{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z2TJQDAZNRRRBIEVJVVEF4XR6G","short_pith_number":"pith:Z2TJQDAZ","canonical_record":{"source":{"id":"1109.5968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-27T16:57:19Z","cross_cats_sorted":["math.KT","math.QA"],"title_canon_sha256":"c6c37e94126b8735bc8ac4f979f6888e2106a317ba5bdb3469a55ef671e23949","abstract_canon_sha256":"952f5a43d234b4a9312eaf0b6f06baca57f92920a81224ec41a61a0fee4eccad"},"schema_version":"1.0"},"canonical_sha256":"cea6980c196c6310a0954d6a42f2f1f1ad72cbb6549feb233f6667c0f2184647","source":{"kind":"arxiv","id":"1109.5968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5968","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5968v1","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5968","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"Z2TJQDAZNRRR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z2TJQDAZNRRRBIEV","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z2TJQDAZ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z2TJQDAZNRRRBIEVJVVEF4XR6G","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-27T16:57:19Z","cross_cats_sorted":["math.KT","math.QA"],"title_canon_sha256":"c6c37e94126b8735bc8ac4f979f6888e2106a317ba5bdb3469a55ef671e23949","abstract_canon_sha256":"952f5a43d234b4a9312eaf0b6f06baca57f92920a81224ec41a61a0fee4eccad"},"schema_version":"1.0"},"canonical_sha256":"cea6980c196c6310a0954d6a42f2f1f1ad72cbb6549feb233f6667c0f2184647","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:10.942338Z","signature_b64":"N/IpAw1Dj04MWa8LFw27yaqiJfeq+M+gCW9AI1luexr9D7gVOUeVxl+mLSSslbzZgLAkz4MgxLVur/LFhK88Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea6980c196c6310a0954d6a42f2f1f1ad72cbb6549feb233f6667c0f2184647","last_reissued_at":"2026-05-18T04:12:10.941807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:10.941807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5968","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":"2026-05-18T04:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOURv0n1/+U3Nu5gWXubsiwdRsfqH8q0vdEtUiwALHVXQposJ/ujQ2MriWRNXiat0iebYH6OoWs5lfPfTf4UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:48:01.070865Z"},"content_sha256":"fe08ad4dd08c003303d7f374122704a30a41421df0545a58a6428b00b1bfd028","schema_version":"1.0","event_id":"sha256:fe08ad4dd08c003303d7f374122704a30a41421df0545a58a6428b00b1bfd028"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z2TJQDAZNRRRBIEVJVVEF4XR6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"KK-fibrations arising from Rieffel deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.QA"],"primary_cat":"math.OA","authors_text":"Amandip Sangha","submitted_at":"2011-09-27T16:57:19Z","abstract_excerpt":"The bundle map $\\pi_{h}: \\Gamma((A_{tJ})_{t\\in [0,1]})\\lra A_{hJ}$, for every $h\\in [0,1]$, of the continuous field $(A_{tJ})_{t\\in [0,1]}$ associated to the Rieffel deformation $A_{J}$ of a C*-algebra $A$ is shown to be a KK-equivalence by using a 2-cocycle twisting approach and RKK-fibrations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5968","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":"2026-05-18T04:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4dFFCYprdJTGDcP1RljI+P3HOYFHy3mfmAxPufkFpxaCA6iyVzeKXFY19SBCSGILWIuWhjMsk+zHWIKuy6hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:48:01.071214Z"},"content_sha256":"76bff1f76cbcd2cbf69ca12a443f032d8aabafd53fcc218955ac06814a44bfd0","schema_version":"1.0","event_id":"sha256:76bff1f76cbcd2cbf69ca12a443f032d8aabafd53fcc218955ac06814a44bfd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G/bundle.json","state_url":"https://pith.science/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G/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":"2026-06-02T19:48:01Z","links":{"resolver":"https://pith.science/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G","bundle":"https://pith.science/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G/bundle.json","state":"https://pith.science/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2TJQDAZNRRRBIEVJVVEF4XR6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z2TJQDAZNRRRBIEVJVVEF4XR6G","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":"952f5a43d234b4a9312eaf0b6f06baca57f92920a81224ec41a61a0fee4eccad","cross_cats_sorted":["math.KT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-27T16:57:19Z","title_canon_sha256":"c6c37e94126b8735bc8ac4f979f6888e2106a317ba5bdb3469a55ef671e23949"},"schema_version":"1.0","source":{"id":"1109.5968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5968","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5968v1","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5968","created_at":"2026-05-18T04:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"Z2TJQDAZNRRR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z2TJQDAZNRRRBIEV","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z2TJQDAZ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:76bff1f76cbcd2cbf69ca12a443f032d8aabafd53fcc218955ac06814a44bfd0","target":"graph","created_at":"2026-05-18T04:12:10Z","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":"The bundle map $\\pi_{h}: \\Gamma((A_{tJ})_{t\\in [0,1]})\\lra A_{hJ}$, for every $h\\in [0,1]$, of the continuous field $(A_{tJ})_{t\\in [0,1]}$ associated to the Rieffel deformation $A_{J}$ of a C*-algebra $A$ is shown to be a KK-equivalence by using a 2-cocycle twisting approach and RKK-fibrations.","authors_text":"Amandip Sangha","cross_cats":["math.KT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-27T16:57:19Z","title":"KK-fibrations arising from Rieffel deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5968","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:fe08ad4dd08c003303d7f374122704a30a41421df0545a58a6428b00b1bfd028","target":"record","created_at":"2026-05-18T04:12:10Z","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":"952f5a43d234b4a9312eaf0b6f06baca57f92920a81224ec41a61a0fee4eccad","cross_cats_sorted":["math.KT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-09-27T16:57:19Z","title_canon_sha256":"c6c37e94126b8735bc8ac4f979f6888e2106a317ba5bdb3469a55ef671e23949"},"schema_version":"1.0","source":{"id":"1109.5968","kind":"arxiv","version":1}},"canonical_sha256":"cea6980c196c6310a0954d6a42f2f1f1ad72cbb6549feb233f6667c0f2184647","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea6980c196c6310a0954d6a42f2f1f1ad72cbb6549feb233f6667c0f2184647","first_computed_at":"2026-05-18T04:12:10.941807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:10.941807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/IpAw1Dj04MWa8LFw27yaqiJfeq+M+gCW9AI1luexr9D7gVOUeVxl+mLSSslbzZgLAkz4MgxLVur/LFhK88Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:10.942338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe08ad4dd08c003303d7f374122704a30a41421df0545a58a6428b00b1bfd028","sha256:76bff1f76cbcd2cbf69ca12a443f032d8aabafd53fcc218955ac06814a44bfd0"],"state_sha256":"be1c1cf4ef3d824043af0c60ff0c4d012618132c88a9230057f9ca143a7c4ba8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySbTOF+N1GquIf3HKbixaK3Hw/E273HRe4stMCuzKQe5xXaJjgBh4meKmXxSNC8pjLXS5Ch2ZL5plC05rO5FDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:48:01.073146Z","bundle_sha256":"1455e7c7f01b09dd3f4058546cb70fc081519a88c23e69cda907fa195c4b7a82"}}