{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6OG2UCBAI2JENZNAJKMK53Z2AG","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":"74786182bf89d116d55ab990b3929c2140ef80e58b673ef908e115377e4191a5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-16T06:21:17Z","title_canon_sha256":"875d84f5f6c57c8cf62880fa150df69f012a9419619311d28ee78118f175bdb2"},"schema_version":"1.0","source":{"id":"1408.3707","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3707","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3707v2","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3707","created_at":"2026-05-18T02:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"6OG2UCBAI2JE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6OG2UCBAI2JENZNA","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6OG2UCBA","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:f8950860e6e99c7b6033f5c15091c652edd4eeef3c992fdb62104ea783c334cc","target":"graph","created_at":"2026-05-18T02:28:40Z","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 quantitative openness theorem for $C^1$ submersions under suitable assumptions on the differential. We then apply our result to a class of exponential maps appearing in Carnot-Carath\\'eodory spaces and we improve a classical completeness result by Palais.","authors_text":"Andrea Bonfiglioli, Annamaria Montanari, Daniele Morbidelli","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-16T06:21:17Z","title":"A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3707","kind":"arxiv","version":2},"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":"sha256:5ea1b11035625396cdf9ea2e5bb7c75329d3e79b66218bc6b8674803a8b4c0df","target":"record","created_at":"2026-05-18T02:28:40Z","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":"74786182bf89d116d55ab990b3929c2140ef80e58b673ef908e115377e4191a5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-16T06:21:17Z","title_canon_sha256":"875d84f5f6c57c8cf62880fa150df69f012a9419619311d28ee78118f175bdb2"},"schema_version":"1.0","source":{"id":"1408.3707","kind":"arxiv","version":2}},"canonical_sha256":"f38daa0820469246e5a04a98aeef3a01aa64ab1f1c066b8cb0dd0cba89317300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f38daa0820469246e5a04a98aeef3a01aa64ab1f1c066b8cb0dd0cba89317300","first_computed_at":"2026-05-18T02:28:40.518501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:40.518501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IUfaOl8O2heefkoZCc2BMb7Zru+CF+t/Afu066rtzqcKRkbnND744xWpiK32hv0wnSWX5bkjH4WtkY9hicpkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:40.518947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3707","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea1b11035625396cdf9ea2e5bb7c75329d3e79b66218bc6b8674803a8b4c0df","sha256:f8950860e6e99c7b6033f5c15091c652edd4eeef3c992fdb62104ea783c334cc"],"state_sha256":"08f6e4a809341af07af64b959558af197ace732d3683416382cafb5182027c6b"}