{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QNGU2Q7CCQHTWMYPWQD5SFXABU","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":"69dd9d55cd4f6eb454dce1d24fec9e9a80074f7065cf38617240864e53c32c73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-27T17:30:52Z","title_canon_sha256":"a80eee1458e068b828fcb1d7bf26a3550b91383e0ae59e97afce972b75c41c31"},"schema_version":"1.0","source":{"id":"1610.08893","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08893","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08893v3","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08893","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"QNGU2Q7CCQHT","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QNGU2Q7CCQHTWMYP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QNGU2Q7C","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:395627bd3896aef7c846107e35893d47eb342d40cec112791ce91ab14dc512e3","target":"graph","created_at":"2026-05-18T00:03:29Z","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":"In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a single fiber of the bundle. By plugging in the correct parameters, we recover several classical theorems. Afterwards, we define a family of invariants of principal bundles that detect the number of group reductions that a principal bundle admits. We prove that they fit into a long exact sequence of abelian groups, together with the cohomology of","authors_text":"Martina Rovelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-27T17:30:52Z","title":"Characteristic classes as complete obstructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08893","kind":"arxiv","version":3},"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:cdc145b451449d8f18e62ca0cd42007187952a9789be5893d6127e590c2fed58","target":"record","created_at":"2026-05-18T00:03:29Z","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":"69dd9d55cd4f6eb454dce1d24fec9e9a80074f7065cf38617240864e53c32c73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-27T17:30:52Z","title_canon_sha256":"a80eee1458e068b828fcb1d7bf26a3550b91383e0ae59e97afce972b75c41c31"},"schema_version":"1.0","source":{"id":"1610.08893","kind":"arxiv","version":3}},"canonical_sha256":"834d4d43e2140f3b330fb407d916e00d07dcdfe67842f858ed3240d45a075cb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"834d4d43e2140f3b330fb407d916e00d07dcdfe67842f858ed3240d45a075cb3","first_computed_at":"2026-05-18T00:03:29.745791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:29.745791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3DY25vVvVMfxM0EwYKVIxpS7oqhQyKmg3GUVaXe4oC+65LLuCm8XnbYQTlPBIiiEr1bOFhFMQ4IF1XCAnbNxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:29.746446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08893","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdc145b451449d8f18e62ca0cd42007187952a9789be5893d6127e590c2fed58","sha256:395627bd3896aef7c846107e35893d47eb342d40cec112791ce91ab14dc512e3"],"state_sha256":"a2dc45c66a751830208799603f4f8cfa4159ef581970d96071edb3623275a615"}