{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UTD6Z77S3UE77QCQQGTVWCND5O","short_pith_number":"pith:UTD6Z77S","canonical_record":{"source":{"id":"1510.08489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T21:15:38Z","cross_cats_sorted":[],"title_canon_sha256":"121642cc29f7dc79fb7dd9fea9f088260af24c2a7980160a5054db897a8b8f05","abstract_canon_sha256":"4a259eb159478416d68f21d3397fb51520ae070da1b94c717d3d45c5a15b4c77"},"schema_version":"1.0"},"canonical_sha256":"a4c7ecfff2dd09ffc05081a75b09a3eba1a3167351b55aa92191033e8808c12e","source":{"kind":"arxiv","id":"1510.08489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08489","created_at":"2026-05-18T01:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08489v1","created_at":"2026-05-18T01:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08489","created_at":"2026-05-18T01:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"UTD6Z77S3UE7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UTD6Z77S3UE77QCQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UTD6Z77S","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UTD6Z77S3UE77QCQQGTVWCND5O","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T21:15:38Z","cross_cats_sorted":[],"title_canon_sha256":"121642cc29f7dc79fb7dd9fea9f088260af24c2a7980160a5054db897a8b8f05","abstract_canon_sha256":"4a259eb159478416d68f21d3397fb51520ae070da1b94c717d3d45c5a15b4c77"},"schema_version":"1.0"},"canonical_sha256":"a4c7ecfff2dd09ffc05081a75b09a3eba1a3167351b55aa92191033e8808c12e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:01.809155Z","signature_b64":"exZDBkGnuphL05qH1uGl5Skk0fyKNCxU7bxRLZCyNgP7UMIH6ayzbTm/enw8qqWgHcnU8w916hcQaZdb4B0IAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4c7ecfff2dd09ffc05081a75b09a3eba1a3167351b55aa92191033e8808c12e","last_reissued_at":"2026-05-18T01:19:01.808683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:01.808683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08489","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":"2026-05-18T01:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRSLUMqDBUlDPIRtlSra30vpXWw+q0crwpEyrHdgdDN+MA20gR5qzvkgB9NuZrKDbwvKlVPHyjS8WbMdsh7wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:06:47.568690Z"},"content_sha256":"472e4e6fd58937b6919b9320d6ede3d7751c083cd5f95207cdbcd75e1278a476","schema_version":"1.0","event_id":"sha256:472e4e6fd58937b6919b9320d6ede3d7751c083cd5f95207cdbcd75e1278a476"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UTD6Z77S3UE77QCQQGTVWCND5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Laplace Normal Vector Field of Skew Ruled Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stylianos Stamatakis","submitted_at":"2015-10-28T21:15:38Z","abstract_excerpt":"We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\\mathbb{R}^{3}$. We determine all ruled surfaces and all relative normalizations for which the Laplace normal image degenerates into a point or into a curve. Moreover, we study the Laplace normal image of a non-conoidal ruled surface whose relative normals lie on the asymptotic plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08489","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":"2026-05-18T01:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITgxiZxBIYwUPZ5fwplTwu5BJZ49Ks7Xt0jlZ0msGNjjpO64kWUUG8Ps+MeVx4MY99eFUVSu9Lqnmdg53ZGWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:06:47.569031Z"},"content_sha256":"a3de7fc6b83128ce548330f8d0da33d08e5ca722b30860a210ef55487c9d2a0d","schema_version":"1.0","event_id":"sha256:a3de7fc6b83128ce548330f8d0da33d08e5ca722b30860a210ef55487c9d2a0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTD6Z77S3UE77QCQQGTVWCND5O/bundle.json","state_url":"https://pith.science/pith/UTD6Z77S3UE77QCQQGTVWCND5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTD6Z77S3UE77QCQQGTVWCND5O/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":"2026-06-23T22:06:47Z","links":{"resolver":"https://pith.science/pith/UTD6Z77S3UE77QCQQGTVWCND5O","bundle":"https://pith.science/pith/UTD6Z77S3UE77QCQQGTVWCND5O/bundle.json","state":"https://pith.science/pith/UTD6Z77S3UE77QCQQGTVWCND5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTD6Z77S3UE77QCQQGTVWCND5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UTD6Z77S3UE77QCQQGTVWCND5O","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":"4a259eb159478416d68f21d3397fb51520ae070da1b94c717d3d45c5a15b4c77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T21:15:38Z","title_canon_sha256":"121642cc29f7dc79fb7dd9fea9f088260af24c2a7980160a5054db897a8b8f05"},"schema_version":"1.0","source":{"id":"1510.08489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08489","created_at":"2026-05-18T01:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08489v1","created_at":"2026-05-18T01:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08489","created_at":"2026-05-18T01:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"UTD6Z77S3UE7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UTD6Z77S3UE77QCQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UTD6Z77S","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:a3de7fc6b83128ce548330f8d0da33d08e5ca722b30860a210ef55487c9d2a0d","target":"graph","created_at":"2026-05-18T01:19:01Z","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 consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\\mathbb{R}^{3}$. We determine all ruled surfaces and all relative normalizations for which the Laplace normal image degenerates into a point or into a curve. Moreover, we study the Laplace normal image of a non-conoidal ruled surface whose relative normals lie on the asymptotic plane.","authors_text":"Stylianos Stamatakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T21:15:38Z","title":"On the Laplace Normal Vector Field of Skew Ruled Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08489","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":"sha256:472e4e6fd58937b6919b9320d6ede3d7751c083cd5f95207cdbcd75e1278a476","target":"record","created_at":"2026-05-18T01:19:01Z","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":"4a259eb159478416d68f21d3397fb51520ae070da1b94c717d3d45c5a15b4c77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-28T21:15:38Z","title_canon_sha256":"121642cc29f7dc79fb7dd9fea9f088260af24c2a7980160a5054db897a8b8f05"},"schema_version":"1.0","source":{"id":"1510.08489","kind":"arxiv","version":1}},"canonical_sha256":"a4c7ecfff2dd09ffc05081a75b09a3eba1a3167351b55aa92191033e8808c12e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4c7ecfff2dd09ffc05081a75b09a3eba1a3167351b55aa92191033e8808c12e","first_computed_at":"2026-05-18T01:19:01.808683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:01.808683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"exZDBkGnuphL05qH1uGl5Skk0fyKNCxU7bxRLZCyNgP7UMIH6ayzbTm/enw8qqWgHcnU8w916hcQaZdb4B0IAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:01.809155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:472e4e6fd58937b6919b9320d6ede3d7751c083cd5f95207cdbcd75e1278a476","sha256:a3de7fc6b83128ce548330f8d0da33d08e5ca722b30860a210ef55487c9d2a0d"],"state_sha256":"33637a8409bc99d7e4b14c853aec0d7ad896260ab92024f0b9d2819864922252"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jgk/NlT06Ix8frq4/nO2M0ZR7Aivh/DM/HxxDkmk7IIc52e+2r46tGAePk0CcfyQszJflvk7Zo0nqC4BAYnnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:06:47.570931Z","bundle_sha256":"f50a351a708ba236cb6c30eafe4d3dcb5aa929ec934ab0cf48ea1b1737283b85"}}