{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YJG5ZD5NBHQI24XPMRM4ORKLQ4","short_pith_number":"pith:YJG5ZD5N","canonical_record":{"source":{"id":"2411.15324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-22T19:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"f235ce95cd11749835f18686f01ac440824719f25b727b0ff92d57bdbf52d7ba","abstract_canon_sha256":"467780c9c3a3323cc42a18bceba39f024fe55035ca6a90372e2b7bcb09d16b0a"},"schema_version":"1.0"},"canonical_sha256":"c24ddc8fad09e08d72ef6459c7454b87034947a01d606ec93ba63f7fb2ee6978","source":{"kind":"arxiv","id":"2411.15324","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15324","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15324v1","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15324","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"YJG5ZD5NBHQI","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"pith_short_16","alias_value":"YJG5ZD5NBHQI24XP","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"pith_short_8","alias_value":"YJG5ZD5N","created_at":"2026-07-05T09:39:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YJG5ZD5NBHQI24XPMRM4ORKLQ4","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-22T19:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"f235ce95cd11749835f18686f01ac440824719f25b727b0ff92d57bdbf52d7ba","abstract_canon_sha256":"467780c9c3a3323cc42a18bceba39f024fe55035ca6a90372e2b7bcb09d16b0a"},"schema_version":"1.0"},"canonical_sha256":"c24ddc8fad09e08d72ef6459c7454b87034947a01d606ec93ba63f7fb2ee6978","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:33.192389Z","signature_b64":"48krA+OrUL8zTP0cmZodFyqImFXOMhXe/FP8l8DWrDphU4wHwOlKtUsWnK5gtsr8QfXE+s2WK2pJmuuu6XRSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c24ddc8fad09e08d72ef6459c7454b87034947a01d606ec93ba63f7fb2ee6978","last_reissued_at":"2026-07-05T09:39:33.191904Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:33.191904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15324","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":"2026-07-05T09:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnSPKjDuCiMxw1f50ndML9jA+KjZs8rmHuRPISRPduw/FkU9RlxM6CcO5tJn+eIhI9jqE19Ic7QLro6bhyF7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:51:18.793444Z"},"content_sha256":"e33d1a0a89a89089bd685504e8be0b0073ee71f0459881049cd8d0accdd45c8c","schema_version":"1.0","event_id":"sha256:e33d1a0a89a89089bd685504e8be0b0073ee71f0459881049cd8d0accdd45c8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YJG5ZD5NBHQI24XPMRM4ORKLQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothness of submetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander Lytchak, Burkhard Wilking","submitted_at":"2024-11-22T19:32:43Z","abstract_excerpt":"We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of the base is implied by the smoothness of the total space. Results are proven in the much more general setting of submetries. These are metric generalizations of Riemannian submersions and isometric actions, which have recently appeared in different areas of geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15324","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15324/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPHp3yxJG+v2sCbCrjLj2IaKzWtU07fEhN/IubhqDMMwzHUHwod1NSOhwFKf8ZLbg2CY1oiBzZL8AHzGAwpMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:51:18.793946Z"},"content_sha256":"43f7a7c47d500193847387e57be0e8743ae29000d59b509f052afef6dde12cd1","schema_version":"1.0","event_id":"sha256:43f7a7c47d500193847387e57be0e8743ae29000d59b509f052afef6dde12cd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4/bundle.json","state_url":"https://pith.science/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4/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":"2026-08-13T02:51:18Z","links":{"resolver":"https://pith.science/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4","bundle":"https://pith.science/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4/bundle.json","state":"https://pith.science/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJG5ZD5NBHQI24XPMRM4ORKLQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YJG5ZD5NBHQI24XPMRM4ORKLQ4","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":"467780c9c3a3323cc42a18bceba39f024fe55035ca6a90372e2b7bcb09d16b0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-22T19:32:43Z","title_canon_sha256":"f235ce95cd11749835f18686f01ac440824719f25b727b0ff92d57bdbf52d7ba"},"schema_version":"1.0","source":{"id":"2411.15324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15324","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15324v1","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15324","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"YJG5ZD5NBHQI","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"pith_short_16","alias_value":"YJG5ZD5NBHQI24XP","created_at":"2026-07-05T09:39:33Z"},{"alias_kind":"pith_short_8","alias_value":"YJG5ZD5N","created_at":"2026-07-05T09:39:33Z"}],"graph_snapshots":[{"event_id":"sha256:43f7a7c47d500193847387e57be0e8743ae29000d59b509f052afef6dde12cd1","target":"graph","created_at":"2026-07-05T09:39:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15324/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of the base is implied by the smoothness of the total space. Results are proven in the much more general setting of submetries. These are metric generalizations of Riemannian submersions and isometric actions, which have recently appeared in different areas of geometry.","authors_text":"Alexander Lytchak, Burkhard Wilking","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-22T19:32:43Z","title":"Smoothness of submetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15324","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:e33d1a0a89a89089bd685504e8be0b0073ee71f0459881049cd8d0accdd45c8c","target":"record","created_at":"2026-07-05T09:39:33Z","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":"467780c9c3a3323cc42a18bceba39f024fe55035ca6a90372e2b7bcb09d16b0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-22T19:32:43Z","title_canon_sha256":"f235ce95cd11749835f18686f01ac440824719f25b727b0ff92d57bdbf52d7ba"},"schema_version":"1.0","source":{"id":"2411.15324","kind":"arxiv","version":1}},"canonical_sha256":"c24ddc8fad09e08d72ef6459c7454b87034947a01d606ec93ba63f7fb2ee6978","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c24ddc8fad09e08d72ef6459c7454b87034947a01d606ec93ba63f7fb2ee6978","first_computed_at":"2026-07-05T09:39:33.191904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:33.191904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"48krA+OrUL8zTP0cmZodFyqImFXOMhXe/FP8l8DWrDphU4wHwOlKtUsWnK5gtsr8QfXE+s2WK2pJmuuu6XRSBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:33.192389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e33d1a0a89a89089bd685504e8be0b0073ee71f0459881049cd8d0accdd45c8c","sha256:43f7a7c47d500193847387e57be0e8743ae29000d59b509f052afef6dde12cd1"],"state_sha256":"4dbf11b39152190eac40888bfb0f6a0f19984486e4f0f840d79c66966b706038"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eebf+aQT86lrUaN/AKmgMVDadyhChhSrlhkAWLP0njvdE/+KHtod5rsDhAgW2kAbXnqh4gLjzrYcXk4Ebvq1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T02:51:18.799126Z","bundle_sha256":"a2717b9177f23429dd08fd4a0b951a27abed3cd2e3bba0a65088df0cdedb260c"}}