{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:IFR5OD5VVDHFLYT54OP67UWBRJ","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":"bb7c37fbd5bce34172669df1b0f955e04d5120bc2b9a6dc8043aada699049c81","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GT","submitted_at":"2001-03-22T11:04:32Z","title_canon_sha256":"eaaaa4c129bdae347652051c4b10224976bfc45a75b661e4599e16be45695290"},"schema_version":"1.0","source":{"id":"math/0103134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103134","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103134v1","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103134","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"IFR5OD5VVDHF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"IFR5OD5VVDHFLYT5","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"IFR5OD5V","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:1c56267c2c520b53f489b41a88558fffe41c3016b7d3170234e267df7a966ae6","target":"graph","created_at":"2026-05-18T03:34:00Z","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":"We classify SO(n)-equivariant principal bundles over $S^n$ in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant $(\\Pi, G)$-bundles over cohomogeneity one manifolds.","authors_text":"Ian Hambleton, Jean-Claude Hausmann","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2001-03-22T11:04:32Z","title":"Equivariant principal bundles over spheres and cohomogeneity one manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103134","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":"sha256:1b42edd20071a6a84bb3554b24f9798f3985db237f2e71c67ceb8bc5fa907df4","target":"record","created_at":"2026-05-18T03:34:00Z","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":"bb7c37fbd5bce34172669df1b0f955e04d5120bc2b9a6dc8043aada699049c81","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GT","submitted_at":"2001-03-22T11:04:32Z","title_canon_sha256":"eaaaa4c129bdae347652051c4b10224976bfc45a75b661e4599e16be45695290"},"schema_version":"1.0","source":{"id":"math/0103134","kind":"arxiv","version":1}},"canonical_sha256":"4163d70fb5a8ce55e27de39fefd2c18a5abb11671c1f94ce2dd7086ba2e904bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4163d70fb5a8ce55e27de39fefd2c18a5abb11671c1f94ce2dd7086ba2e904bc","first_computed_at":"2026-05-18T03:34:00.600706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:00.600706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eF/W6wYjUj7vUcGU49k/zev9MPw80wc+8kwUS3P2aj+FMG8oxFiIPm18ZcfByXtEiZewXcUh25UB1tUeksP+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:00.601303Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0103134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b42edd20071a6a84bb3554b24f9798f3985db237f2e71c67ceb8bc5fa907df4","sha256:1c56267c2c520b53f489b41a88558fffe41c3016b7d3170234e267df7a966ae6"],"state_sha256":"4c4759057c076898899f9cd9dc375b4b72a1e15c3c2d86a5af0d7802b5124102"}