{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XI2G2LTKVFK26VJWCWVUI5V5TB","short_pith_number":"pith:XI2G2LTK","canonical_record":{"source":{"id":"1506.08111","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2015-06-26T15:13:49Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"e4992857d67042272bb58628926ca0c942b07949339dbb46726d4ab3b99f81a3","abstract_canon_sha256":"f5f0f6d905206377d0a0ee5cb96245cd0a7a5a6ee44cf36b78141d5be8bb56ce"},"schema_version":"1.0"},"canonical_sha256":"ba346d2e6aa955af553615ab4476bd986b8e8f48fc752b1bdde7c7a86e2338c4","source":{"kind":"arxiv","id":"1506.08111","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08111","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08111v2","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08111","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"XI2G2LTKVFK2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XI2G2LTKVFK26VJW","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XI2G2LTK","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XI2G2LTKVFK26VJWCWVUI5V5TB","target":"record","payload":{"canonical_record":{"source":{"id":"1506.08111","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2015-06-26T15:13:49Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"e4992857d67042272bb58628926ca0c942b07949339dbb46726d4ab3b99f81a3","abstract_canon_sha256":"f5f0f6d905206377d0a0ee5cb96245cd0a7a5a6ee44cf36b78141d5be8bb56ce"},"schema_version":"1.0"},"canonical_sha256":"ba346d2e6aa955af553615ab4476bd986b8e8f48fc752b1bdde7c7a86e2338c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:04.560729Z","signature_b64":"JhyCXbxm/FajuDRERVnJrqtNPH3WjFMjowSXBSRMngtD4+xnQ4OKRRpPSPCOnS4dbbqomCKBtTS225lCFElUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba346d2e6aa955af553615ab4476bd986b8e8f48fc752b1bdde7c7a86e2338c4","last_reissued_at":"2026-05-18T00:10:04.559993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:04.559993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.08111","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":"2026-05-18T00:10:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZLJ1wjorfS8PB/ISh2OyUJBTFd2gqIH38eO4h+MdP37bTs02FonmfKZQOWkupF45VHSs4juokia930v7GgdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:44:21.330487Z"},"content_sha256":"a2f30e94b83beacbdef1fed23450ef4b48c4966cee9943927f851482690eba46","schema_version":"1.0","event_id":"sha256:a2f30e94b83beacbdef1fed23450ef4b48c4966cee9943927f851482690eba46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XI2G2LTKVFK26VJWCWVUI5V5TB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obstructions to algebraizing topological vector bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Aravind Asok, Jean Fasel, Michael J. Hopkins","submitted_at":"2015-06-26T15:13:49Z","abstract_excerpt":"Suppose $X$ is a smooth complex algebraic variety. A necessary condition for a complex topological vector bundle on $X$ (viewed as a complex manifold) to be algebraic is that all Chern classes must be algebraic cohomology classes, i.e., lie in the image of the cycle class map. We analyze the question of whether algebraicity of Chern classes is sufficient to guarantee algebraizability of complex topological vector bundles. For affine varieties of dimension $\\leq 3$, it is known that algebraicity of Chern classes of a vector bundle guarantees algebraizability of the vector bundle. In contrast, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08111","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":"2026-05-18T00:10:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yf9lyY0CHHa/8RRhSxX7iRR3KydBTgvmyWI0249uuQvBo+TdA++hxUWX+JbOV2MEQDQoUyMmkFQ1dtspwXiYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:44:21.331218Z"},"content_sha256":"8b25bc10fb48a6c1559de6ab1b24725c1a8eea396a0ae2b0d31583285427f6dd","schema_version":"1.0","event_id":"sha256:8b25bc10fb48a6c1559de6ab1b24725c1a8eea396a0ae2b0d31583285427f6dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XI2G2LTKVFK26VJWCWVUI5V5TB/bundle.json","state_url":"https://pith.science/pith/XI2G2LTKVFK26VJWCWVUI5V5TB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XI2G2LTKVFK26VJWCWVUI5V5TB/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":"2026-05-30T10:44:21Z","links":{"resolver":"https://pith.science/pith/XI2G2LTKVFK26VJWCWVUI5V5TB","bundle":"https://pith.science/pith/XI2G2LTKVFK26VJWCWVUI5V5TB/bundle.json","state":"https://pith.science/pith/XI2G2LTKVFK26VJWCWVUI5V5TB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XI2G2LTKVFK26VJWCWVUI5V5TB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XI2G2LTKVFK26VJWCWVUI5V5TB","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":"f5f0f6d905206377d0a0ee5cb96245cd0a7a5a6ee44cf36b78141d5be8bb56ce","cross_cats_sorted":["math.AT","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2015-06-26T15:13:49Z","title_canon_sha256":"e4992857d67042272bb58628926ca0c942b07949339dbb46726d4ab3b99f81a3"},"schema_version":"1.0","source":{"id":"1506.08111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08111","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08111v2","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08111","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"XI2G2LTKVFK2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XI2G2LTKVFK26VJW","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XI2G2LTK","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:8b25bc10fb48a6c1559de6ab1b24725c1a8eea396a0ae2b0d31583285427f6dd","target":"graph","created_at":"2026-05-18T00:10:04Z","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":"Suppose $X$ is a smooth complex algebraic variety. A necessary condition for a complex topological vector bundle on $X$ (viewed as a complex manifold) to be algebraic is that all Chern classes must be algebraic cohomology classes, i.e., lie in the image of the cycle class map. We analyze the question of whether algebraicity of Chern classes is sufficient to guarantee algebraizability of complex topological vector bundles. For affine varieties of dimension $\\leq 3$, it is known that algebraicity of Chern classes of a vector bundle guarantees algebraizability of the vector bundle. In contrast, w","authors_text":"Aravind Asok, Jean Fasel, Michael J. Hopkins","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2015-06-26T15:13:49Z","title":"Obstructions to algebraizing topological vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08111","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:a2f30e94b83beacbdef1fed23450ef4b48c4966cee9943927f851482690eba46","target":"record","created_at":"2026-05-18T00:10:04Z","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":"f5f0f6d905206377d0a0ee5cb96245cd0a7a5a6ee44cf36b78141d5be8bb56ce","cross_cats_sorted":["math.AT","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2015-06-26T15:13:49Z","title_canon_sha256":"e4992857d67042272bb58628926ca0c942b07949339dbb46726d4ab3b99f81a3"},"schema_version":"1.0","source":{"id":"1506.08111","kind":"arxiv","version":2}},"canonical_sha256":"ba346d2e6aa955af553615ab4476bd986b8e8f48fc752b1bdde7c7a86e2338c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba346d2e6aa955af553615ab4476bd986b8e8f48fc752b1bdde7c7a86e2338c4","first_computed_at":"2026-05-18T00:10:04.559993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:04.559993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JhyCXbxm/FajuDRERVnJrqtNPH3WjFMjowSXBSRMngtD4+xnQ4OKRRpPSPCOnS4dbbqomCKBtTS225lCFElUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:04.560729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2f30e94b83beacbdef1fed23450ef4b48c4966cee9943927f851482690eba46","sha256:8b25bc10fb48a6c1559de6ab1b24725c1a8eea396a0ae2b0d31583285427f6dd"],"state_sha256":"56ce7ea454b1344fd6461a2eb6e42f7279519dc4bbb4a9efee6bdfe3e8ebb47e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0vw0J0PqllkS8URzyhnoa0HCt2/yQhsTm/oMNeNceNnyrq4H/htGN7cK0MCa13AaxN5ZtqqQlDBaOSQan3VAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:44:21.335271Z","bundle_sha256":"1f796eca8bf10c170e8a774d58eecd0653a6e4ac2496884897556e226f7bd29e"}}