{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:U4TQX5LVRULYWZ5FSRYISE2UME","short_pith_number":"pith:U4TQX5LV","canonical_record":{"source":{"id":"1606.08479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T20:31:06Z","cross_cats_sorted":[],"title_canon_sha256":"4b3649fe3e6a6e9466baa715be55e9858425a11ad4ab23b4fa6e458d4dd27232","abstract_canon_sha256":"f4e013949a8fe1e675d342b33eec971850b14c5f9cbecdc43279789ff887a468"},"schema_version":"1.0"},"canonical_sha256":"a7270bf5758d178b67a59470891354612c422c640564276b4909b79889047e3f","source":{"kind":"arxiv","id":"1606.08479","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08479","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08479v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08479","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"U4TQX5LVRULY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U4TQX5LVRULYWZ5F","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U4TQX5LV","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:U4TQX5LVRULYWZ5FSRYISE2UME","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T20:31:06Z","cross_cats_sorted":[],"title_canon_sha256":"4b3649fe3e6a6e9466baa715be55e9858425a11ad4ab23b4fa6e458d4dd27232","abstract_canon_sha256":"f4e013949a8fe1e675d342b33eec971850b14c5f9cbecdc43279789ff887a468"},"schema_version":"1.0"},"canonical_sha256":"a7270bf5758d178b67a59470891354612c422c640564276b4909b79889047e3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:47.605812Z","signature_b64":"Cz8yuBDOFylFVrmOnWxGXm3Tat7zYP/OzUON5rbfIWXelLv13H8U6PlzzceP9GAaFuojJcJpFfXrvMzlnxdsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7270bf5758d178b67a59470891354612c422c640564276b4909b79889047e3f","last_reissued_at":"2026-05-18T01:11:47.605483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:47.605483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08479","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":"2026-05-18T01:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTI6ehyEKilJpL7h6L6+ErEl/xIq+uSFtFgirq2JhRHPAlZ/FbL60A2HGyfK6KTE8zR2HOtbVGhBNkmW1CPQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:31:58.911794Z"},"content_sha256":"e4469910d420d5769b846df48a2cb1eb01b3d97eec129300641cb5c6873dcc6d","schema_version":"1.0","event_id":"sha256:e4469910d420d5769b846df48a2cb1eb01b3d97eec129300641cb5c6873dcc6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:U4TQX5LVRULYWZ5FSRYISE2UME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classes of Weingarten Surfaces in S^2xR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Armando V Corro, Marcelo A. Souza, Romildo Pina","submitted_at":"2016-06-27T20:31:06Z","abstract_excerpt":"In this work we study surfaces in radial conformally flat spaces. We characterize surfaces of rotation with constant Gaussian and Extrinsic curvature in these radial 3-spaces. We prove that all the spheres in the conformal 3-space have constant Gaussian curvature  $K=1$  if, and only if, the conformal factor is special. In this special case we study geometric properties of this ambient 3-space, and as an application we prove that it is isometric to the space ${\\mathbb{S}}^2\\times {\\mathbb{R}}$, so we consider it as the {\\em Radial Model} of ${\\mathbb{S}}^2\\times {\\mathbb{R}}$.  We obtain  two "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08479","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":"2026-05-18T01:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wb1sW0Uf+wmeqidsTcpafpsTuTesEs9gtIh80o++TTtfSM3q44aNi2c8Tax66WuasqzkwiEG7DcKy1rMa04nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:31:58.912129Z"},"content_sha256":"8ba4312cd079eaf7e3155e20927acc4e1c18db519b609038ecc7f18d11c138ff","schema_version":"1.0","event_id":"sha256:8ba4312cd079eaf7e3155e20927acc4e1c18db519b609038ecc7f18d11c138ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4TQX5LVRULYWZ5FSRYISE2UME/bundle.json","state_url":"https://pith.science/pith/U4TQX5LVRULYWZ5FSRYISE2UME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4TQX5LVRULYWZ5FSRYISE2UME/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":"2026-06-24T06:31:58Z","links":{"resolver":"https://pith.science/pith/U4TQX5LVRULYWZ5FSRYISE2UME","bundle":"https://pith.science/pith/U4TQX5LVRULYWZ5FSRYISE2UME/bundle.json","state":"https://pith.science/pith/U4TQX5LVRULYWZ5FSRYISE2UME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4TQX5LVRULYWZ5FSRYISE2UME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U4TQX5LVRULYWZ5FSRYISE2UME","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":"f4e013949a8fe1e675d342b33eec971850b14c5f9cbecdc43279789ff887a468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T20:31:06Z","title_canon_sha256":"4b3649fe3e6a6e9466baa715be55e9858425a11ad4ab23b4fa6e458d4dd27232"},"schema_version":"1.0","source":{"id":"1606.08479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08479","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08479v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08479","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"U4TQX5LVRULY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U4TQX5LVRULYWZ5F","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U4TQX5LV","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:8ba4312cd079eaf7e3155e20927acc4e1c18db519b609038ecc7f18d11c138ff","target":"graph","created_at":"2026-05-18T01:11:47Z","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":"In this work we study surfaces in radial conformally flat spaces. We characterize surfaces of rotation with constant Gaussian and Extrinsic curvature in these radial 3-spaces. We prove that all the spheres in the conformal 3-space have constant Gaussian curvature  $K=1$  if, and only if, the conformal factor is special. In this special case we study geometric properties of this ambient 3-space, and as an application we prove that it is isometric to the space ${\\mathbb{S}}^2\\times {\\mathbb{R}}$, so we consider it as the {\\em Radial Model} of ${\\mathbb{S}}^2\\times {\\mathbb{R}}$.  We obtain  two ","authors_text":"Armando V Corro, Marcelo A. Souza, Romildo Pina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T20:31:06Z","title":"Classes of Weingarten Surfaces in S^2xR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08479","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:e4469910d420d5769b846df48a2cb1eb01b3d97eec129300641cb5c6873dcc6d","target":"record","created_at":"2026-05-18T01:11:47Z","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":"f4e013949a8fe1e675d342b33eec971850b14c5f9cbecdc43279789ff887a468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-27T20:31:06Z","title_canon_sha256":"4b3649fe3e6a6e9466baa715be55e9858425a11ad4ab23b4fa6e458d4dd27232"},"schema_version":"1.0","source":{"id":"1606.08479","kind":"arxiv","version":1}},"canonical_sha256":"a7270bf5758d178b67a59470891354612c422c640564276b4909b79889047e3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7270bf5758d178b67a59470891354612c422c640564276b4909b79889047e3f","first_computed_at":"2026-05-18T01:11:47.605483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:47.605483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cz8yuBDOFylFVrmOnWxGXm3Tat7zYP/OzUON5rbfIWXelLv13H8U6PlzzceP9GAaFuojJcJpFfXrvMzlnxdsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:47.605812Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4469910d420d5769b846df48a2cb1eb01b3d97eec129300641cb5c6873dcc6d","sha256:8ba4312cd079eaf7e3155e20927acc4e1c18db519b609038ecc7f18d11c138ff"],"state_sha256":"24f6838231fbd1b7881dc7abbbb5489148632cf3cd630a165f24a721f8366f2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O77Jpuac9ah1O8u7n5KITemfSQ5/Uw3+rzE1/ykbGv1/P/bPEGDRQk1Q635Mj7tJYPGUgUAh78WeFE8ZcAcTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:31:58.914037Z","bundle_sha256":"7bb7e13781a265e738ef756330eee70cc51b83fd7938784ecc2b8c2d2459e90c"}}