{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FODNJACMIELKZKWJ3Q4AJSZ7F5","short_pith_number":"pith:FODNJACM","canonical_record":{"source":{"id":"1107.4811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-07-24T22:29:22Z","cross_cats_sorted":[],"title_canon_sha256":"5f1621bd1e3f199ff406f424394cf058115d43781c0227ff3324d2a093bb1fec","abstract_canon_sha256":"0e404a97e5e93b7b133d5ccb4ab278dabbc20eb36e5569edf5cfb4cee13a8b54"},"schema_version":"1.0"},"canonical_sha256":"2b86d4804c4116acaac9dc3804cb3f2f64ad2fb006e9ea6325856fe5a06c3e62","source":{"kind":"arxiv","id":"1107.4811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4811","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4811v1","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4811","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"pith_short_12","alias_value":"FODNJACMIELK","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FODNJACMIELKZKWJ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FODNJACM","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FODNJACMIELKZKWJ3Q4AJSZ7F5","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-07-24T22:29:22Z","cross_cats_sorted":[],"title_canon_sha256":"5f1621bd1e3f199ff406f424394cf058115d43781c0227ff3324d2a093bb1fec","abstract_canon_sha256":"0e404a97e5e93b7b133d5ccb4ab278dabbc20eb36e5569edf5cfb4cee13a8b54"},"schema_version":"1.0"},"canonical_sha256":"2b86d4804c4116acaac9dc3804cb3f2f64ad2fb006e9ea6325856fe5a06c3e62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:54.577583Z","signature_b64":"klPBBh7ZSbIW+XHj2IfgPNm2EyI0Ts3igtB4xSkt2JLr3ZWF+6+siX7LVpQ0/tm9SjWMLxNpQp+5tL2o7vpiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b86d4804c4116acaac9dc3804cb3f2f64ad2fb006e9ea6325856fe5a06c3e62","last_reissued_at":"2026-05-18T04:16:54.577055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:54.577055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4811","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":"2026-05-18T04:16:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vyi6XUWyAS642cBb4ToWgzFIyX/g0e/JQGkBLWu0x9FdPc1Y9G0dynXYhyI+GqaO4WZYLtOrgD+gViOHVc3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T13:22:40.767670Z"},"content_sha256":"09c1cdf8a4f17b8fac64cb1361fe4f8e04e30452d8eb1d30ee72e42da04e59a2","schema_version":"1.0","event_id":"sha256:09c1cdf8a4f17b8fac64cb1361fe4f8e04e30452d8eb1d30ee72e42da04e59a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FODNJACMIELKZKWJ3Q4AJSZ7F5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K-Theories for Certain Infinite Rank Bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Andres Larrain-Hubach","submitted_at":"2011-07-24T22:29:22Z","abstract_excerpt":"Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite rank bundles in the families index theorem, and bundles with pseudodifferential operators as structure group. In this paper, we construct the corresponding K-theories for these types of bundles. We develop the formalism of these theories and use their Chern character to detect a large class of nontrivial elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4811","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":"2026-05-18T04:16:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAfgwzEYV+1YkeOGIvjTh36gd02Z6OAN1XQV5chp/rgxbyrfsp52XkE0cKMH/ZaBc7t46lddxj1raEa6VVLQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T13:22:40.768040Z"},"content_sha256":"d733969d094700087a2dd5877e832d7e67c1f9adf1a1023b586b33cdbd843247","schema_version":"1.0","event_id":"sha256:d733969d094700087a2dd5877e832d7e67c1f9adf1a1023b586b33cdbd843247"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5/bundle.json","state_url":"https://pith.science/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5/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":"2026-07-02T13:22:40Z","links":{"resolver":"https://pith.science/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5","bundle":"https://pith.science/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5/bundle.json","state":"https://pith.science/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FODNJACMIELKZKWJ3Q4AJSZ7F5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FODNJACMIELKZKWJ3Q4AJSZ7F5","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":"0e404a97e5e93b7b133d5ccb4ab278dabbc20eb36e5569edf5cfb4cee13a8b54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-07-24T22:29:22Z","title_canon_sha256":"5f1621bd1e3f199ff406f424394cf058115d43781c0227ff3324d2a093bb1fec"},"schema_version":"1.0","source":{"id":"1107.4811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4811","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4811v1","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4811","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"pith_short_12","alias_value":"FODNJACMIELK","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FODNJACMIELKZKWJ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FODNJACM","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:d733969d094700087a2dd5877e832d7e67c1f9adf1a1023b586b33cdbd843247","target":"graph","created_at":"2026-05-18T04:16:54Z","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":"Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite rank bundles in the families index theorem, and bundles with pseudodifferential operators as structure group. In this paper, we construct the corresponding K-theories for these types of bundles. We develop the formalism of these theories and use their Chern character to detect a large class of nontrivial elements.","authors_text":"Andres Larrain-Hubach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-07-24T22:29:22Z","title":"K-Theories for Certain Infinite Rank Bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4811","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":"sha256:09c1cdf8a4f17b8fac64cb1361fe4f8e04e30452d8eb1d30ee72e42da04e59a2","target":"record","created_at":"2026-05-18T04:16:54Z","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":"0e404a97e5e93b7b133d5ccb4ab278dabbc20eb36e5569edf5cfb4cee13a8b54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-07-24T22:29:22Z","title_canon_sha256":"5f1621bd1e3f199ff406f424394cf058115d43781c0227ff3324d2a093bb1fec"},"schema_version":"1.0","source":{"id":"1107.4811","kind":"arxiv","version":1}},"canonical_sha256":"2b86d4804c4116acaac9dc3804cb3f2f64ad2fb006e9ea6325856fe5a06c3e62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b86d4804c4116acaac9dc3804cb3f2f64ad2fb006e9ea6325856fe5a06c3e62","first_computed_at":"2026-05-18T04:16:54.577055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:54.577055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"klPBBh7ZSbIW+XHj2IfgPNm2EyI0Ts3igtB4xSkt2JLr3ZWF+6+siX7LVpQ0/tm9SjWMLxNpQp+5tL2o7vpiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:54.577583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09c1cdf8a4f17b8fac64cb1361fe4f8e04e30452d8eb1d30ee72e42da04e59a2","sha256:d733969d094700087a2dd5877e832d7e67c1f9adf1a1023b586b33cdbd843247"],"state_sha256":"3ccc5539c8667017d686881fbd925dca94b2c93991e9492a3f3491cefc51edbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dg9FN/6fOKAWAgndhfRfHjRQQjQNseYHSPBmOhZvk8EPI+pTRrEDMvqfAaomeTcS3WzcroeOz2MQtbmlRkIiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T13:22:40.769929Z","bundle_sha256":"64e56de7e5d1195b64468c25d779d7a4c4843239c0a1c6fd2e9c22aea78a4374"}}