{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VTRK4RB46P45V2IDMIEWTEKMLT","short_pith_number":"pith:VTRK4RB4","schema_version":"1.0","canonical_sha256":"ace2ae443cf3f9dae903620969914c5cc238f1ebef83eff09c876dcf509b977b","source":{"kind":"arxiv","id":"2404.06840","version":1},"attestation_state":"computed","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.06840","created_at":"2026-07-05T08:06:30.902618+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.06840v1","created_at":"2026-07-05T08:06:30.902618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06840","created_at":"2026-07-05T08:06:30.902618+00:00"},{"alias_kind":"pith_short_12","alias_value":"VTRK4RB46P45","created_at":"2026-07-05T08:06:30.902618+00:00"},{"alias_kind":"pith_short_16","alias_value":"VTRK4RB46P45V2ID","created_at":"2026-07-05T08:06:30.902618+00:00"},{"alias_kind":"pith_short_8","alias_value":"VTRK4RB4","created_at":"2026-07-05T08:06:30.902618+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.16238","citing_title":"Equivariant $KK$-theory and model categories","ref_index":210,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT","json":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT.json","graph_json":"https://pith.science/api/pith-number/VTRK4RB46P45V2IDMIEWTEKMLT/graph.json","events_json":"https://pith.science/api/pith-number/VTRK4RB46P45V2IDMIEWTEKMLT/events.json","paper":"https://pith.science/paper/VTRK4RB4"},"agent_actions":{"view_html":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT","download_json":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT.json","view_paper":"https://pith.science/paper/VTRK4RB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.06840&json=true","fetch_graph":"https://pith.science/api/pith-number/VTRK4RB46P45V2IDMIEWTEKMLT/graph.json","fetch_events":"https://pith.science/api/pith-number/VTRK4RB46P45V2IDMIEWTEKMLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/action/storage_attestation","attest_author":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/action/author_attestation","sign_citation":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/action/citation_signature","submit_replication":"https://pith.science/pith/VTRK4RB46P45V2IDMIEWTEKMLT/action/replication_record"}},"created_at":"2026-07-05T08:06:30.902618+00:00","updated_at":"2026-07-05T08:06:30.902618+00:00"}