{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:45NZDO643FANV4T553AAKYVC7B","short_pith_number":"pith:45NZDO64","canonical_record":{"source":{"id":"1302.6924","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-27T17:00:07Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"3286b6d107f3a0387633a791df549f858e19b42059095c0d6a71e7c6f165bef2","abstract_canon_sha256":"5e5d9431ea867d6188b1ee9f7fa1446cbcc4f1e82e64e923411fbc535d6e9924"},"schema_version":"1.0"},"canonical_sha256":"e75b91bbdcd940daf27deec00562a2f841cc6dbfb359ca3b54080ddd029ec81a","source":{"kind":"arxiv","id":"1302.6924","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6924","created_at":"2026-05-18T02:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6924v2","created_at":"2026-05-18T02:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6924","created_at":"2026-05-18T02:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"45NZDO643FAN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"45NZDO643FANV4T5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"45NZDO64","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:45NZDO643FANV4T553AAKYVC7B","target":"record","payload":{"canonical_record":{"source":{"id":"1302.6924","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-27T17:00:07Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"3286b6d107f3a0387633a791df549f858e19b42059095c0d6a71e7c6f165bef2","abstract_canon_sha256":"5e5d9431ea867d6188b1ee9f7fa1446cbcc4f1e82e64e923411fbc535d6e9924"},"schema_version":"1.0"},"canonical_sha256":"e75b91bbdcd940daf27deec00562a2f841cc6dbfb359ca3b54080ddd029ec81a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:21.331050Z","signature_b64":"F0jCe/xwy6tew1GY2pbNhwGbPYfDR9bnyPZv2tyFB9/0yjwlj2wNeuZqOV2oibum4D4opd5Ma0du25YwVRVsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e75b91bbdcd940daf27deec00562a2f841cc6dbfb359ca3b54080ddd029ec81a","last_reissued_at":"2026-05-18T02:56:21.330332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:21.330332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.6924","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":"2026-05-18T02:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3j3Mcb8K0VbQbEqVdkWQOfriiFuIFA9NpcOhkgsXeeH1cFBfeCj59aA3ELkl9BGU8g+44r7zvkKcN9dmxHuQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:53:35.803867Z"},"content_sha256":"81007992b9b8c62eafdc034cb85d725e19adb789acaee8f896e7666341230b62","schema_version":"1.0","event_id":"sha256:81007992b9b8c62eafdc034cb85d725e19adb789acaee8f896e7666341230b62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:45NZDO643FANV4T553AAKYVC7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy-theoretic E-theory and n-order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.OA","authors_text":"Rasmus Bentmann","submitted_at":"2013-02-27T17:00:07Z","abstract_excerpt":"The bootstrap category in E-theory for C*-algebras over a finite space X is embedded into the homotopy category of certain diagrams of K-module spectra. Therefore it has infinite n-order for every n. The same holds for the bootstrap category in G-equivariant E-theory for a compact group G and for the Spanier--Whitehead category in connective E-theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6924","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":"2026-05-18T02:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hNBusqCz8J6ycW6LDzmuw7/VoI63eShetXNZeb+c11V1SEh+B/p8JuDCOc3fJ+5AvPUQglbKRh/2ZeIXaHAlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:53:35.804217Z"},"content_sha256":"cc3d0f903f9a524287ecf0ad2fccb2581bc31f07e95d3d689a3730ab9d0a41c3","schema_version":"1.0","event_id":"sha256:cc3d0f903f9a524287ecf0ad2fccb2581bc31f07e95d3d689a3730ab9d0a41c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45NZDO643FANV4T553AAKYVC7B/bundle.json","state_url":"https://pith.science/pith/45NZDO643FANV4T553AAKYVC7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45NZDO643FANV4T553AAKYVC7B/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":"2026-06-12T07:53:35Z","links":{"resolver":"https://pith.science/pith/45NZDO643FANV4T553AAKYVC7B","bundle":"https://pith.science/pith/45NZDO643FANV4T553AAKYVC7B/bundle.json","state":"https://pith.science/pith/45NZDO643FANV4T553AAKYVC7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45NZDO643FANV4T553AAKYVC7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:45NZDO643FANV4T553AAKYVC7B","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":"5e5d9431ea867d6188b1ee9f7fa1446cbcc4f1e82e64e923411fbc535d6e9924","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-27T17:00:07Z","title_canon_sha256":"3286b6d107f3a0387633a791df549f858e19b42059095c0d6a71e7c6f165bef2"},"schema_version":"1.0","source":{"id":"1302.6924","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6924","created_at":"2026-05-18T02:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6924v2","created_at":"2026-05-18T02:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6924","created_at":"2026-05-18T02:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"45NZDO643FAN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"45NZDO643FANV4T5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"45NZDO64","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:cc3d0f903f9a524287ecf0ad2fccb2581bc31f07e95d3d689a3730ab9d0a41c3","target":"graph","created_at":"2026-05-18T02:56:21Z","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 bootstrap category in E-theory for C*-algebras over a finite space X is embedded into the homotopy category of certain diagrams of K-module spectra. Therefore it has infinite n-order for every n. The same holds for the bootstrap category in G-equivariant E-theory for a compact group G and for the Spanier--Whitehead category in connective E-theory.","authors_text":"Rasmus Bentmann","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-27T17:00:07Z","title":"Homotopy-theoretic E-theory and n-order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6924","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":"sha256:81007992b9b8c62eafdc034cb85d725e19adb789acaee8f896e7666341230b62","target":"record","created_at":"2026-05-18T02:56:21Z","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":"5e5d9431ea867d6188b1ee9f7fa1446cbcc4f1e82e64e923411fbc535d6e9924","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-27T17:00:07Z","title_canon_sha256":"3286b6d107f3a0387633a791df549f858e19b42059095c0d6a71e7c6f165bef2"},"schema_version":"1.0","source":{"id":"1302.6924","kind":"arxiv","version":2}},"canonical_sha256":"e75b91bbdcd940daf27deec00562a2f841cc6dbfb359ca3b54080ddd029ec81a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e75b91bbdcd940daf27deec00562a2f841cc6dbfb359ca3b54080ddd029ec81a","first_computed_at":"2026-05-18T02:56:21.330332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:21.330332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F0jCe/xwy6tew1GY2pbNhwGbPYfDR9bnyPZv2tyFB9/0yjwlj2wNeuZqOV2oibum4D4opd5Ma0du25YwVRVsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:21.331050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6924","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81007992b9b8c62eafdc034cb85d725e19adb789acaee8f896e7666341230b62","sha256:cc3d0f903f9a524287ecf0ad2fccb2581bc31f07e95d3d689a3730ab9d0a41c3"],"state_sha256":"90482a9a00835beffc9b50f2ef5b375503d2150c66e0612481f23f2933f77674"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AzUnlIAhdkByFvxO89BGdXSiHnlRuiqeSSB9VkKxVz7khoALo5qveYrt/JzFoFm2JrgGnu4ohYG4ZgwW749tDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:53:35.806133Z","bundle_sha256":"2ad15fed240cfefd15bde4ccc04d3f0264cdb8d42213d983f6da7c15dab759a7"}}