{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KMS4BDH4XH7W5RYFZVG3T5G2ZU","short_pith_number":"pith:KMS4BDH4","canonical_record":{"source":{"id":"1109.5150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-23T18:23:32Z","cross_cats_sorted":[],"title_canon_sha256":"d5c10ac1f95220f99920e93732f1900f3c4e0cbf1525c430475c6bd3716fcbfa","abstract_canon_sha256":"e68253f07f61e6a1ffae136068412d16aa88216823c549b4e6cfb3ceb643c1cd"},"schema_version":"1.0"},"canonical_sha256":"5325c08cfcb9ff6ec705cd4db9f4dacd0b5c42bca7bf316908f3e0da8ef75547","source":{"kind":"arxiv","id":"1109.5150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5150","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5150v1","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5150","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"KMS4BDH4XH7W","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KMS4BDH4XH7W5RYF","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KMS4BDH4","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KMS4BDH4XH7W5RYFZVG3T5G2ZU","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-23T18:23:32Z","cross_cats_sorted":[],"title_canon_sha256":"d5c10ac1f95220f99920e93732f1900f3c4e0cbf1525c430475c6bd3716fcbfa","abstract_canon_sha256":"e68253f07f61e6a1ffae136068412d16aa88216823c549b4e6cfb3ceb643c1cd"},"schema_version":"1.0"},"canonical_sha256":"5325c08cfcb9ff6ec705cd4db9f4dacd0b5c42bca7bf316908f3e0da8ef75547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.045759Z","signature_b64":"PE8F7Sh8Wo2CmrS1CVOk762q9vTuRYaBls1qi0Fs1D6lspAcdtdao/s3LxjdtZV2oKE8XN8Cxzk8iHXXmHNpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5325c08cfcb9ff6ec705cd4db9f4dacd0b5c42bca7bf316908f3e0da8ef75547","last_reissued_at":"2026-05-18T02:38:18.045241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.045241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5150","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lPRFsj3GKweYsNL8XhefzM+ERFTO5kAyKmQHwtCqDlipGjCuTaLaYJwuiZ5lCtmNIa4s1ReNoFyDpczyYLFjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:06:49.609934Z"},"content_sha256":"bbb20e759092fffdf5e569cbe482de424553a010869ddde470cc0c820678f6f4","schema_version":"1.0","event_id":"sha256:bbb20e759092fffdf5e569cbe482de424553a010869ddde470cc0c820678f6f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KMS4BDH4XH7W5RYFZVG3T5G2ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity for Odd-Dimensional Souls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kristopher Tapp","submitted_at":"2011-09-23T18:23:32Z","abstract_excerpt":"We prove a new rigidity result for an open manifold M with nonnegative sectional curvature whose soul S is odd-dimensional. Specifically, there exists a geodesic in S and a parallel vertical plane field along it with constant vertical curvature and vanishing normal curvature. Under the added assumption that the Sharafutdinov fibers are rotationally symmetric, this implies that for small r, the distance sphere of radius r about S contains an immersed flat cylinder, and thus could not have positive curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5150","kind":"arxiv","version":1},"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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHlE5M6ry5I83NAjMt4WjrZUJLz1k1bwB5flyFmw8sseArvDoRlpZ1K20OOridvmZuZ987RCXbNmK9f94wcqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:06:49.610267Z"},"content_sha256":"f786c58707f99d5d45ec9de896b362ad3eaaf41b932007abcae029c3643cad5b","schema_version":"1.0","event_id":"sha256:f786c58707f99d5d45ec9de896b362ad3eaaf41b932007abcae029c3643cad5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU/bundle.json","state_url":"https://pith.science/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU/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":"2026-06-23T07:06:49Z","links":{"resolver":"https://pith.science/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU","bundle":"https://pith.science/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU/bundle.json","state":"https://pith.science/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMS4BDH4XH7W5RYFZVG3T5G2ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KMS4BDH4XH7W5RYFZVG3T5G2ZU","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":"e68253f07f61e6a1ffae136068412d16aa88216823c549b4e6cfb3ceb643c1cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-23T18:23:32Z","title_canon_sha256":"d5c10ac1f95220f99920e93732f1900f3c4e0cbf1525c430475c6bd3716fcbfa"},"schema_version":"1.0","source":{"id":"1109.5150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5150","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5150v1","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5150","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"KMS4BDH4XH7W","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KMS4BDH4XH7W5RYF","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KMS4BDH4","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:f786c58707f99d5d45ec9de896b362ad3eaaf41b932007abcae029c3643cad5b","target":"graph","created_at":"2026-05-18T02:38:18Z","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 prove a new rigidity result for an open manifold M with nonnegative sectional curvature whose soul S is odd-dimensional. Specifically, there exists a geodesic in S and a parallel vertical plane field along it with constant vertical curvature and vanishing normal curvature. Under the added assumption that the Sharafutdinov fibers are rotationally symmetric, this implies that for small r, the distance sphere of radius r about S contains an immersed flat cylinder, and thus could not have positive curvature.","authors_text":"Kristopher Tapp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-23T18:23:32Z","title":"Rigidity for Odd-Dimensional Souls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5150","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:bbb20e759092fffdf5e569cbe482de424553a010869ddde470cc0c820678f6f4","target":"record","created_at":"2026-05-18T02:38:18Z","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":"e68253f07f61e6a1ffae136068412d16aa88216823c549b4e6cfb3ceb643c1cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-23T18:23:32Z","title_canon_sha256":"d5c10ac1f95220f99920e93732f1900f3c4e0cbf1525c430475c6bd3716fcbfa"},"schema_version":"1.0","source":{"id":"1109.5150","kind":"arxiv","version":1}},"canonical_sha256":"5325c08cfcb9ff6ec705cd4db9f4dacd0b5c42bca7bf316908f3e0da8ef75547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5325c08cfcb9ff6ec705cd4db9f4dacd0b5c42bca7bf316908f3e0da8ef75547","first_computed_at":"2026-05-18T02:38:18.045241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.045241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PE8F7Sh8Wo2CmrS1CVOk762q9vTuRYaBls1qi0Fs1D6lspAcdtdao/s3LxjdtZV2oKE8XN8Cxzk8iHXXmHNpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.045759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbb20e759092fffdf5e569cbe482de424553a010869ddde470cc0c820678f6f4","sha256:f786c58707f99d5d45ec9de896b362ad3eaaf41b932007abcae029c3643cad5b"],"state_sha256":"e6795e2731f6f906aed52132357fd0a5d4342cb416c31aa7cf104d42667e639a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HV7f9EW4Rjv8gQk0jXZ823aPuH1Gs5h5Qb8x4Je7/lmRZ+QWmg/hvzH//TUCG1JHKZg+XY5x/xIfQlIGE0RjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:06:49.612170Z","bundle_sha256":"e279d527d0a813e1d1567e24acc1f2bab8946908478e8013b9e9a08396d8f275"}}