{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HLMP6E3N5T7DLGL3UDTOTBAV4G","short_pith_number":"pith:HLMP6E3N","canonical_record":{"source":{"id":"1210.3133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-11T06:03:39Z","cross_cats_sorted":[],"title_canon_sha256":"180eb55852368870a654958245a4944ca58aebc6289f490770bb95c0d0b5d5cb","abstract_canon_sha256":"52b39fc1acfcaf49a060f050969cc642628a0b35a1d72449a1b34fab3a96e566"},"schema_version":"1.0"},"canonical_sha256":"3ad8ff136decfe35997ba0e6e98415e19c9f1f9e84303a3250660a3b43a83a96","source":{"kind":"arxiv","id":"1210.3133","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3133","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3133v2","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3133","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"HLMP6E3N5T7D","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HLMP6E3N5T7DLGL3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HLMP6E3N","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HLMP6E3N5T7DLGL3UDTOTBAV4G","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-11T06:03:39Z","cross_cats_sorted":[],"title_canon_sha256":"180eb55852368870a654958245a4944ca58aebc6289f490770bb95c0d0b5d5cb","abstract_canon_sha256":"52b39fc1acfcaf49a060f050969cc642628a0b35a1d72449a1b34fab3a96e566"},"schema_version":"1.0"},"canonical_sha256":"3ad8ff136decfe35997ba0e6e98415e19c9f1f9e84303a3250660a3b43a83a96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:08.993483Z","signature_b64":"kbSnl8/YPCvHT9noPvJ4BV04uVf7sEX6Ot2VepIu2J7MX41NVgt7tRPeNvvFRA+18ntQVzBLIw5jzkJHVeRFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ad8ff136decfe35997ba0e6e98415e19c9f1f9e84303a3250660a3b43a83a96","last_reissued_at":"2026-05-18T01:25:08.992981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:08.992981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3133","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":"2026-05-18T01:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVRhCJTDNqUEfK151IrMtAEP4PQL80ivXfeGnGeJqFldJFxBIaEFV3UFjHh+os/p/v8LfpWUwyOSvJqgw6IIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:52:33.084528Z"},"content_sha256":"beb868067d21b6965133462311884f7d7cd16a251a94297658dd7c880e60b1b0","schema_version":"1.0","event_id":"sha256:beb868067d21b6965133462311884f7d7cd16a251a94297658dd7c880e60b1b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HLMP6E3N5T7DLGL3UDTOTBAV4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pictures of KK-theory for real C*-algebras and almost commuting matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Efren Ruiz, Jeffrey L. Boersema, Terry A. Loring","submitted_at":"2012-10-11T06:03:39Z","abstract_excerpt":"We give a systematic account of the various pictures of KK-theory for real C*-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of KK-theory, and we use CRT-structures to prove that a natural transformation from F(A) to G(A) between homotopy equivalent, stable, half-exact functors defined on real C*-algebras is an isomorphism provided it is an isomorphism on the smaller class of C*-algebras. Finally, we develop E-theory for real C*-algebras and use that to obtain new negative results regarding th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3133","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":"2026-05-18T01:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOOj3HIY69B30BeUAasb3QwldZyiGkYmTmhu4nzDX0UxLPhfCnNnGUIv2VtdpXqe1NlWbTiXklu4nt+uM7keAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:52:33.084875Z"},"content_sha256":"d60691882f51b2aa074ed9ca4e0bc1efd80ef2fdf2bf71683160c6b922b56f4b","schema_version":"1.0","event_id":"sha256:d60691882f51b2aa074ed9ca4e0bc1efd80ef2fdf2bf71683160c6b922b56f4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G/bundle.json","state_url":"https://pith.science/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G/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":"2026-05-30T20:52:33Z","links":{"resolver":"https://pith.science/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G","bundle":"https://pith.science/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G/bundle.json","state":"https://pith.science/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLMP6E3N5T7DLGL3UDTOTBAV4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HLMP6E3N5T7DLGL3UDTOTBAV4G","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":"52b39fc1acfcaf49a060f050969cc642628a0b35a1d72449a1b34fab3a96e566","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-11T06:03:39Z","title_canon_sha256":"180eb55852368870a654958245a4944ca58aebc6289f490770bb95c0d0b5d5cb"},"schema_version":"1.0","source":{"id":"1210.3133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3133","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3133v2","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3133","created_at":"2026-05-18T01:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"HLMP6E3N5T7D","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HLMP6E3N5T7DLGL3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HLMP6E3N","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:d60691882f51b2aa074ed9ca4e0bc1efd80ef2fdf2bf71683160c6b922b56f4b","target":"graph","created_at":"2026-05-18T01:25:08Z","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 give a systematic account of the various pictures of KK-theory for real C*-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of KK-theory, and we use CRT-structures to prove that a natural transformation from F(A) to G(A) between homotopy equivalent, stable, half-exact functors defined on real C*-algebras is an isomorphism provided it is an isomorphism on the smaller class of C*-algebras. Finally, we develop E-theory for real C*-algebras and use that to obtain new negative results regarding th","authors_text":"Efren Ruiz, Jeffrey L. Boersema, Terry A. Loring","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-11T06:03:39Z","title":"Pictures of KK-theory for real C*-algebras and almost commuting matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3133","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:beb868067d21b6965133462311884f7d7cd16a251a94297658dd7c880e60b1b0","target":"record","created_at":"2026-05-18T01:25:08Z","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":"52b39fc1acfcaf49a060f050969cc642628a0b35a1d72449a1b34fab3a96e566","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-11T06:03:39Z","title_canon_sha256":"180eb55852368870a654958245a4944ca58aebc6289f490770bb95c0d0b5d5cb"},"schema_version":"1.0","source":{"id":"1210.3133","kind":"arxiv","version":2}},"canonical_sha256":"3ad8ff136decfe35997ba0e6e98415e19c9f1f9e84303a3250660a3b43a83a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ad8ff136decfe35997ba0e6e98415e19c9f1f9e84303a3250660a3b43a83a96","first_computed_at":"2026-05-18T01:25:08.992981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:08.992981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kbSnl8/YPCvHT9noPvJ4BV04uVf7sEX6Ot2VepIu2J7MX41NVgt7tRPeNvvFRA+18ntQVzBLIw5jzkJHVeRFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:08.993483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:beb868067d21b6965133462311884f7d7cd16a251a94297658dd7c880e60b1b0","sha256:d60691882f51b2aa074ed9ca4e0bc1efd80ef2fdf2bf71683160c6b922b56f4b"],"state_sha256":"984f5ccb7fbad41f84f0fd819f67b2cf2b510ed1bd1f783c919321d5ea44641e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyw8DaxdW9mH0aeWP+VsQDt8+9ovHOdfn1eWx0uXYyzwk6VVc7xat54h5Bprllw7AIInIS8eoyV1xGhX0McaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:52:33.086837Z","bundle_sha256":"a47d8f65d9f51c623fb422bf0fedf415e73e8d87a2abb68d55d8e53b7911b130"}}