a023ae9ff25efaa18c23f126c2ea78946e4de80e851b38d4180919947"},"schema_version":"1.0","source":{"id":"2404.06840","kind":"arxiv","version":1}},"canonical_sha256":"ace2ae443cf3f9dae903620969914c5cc238f1ebef83eff09c876dcf509b977b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ace2ae443cf3f9dae903620969914c5cc238f1ebef83eff09c876dcf509b977b","first_computed_at":"2026-07-05T08:06:30.902554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:06:30.902554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aylEMGDVcQ5OKuUtatdRk2v8E3tk2bVvkiRfQX1v34aq/7eum9HFi5AOLJtOMlIcz41aiMXNP7KU0xnLAWzvCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:06:30.903049Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.06840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ca777c1414ba0c5b6c70642ea44c47427503d083926bb1a10ec6dd0058c0048","sha256:a2817f424a3fb6fe7ca0801bc77903113a517ff59c8e374927c6c5408eb39b17"],"state_sha256":"59a1fccb14d2608d468ae5abc454d2df36a6acb07c0c8f6f1f7d87126537f4af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PtVBF5EszVFgN0QFOZxReoMUXz3hBIeQQMJGz2xZNumGSQabFmSSDMSITRhSt0JyC9zrmt7DvNC3LNmm0SfRDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T20:57:03.947223Z","bundle_sha256":"548d2e442c6e8160d7969249ca8963a94e7e84c256852fc8d14b2579af3a027a"}}