{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W6NJZRM3JB6UNEWN3Z2Y4V3C3F","short_pith_number":"pith:W6NJZRM3","canonical_record":{"source":{"id":"1304.4532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-16T17:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"54727ead160e713afbd368d8d82390fe63f300a6a6cc13cfa5142399c38fa649","abstract_canon_sha256":"5207b1eacd026dbadc757bff71b84d522438560e45ba802acf04fbd7bc979359"},"schema_version":"1.0"},"canonical_sha256":"b79a9cc59b487d4692cdde758e5762d97ac6f501f8f275e6be69d2df8fb05b5c","source":{"kind":"arxiv","id":"1304.4532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4532","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4532v1","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4532","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"W6NJZRM3JB6U","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W6NJZRM3JB6UNEWN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W6NJZRM3","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W6NJZRM3JB6UNEWN3Z2Y4V3C3F","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-16T17:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"54727ead160e713afbd368d8d82390fe63f300a6a6cc13cfa5142399c38fa649","abstract_canon_sha256":"5207b1eacd026dbadc757bff71b84d522438560e45ba802acf04fbd7bc979359"},"schema_version":"1.0"},"canonical_sha256":"b79a9cc59b487d4692cdde758e5762d97ac6f501f8f275e6be69d2df8fb05b5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:52.759347Z","signature_b64":"6MLrNd8awawWYr72oRk/rSHmpJ/PQxMs/4Xc4SChwEn8W5AbIxMWDSCWK+gyDw8wULEsV0byI94Im7Pf+eIaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b79a9cc59b487d4692cdde758e5762d97ac6f501f8f275e6be69d2df8fb05b5c","last_reissued_at":"2026-05-18T03:27:52.758744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:52.758744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4532","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":"2026-05-18T03:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RfqLm2/vuA4xW0peDk6zHExY/RLDP6G/ZQI0h9ltxWk2aqGm6WJBxTlMv9cb0sUeP7DjxIAyM7Qlw+RQ5W55Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:39:51.504200Z"},"content_sha256":"2500b1f74eaffe693ead482b9e08d3cd69779521b2066881f334b728e52e67aa","schema_version":"1.0","event_id":"sha256:2500b1f74eaffe693ead482b9e08d3cd69779521b2066881f334b728e52e67aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W6NJZRM3JB6UNEWN3Z2Y4V3C3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flat Sections and Non-negative Curvature in Pullback Bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C. Dur\\'an, L. D. Speran\\c{c}a","submitted_at":"2013-04-16T17:42:04Z","abstract_excerpt":"We give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of certain Riemannian submersions with totally geodesic fibers; applications of this obstruction to several examples are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4532","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":"2026-05-18T03:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YPBqHM7mjzuUs33Txm1RKk9m6x9OQe9Kokarl34BprYl4iUiX67QvmRAt/Iu3fajzsfn1eXHNiuGTsRjlskBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:39:51.504581Z"},"content_sha256":"4a7adf02a46d6fa390b6834b221826478a77a76d86e2ce362ab1ecc5bc55a0e0","schema_version":"1.0","event_id":"sha256:4a7adf02a46d6fa390b6834b221826478a77a76d86e2ce362ab1ecc5bc55a0e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F/bundle.json","state_url":"https://pith.science/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F/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":"2026-06-24T07:39:51Z","links":{"resolver":"https://pith.science/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F","bundle":"https://pith.science/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F/bundle.json","state":"https://pith.science/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6NJZRM3JB6UNEWN3Z2Y4V3C3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W6NJZRM3JB6UNEWN3Z2Y4V3C3F","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":"5207b1eacd026dbadc757bff71b84d522438560e45ba802acf04fbd7bc979359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-16T17:42:04Z","title_canon_sha256":"54727ead160e713afbd368d8d82390fe63f300a6a6cc13cfa5142399c38fa649"},"schema_version":"1.0","source":{"id":"1304.4532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4532","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4532v1","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4532","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"W6NJZRM3JB6U","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W6NJZRM3JB6UNEWN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W6NJZRM3","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:4a7adf02a46d6fa390b6834b221826478a77a76d86e2ce362ab1ecc5bc55a0e0","target":"graph","created_at":"2026-05-18T03:27:52Z","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 give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of certain Riemannian submersions with totally geodesic fibers; applications of this obstruction to several examples are given.","authors_text":"C. Dur\\'an, L. D. Speran\\c{c}a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-16T17:42:04Z","title":"Flat Sections and Non-negative Curvature in Pullback Bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4532","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":"sha256:2500b1f74eaffe693ead482b9e08d3cd69779521b2066881f334b728e52e67aa","target":"record","created_at":"2026-05-18T03:27:52Z","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":"5207b1eacd026dbadc757bff71b84d522438560e45ba802acf04fbd7bc979359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-16T17:42:04Z","title_canon_sha256":"54727ead160e713afbd368d8d82390fe63f300a6a6cc13cfa5142399c38fa649"},"schema_version":"1.0","source":{"id":"1304.4532","kind":"arxiv","version":1}},"canonical_sha256":"b79a9cc59b487d4692cdde758e5762d97ac6f501f8f275e6be69d2df8fb05b5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b79a9cc59b487d4692cdde758e5762d97ac6f501f8f275e6be69d2df8fb05b5c","first_computed_at":"2026-05-18T03:27:52.758744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:52.758744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MLrNd8awawWYr72oRk/rSHmpJ/PQxMs/4Xc4SChwEn8W5AbIxMWDSCWK+gyDw8wULEsV0byI94Im7Pf+eIaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:52.759347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2500b1f74eaffe693ead482b9e08d3cd69779521b2066881f334b728e52e67aa","sha256:4a7adf02a46d6fa390b6834b221826478a77a76d86e2ce362ab1ecc5bc55a0e0"],"state_sha256":"099ec36cbf5a72fb0f51542d6c198cfc67b661aceb489db918d6769371797d65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yw5vA0vLUwIAWqAhiTHMoDFReEPpkNl0X4A1nXIFU24eMR0A+PUMMDfRjYE+KukM68U3aaT78nbsTvicfqLECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:39:51.506615Z","bundle_sha256":"99b7b9cff45c369c81790a9574c40e32f6d0195228938f48c80abf8c6f733b80"}}