{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5KHNQ6264E3SGOP5CMIPYBLSDF","short_pith_number":"pith:5KHNQ626","canonical_record":{"source":{"id":"1706.02405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-07T22:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"6e0864e9a2292cdd8c78a2027001cbe9616a0fdc49458bf65ce6162dc2a60cee","abstract_canon_sha256":"9040b591481b960b0e4be7a541a5a748496aba2cf8f0282b1beb9bd825c767ec"},"schema_version":"1.0"},"canonical_sha256":"ea8ed87b5ee1372339fd1310fc05721976395d6567b02da2a695039f6b1938a5","source":{"kind":"arxiv","id":"1706.02405","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02405","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02405v1","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02405","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"5KHNQ6264E3S","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5KHNQ6264E3SGOP5","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5KHNQ626","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5KHNQ6264E3SGOP5CMIPYBLSDF","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-07T22:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"6e0864e9a2292cdd8c78a2027001cbe9616a0fdc49458bf65ce6162dc2a60cee","abstract_canon_sha256":"9040b591481b960b0e4be7a541a5a748496aba2cf8f0282b1beb9bd825c767ec"},"schema_version":"1.0"},"canonical_sha256":"ea8ed87b5ee1372339fd1310fc05721976395d6567b02da2a695039f6b1938a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:45.550330Z","signature_b64":"y9iYADI8koIE/CVD0UQ0MIReI57HzJ99qDMn0XLPySypD3c0MdFzBr9DpEtgi0dnR4H/zSSb+kGsOn2GT00YBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea8ed87b5ee1372339fd1310fc05721976395d6567b02da2a695039f6b1938a5","last_reissued_at":"2026-05-18T00:42:45.549843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:45.549843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02405","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":"2026-05-18T00:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3fYMlLrPTq2SO3dnqYoyTRzHkPOm7ZIlB5z4yqOLxHp2RyKfGZJk9FI9CnfOIKHiH/8yyAUN7uXONBQgsOFUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:24:18.090083Z"},"content_sha256":"f3db73d311b9ba504764a4356d5774c7c6a4acc437fbe46e36c5d66f3bf016fb","schema_version":"1.0","event_id":"sha256:f3db73d311b9ba504764a4356d5774c7c6a4acc437fbe46e36c5d66f3bf016fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5KHNQ6264E3SGOP5CMIPYBLSDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The vectorial Ribaucour transformation for submanifolds of constant sectional curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Guimar\\~aes, Ruy Tojeiro","submitted_at":"2017-06-07T22:50:29Z","abstract_excerpt":"We obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds of constant sectional curvature of space forms, which we call the $L$-transformation. It allows to construct a family of such submanifolds starting with a given one and a vector-valued solution of a system of linear partial differential equations. We prove a decomposition theorem for the $L$-transformation, which is a far-reaching generalization of the classical permutability formula for the Ribaucour transformation of surfaces of constant curvature in Euclidean three space. As a consequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02405","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":"2026-05-18T00:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yUOkJDJD8mez9bMXwtp50CTsQLGlhMGz6N++V4740lzCOeOPz/huxLWwVMFRVTUxtfdF1BsQtaK9ZEmfmn3sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:24:18.090433Z"},"content_sha256":"603032902a0eb904bb4069035d100446145778f217317ea70d387c0743226825","schema_version":"1.0","event_id":"sha256:603032902a0eb904bb4069035d100446145778f217317ea70d387c0743226825"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KHNQ6264E3SGOP5CMIPYBLSDF/bundle.json","state_url":"https://pith.science/pith/5KHNQ6264E3SGOP5CMIPYBLSDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KHNQ6264E3SGOP5CMIPYBLSDF/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":"2026-06-26T21:24:18Z","links":{"resolver":"https://pith.science/pith/5KHNQ6264E3SGOP5CMIPYBLSDF","bundle":"https://pith.science/pith/5KHNQ6264E3SGOP5CMIPYBLSDF/bundle.json","state":"https://pith.science/pith/5KHNQ6264E3SGOP5CMIPYBLSDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KHNQ6264E3SGOP5CMIPYBLSDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5KHNQ6264E3SGOP5CMIPYBLSDF","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":"9040b591481b960b0e4be7a541a5a748496aba2cf8f0282b1beb9bd825c767ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-07T22:50:29Z","title_canon_sha256":"6e0864e9a2292cdd8c78a2027001cbe9616a0fdc49458bf65ce6162dc2a60cee"},"schema_version":"1.0","source":{"id":"1706.02405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02405","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02405v1","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02405","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"5KHNQ6264E3S","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5KHNQ6264E3SGOP5","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5KHNQ626","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:603032902a0eb904bb4069035d100446145778f217317ea70d387c0743226825","target":"graph","created_at":"2026-05-18T00:42:45Z","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 obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds of constant sectional curvature of space forms, which we call the $L$-transformation. It allows to construct a family of such submanifolds starting with a given one and a vector-valued solution of a system of linear partial differential equations. We prove a decomposition theorem for the $L$-transformation, which is a far-reaching generalization of the classical permutability formula for the Ribaucour transformation of surfaces of constant curvature in Euclidean three space. As a consequenc","authors_text":"Daniel Guimar\\~aes, Ruy Tojeiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-07T22:50:29Z","title":"The vectorial Ribaucour transformation for submanifolds of constant sectional curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02405","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:f3db73d311b9ba504764a4356d5774c7c6a4acc437fbe46e36c5d66f3bf016fb","target":"record","created_at":"2026-05-18T00:42:45Z","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":"9040b591481b960b0e4be7a541a5a748496aba2cf8f0282b1beb9bd825c767ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-07T22:50:29Z","title_canon_sha256":"6e0864e9a2292cdd8c78a2027001cbe9616a0fdc49458bf65ce6162dc2a60cee"},"schema_version":"1.0","source":{"id":"1706.02405","kind":"arxiv","version":1}},"canonical_sha256":"ea8ed87b5ee1372339fd1310fc05721976395d6567b02da2a695039f6b1938a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea8ed87b5ee1372339fd1310fc05721976395d6567b02da2a695039f6b1938a5","first_computed_at":"2026-05-18T00:42:45.549843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:45.549843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y9iYADI8koIE/CVD0UQ0MIReI57HzJ99qDMn0XLPySypD3c0MdFzBr9DpEtgi0dnR4H/zSSb+kGsOn2GT00YBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:45.550330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3db73d311b9ba504764a4356d5774c7c6a4acc437fbe46e36c5d66f3bf016fb","sha256:603032902a0eb904bb4069035d100446145778f217317ea70d387c0743226825"],"state_sha256":"d989af9116e62cb87eec4641ce7765257396b656593ea24dbe0d8cdb663838b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgBkm4Zvx+2NJb9ft4vip9u5mnEmfmcX/M2gy48rRlocB+wBzRIMtXyQDOmpX4PvfKg+B1SG6/w+SF6gR4RGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:24:18.092372Z","bundle_sha256":"56cbd82d18a4a2d71c3701d591e1b9803da6350a088efc7c89bf6770618e19f4"}}