{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:VEPJPOQVHP7ABVK27HKRHYYY32","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":"356cfbdae80b6b13235596de68bc84e7a5365349e571dbf033c949143e11607c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-06-24T06:33:58Z","title_canon_sha256":"13248ea42b3ea1afb19aea6975586303121c572810eea79656ce103c60db7f44"},"schema_version":"1.0","source":{"id":"0806.3824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3824","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3824v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3824","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"VEPJPOQVHP7A","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"VEPJPOQVHP7ABVK2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"VEPJPOQV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:1f28d2ed2ca892d3c9fc8ecc4cd422a1d602e5a83bf61c552ea160bbe19f907c","target":"graph","created_at":"2026-05-18T02:58:11Z","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 consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundle, then we show that its rank has to be in $\\{2,3,4,6,8\\}$. Moreover, we give a complete classification of such bundles of rank 6 and 8, and a partial classification for rank 3.","authors_text":"Kristopher Tapp, Lorenz J. Schwachhoefer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-06-24T06:33:58Z","title":"Cohomogeneity one disk bundles with normal homogeneous collars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3824","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":"sha256:67688046ed6fb2f4c6d6c5dbe10625285fe275b42e052b96682aee5b9581eb06","target":"record","created_at":"2026-05-18T02:58:11Z","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":"356cfbdae80b6b13235596de68bc84e7a5365349e571dbf033c949143e11607c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-06-24T06:33:58Z","title_canon_sha256":"13248ea42b3ea1afb19aea6975586303121c572810eea79656ce103c60db7f44"},"schema_version":"1.0","source":{"id":"0806.3824","kind":"arxiv","version":1}},"canonical_sha256":"a91e97ba153bfe00d55af9d513e318de9b61a4a65eac974997be4cfac3ee6897","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a91e97ba153bfe00d55af9d513e318de9b61a4a65eac974997be4cfac3ee6897","first_computed_at":"2026-05-18T02:58:11.406799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.406799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gW5jCS6HRGjsvBYPv/fHl7ZL173y+FoPZOZMX4ZZTtVM1mSA9zEtfFShxhsXJoDBRJmWKACM7yx+xnkLxqABCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.407383Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.3824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67688046ed6fb2f4c6d6c5dbe10625285fe275b42e052b96682aee5b9581eb06","sha256:1f28d2ed2ca892d3c9fc8ecc4cd422a1d602e5a83bf61c552ea160bbe19f907c"],"state_sha256":"f457060e4a6b84abf2ce498616501af29f19d38849d1eab990ca1aa82d82075b"}