{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YAT42V7SH35R4LNNKHFOUSUT7U","short_pith_number":"pith:YAT42V7S","canonical_record":{"source":{"id":"1706.00366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-01T16:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"c558c9be534cd377c651c474ba38a4a58e22e04d2e7d8c855bd34a6a94ea290a","abstract_canon_sha256":"6aee51b2fd6053638ce520aa652a688993b70bfcf18c2b50eeb03c830f5478e4"},"schema_version":"1.0"},"canonical_sha256":"c027cd57f23efb1e2dad51caea4a93fd24282e0770328c39122aaba011acad86","source":{"kind":"arxiv","id":"1706.00366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00366","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00366v1","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00366","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"YAT42V7SH35R","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YAT42V7SH35R4LNN","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YAT42V7S","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YAT42V7SH35R4LNNKHFOUSUT7U","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-01T16:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"c558c9be534cd377c651c474ba38a4a58e22e04d2e7d8c855bd34a6a94ea290a","abstract_canon_sha256":"6aee51b2fd6053638ce520aa652a688993b70bfcf18c2b50eeb03c830f5478e4"},"schema_version":"1.0"},"canonical_sha256":"c027cd57f23efb1e2dad51caea4a93fd24282e0770328c39122aaba011acad86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:14.238480Z","signature_b64":"x33Njoj5gLZrHs8PCEQgxReMaurs0nGbM6C//k2PLg2dJ/p9gPTf7MnTS0klUFj34WRu8gy42yoDnA+QnJzUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c027cd57f23efb1e2dad51caea4a93fd24282e0770328c39122aaba011acad86","last_reissued_at":"2026-05-18T00:43:14.237721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:14.237721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00366","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":"2026-05-18T00:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNX9nxIOJS8ncP+AnaxuC8RRLwyCC6RGGA5EyWpoCpFz20Pu5VE/KtzsB/4o20kf5tliECJNbdxmdwGPQut/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:01:32.565459Z"},"content_sha256":"57b4b8f750e215828e30868b773ebe0f0a1a7484fee8cc4dab4632e91cc0b4d4","schema_version":"1.0","event_id":"sha256:57b4b8f750e215828e30868b773ebe0f0a1a7484fee8cc4dab4632e91cc0b4d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YAT42V7SH35R4LNNKHFOUSUT7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the Petersen-Wilhelm conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Gonz\\'alez-\\'Alvaro, Marco Radeschi","submitted_at":"2017-06-01T16:22:43Z","abstract_excerpt":"In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the fiber. Together with previous results, this proves the Petersen-Wilhelm Conjecture for all the known compact manifolds with positive curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00366","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":"2026-05-18T00:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Og3QGjMkWQGqTvikZGlliA2IaI9rrjzv2VGFnuKsSW50TcPouGKZTSXW/dWOY6iU5QjCFzkzyv5lKZM2RkSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:01:32.565841Z"},"content_sha256":"323c6f823005c50994dc44a5a1d1bc3ca2fda19f9b125f762aa47e77f2a96141","schema_version":"1.0","event_id":"sha256:323c6f823005c50994dc44a5a1d1bc3ca2fda19f9b125f762aa47e77f2a96141"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAT42V7SH35R4LNNKHFOUSUT7U/bundle.json","state_url":"https://pith.science/pith/YAT42V7SH35R4LNNKHFOUSUT7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAT42V7SH35R4LNNKHFOUSUT7U/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":"2026-06-10T01:01:32Z","links":{"resolver":"https://pith.science/pith/YAT42V7SH35R4LNNKHFOUSUT7U","bundle":"https://pith.science/pith/YAT42V7SH35R4LNNKHFOUSUT7U/bundle.json","state":"https://pith.science/pith/YAT42V7SH35R4LNNKHFOUSUT7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAT42V7SH35R4LNNKHFOUSUT7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YAT42V7SH35R4LNNKHFOUSUT7U","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":"6aee51b2fd6053638ce520aa652a688993b70bfcf18c2b50eeb03c830f5478e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-01T16:22:43Z","title_canon_sha256":"c558c9be534cd377c651c474ba38a4a58e22e04d2e7d8c855bd34a6a94ea290a"},"schema_version":"1.0","source":{"id":"1706.00366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00366","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00366v1","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00366","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"YAT42V7SH35R","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YAT42V7SH35R4LNN","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YAT42V7S","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:323c6f823005c50994dc44a5a1d1bc3ca2fda19f9b125f762aa47e77f2a96141","target":"graph","created_at":"2026-05-18T00:43:14Z","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 this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the fiber. Together with previous results, this proves the Petersen-Wilhelm Conjecture for all the known compact manifolds with positive curvature.","authors_text":"David Gonz\\'alez-\\'Alvaro, Marco Radeschi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-01T16:22:43Z","title":"A note on the Petersen-Wilhelm conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00366","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":"sha256:57b4b8f750e215828e30868b773ebe0f0a1a7484fee8cc4dab4632e91cc0b4d4","target":"record","created_at":"2026-05-18T00:43:14Z","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":"6aee51b2fd6053638ce520aa652a688993b70bfcf18c2b50eeb03c830f5478e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-01T16:22:43Z","title_canon_sha256":"c558c9be534cd377c651c474ba38a4a58e22e04d2e7d8c855bd34a6a94ea290a"},"schema_version":"1.0","source":{"id":"1706.00366","kind":"arxiv","version":1}},"canonical_sha256":"c027cd57f23efb1e2dad51caea4a93fd24282e0770328c39122aaba011acad86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c027cd57f23efb1e2dad51caea4a93fd24282e0770328c39122aaba011acad86","first_computed_at":"2026-05-18T00:43:14.237721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:14.237721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x33Njoj5gLZrHs8PCEQgxReMaurs0nGbM6C//k2PLg2dJ/p9gPTf7MnTS0klUFj34WRu8gy42yoDnA+QnJzUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:14.238480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57b4b8f750e215828e30868b773ebe0f0a1a7484fee8cc4dab4632e91cc0b4d4","sha256:323c6f823005c50994dc44a5a1d1bc3ca2fda19f9b125f762aa47e77f2a96141"],"state_sha256":"fb872548d4a686801a1fbc3a3a2d9279df68721abc6c69cae42834278a828ca2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YuRHSmnfWSVT//ux7xWL2dB4xg7NZf9ZOfi8A2DSnrUPVTF1v12xWqmUNWQR2BMObxGJGWzNSZUYekkiapi0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:01:32.568833Z","bundle_sha256":"40ea22aceb49a6b9ff29612448ba5aa7b1282c2777afb459d4b7664af21dab8b"}}