{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ICOOVT4DSQIIODS6CBPO6WAKZF","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":"7004ed85c58c437facab5ebb7d5a2f303245d54ec70bd50e67af631fa5cb37be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-29T14:30:40Z","title_canon_sha256":"189d34bd7868c073a051ca9ad64b0b5114eb494e36b0c986b6da8b8e686204e4"},"schema_version":"1.0","source":{"id":"1508.07454","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07454","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07454v3","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07454","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"ICOOVT4DSQII","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ICOOVT4DSQIIODS6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ICOOVT4D","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:11be973c3604f9b32286180bbe583ef9b07ee9575c4b2e7fe5369540e52aba5c","target":"graph","created_at":"2026-05-18T01:28:37Z","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":"Consider a codimension $1$ submanifold $N^n\\subset M^{n+1}$, where $M^{n+1}\\subset\\mathbb{R}^{n+2}$ is a hypersurface. The envelope of tangent spaces of $M$ along $N$ generalizes the concept of tangent developable surface of a surface along a curve. In this paper, we study the singularities of these envelopes.\n  There are some important examples of submanifolds that admit a vector field tangent to $M$ and transversal to $N$ whose derivative in any direction of $N$ is contained in $N$. When this is the case, one can construct transversal plane bundles and affine metrics on $N$ with the desirabl","authors_text":"Luis F. S\\'anchez, Marcelo J. Saia, Marcos Craizer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-29T14:30:40Z","title":"Equiaffine Darboux Frames for Codimension 2 Submanifolds contained in Hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07454","kind":"arxiv","version":3},"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:c4f51c8d346156fbbc628ad9895714c589bac6818b9c8eb6a4c9aff63c8f1efe","target":"record","created_at":"2026-05-18T01:28:37Z","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":"7004ed85c58c437facab5ebb7d5a2f303245d54ec70bd50e67af631fa5cb37be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-29T14:30:40Z","title_canon_sha256":"189d34bd7868c073a051ca9ad64b0b5114eb494e36b0c986b6da8b8e686204e4"},"schema_version":"1.0","source":{"id":"1508.07454","kind":"arxiv","version":3}},"canonical_sha256":"409ceacf839410870e5e105eef580ac94c62ba7e7c4a7a4ee1bcd40b67a3e65b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"409ceacf839410870e5e105eef580ac94c62ba7e7c4a7a4ee1bcd40b67a3e65b","first_computed_at":"2026-05-18T01:28:37.890144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:37.890144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7tN/iNpmjdCwC8/Of5kAMUr/iZr5QzFLLZF48jnFNNIeZC0BLOS2maJBQAY/BAMqcc52Oshk9xeJWc6gyxRVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:37.890821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07454","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4f51c8d346156fbbc628ad9895714c589bac6818b9c8eb6a4c9aff63c8f1efe","sha256:11be973c3604f9b32286180bbe583ef9b07ee9575c4b2e7fe5369540e52aba5c"],"state_sha256":"bfc307e8a14c6311cd31846c755b6bc5e5e1a63a9a7498fe4dadc20e37f88854"}