{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:57Z73SBE3ROM246UHD5I3RNOMQ","short_pith_number":"pith:57Z73SBE","canonical_record":{"source":{"id":"1812.08676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-20T16:25:24Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"bd3bf5314b2939687f8531debc9ef34a13e807e343e166b29abf6825e7d4f9e3","abstract_canon_sha256":"f0f7cdeb10c73052cf2a589af1dd0493e7ac8292f6da24f0ecf7a3afc6282cac"},"schema_version":"1.0"},"canonical_sha256":"eff3fdc824dc5ccd73d438fa8dc5ae643ff47c3fe9b73af40d987f7a7a99dda0","source":{"kind":"arxiv","id":"1812.08676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08676","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08676v1","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08676","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"57Z73SBE3ROM","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"57Z73SBE3ROM246U","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"57Z73SBE","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:57Z73SBE3ROM246UHD5I3RNOMQ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.08676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-20T16:25:24Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"bd3bf5314b2939687f8531debc9ef34a13e807e343e166b29abf6825e7d4f9e3","abstract_canon_sha256":"f0f7cdeb10c73052cf2a589af1dd0493e7ac8292f6da24f0ecf7a3afc6282cac"},"schema_version":"1.0"},"canonical_sha256":"eff3fdc824dc5ccd73d438fa8dc5ae643ff47c3fe9b73af40d987f7a7a99dda0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:49.399959Z","signature_b64":"dgnDoLmPwJaOmbBJSFKk3JQ6tbzwEB2efBxi45v2T00MX9oN1iWM1PEYu8Wd7YGakdkUUXv3fEbp6+rsBBkrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eff3fdc824dc5ccd73d438fa8dc5ae643ff47c3fe9b73af40d987f7a7a99dda0","last_reissued_at":"2026-05-17T23:57:49.399404Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:49.399404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.08676","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":"2026-05-17T23:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YOcogqgVauVfEcrjBL7hKmS3rgR88qaXeYfz1iCAEtU7dnCFn7CejkgBWJbE8dRwVwNRbEl9wYrKICLF8IoGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:53:31.552236Z"},"content_sha256":"bd6d28bcc0ec174914f720e1ea1031ae0dd83ef66b226accfb74092c3f6898e3","schema_version":"1.0","event_id":"sha256:bd6d28bcc0ec174914f720e1ea1031ae0dd83ef66b226accfb74092c3f6898e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:57Z73SBE3ROM246UHD5I3RNOMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rotational Surfaces with second fundamental form of constant length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Alexandre P. Barreto, Francisco Fontenele, Luiz Hartmann","submitted_at":"2018-12-20T16:25:24Z","abstract_excerpt":"We obtain an infinite family of complete non embedded rotational surfaces in $\\mathbb R^3$ whose second fundamental forms have length equal to one at any point. Also we prove that a complete rotational surface with second fundamental form of constant length is either a round sphere, a circular cylinder or, up to a homothety and a rigid motion, a member of that family. In particular, the round sphere and the circular cylinder are the only complete embedded rotational surfaces in $\\mathbb R^3$ with second fundamental form of constant length."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08676","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":"2026-05-17T23:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zzof6rd12WJLSyY762X2s/B/ziYQD3FXt6xd5xCrIPQUZAEqArOhEbMsk9eAL7uZS/yRN9PHxg+Za6bxJP/cDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:53:31.552951Z"},"content_sha256":"1a7add4dd4b3bca59c8c4cd3908c384c530e35dc70adc568b2bd564ba4a1ec17","schema_version":"1.0","event_id":"sha256:1a7add4dd4b3bca59c8c4cd3908c384c530e35dc70adc568b2bd564ba4a1ec17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57Z73SBE3ROM246UHD5I3RNOMQ/bundle.json","state_url":"https://pith.science/pith/57Z73SBE3ROM246UHD5I3RNOMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57Z73SBE3ROM246UHD5I3RNOMQ/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":"2026-06-11T15:53:31Z","links":{"resolver":"https://pith.science/pith/57Z73SBE3ROM246UHD5I3RNOMQ","bundle":"https://pith.science/pith/57Z73SBE3ROM246UHD5I3RNOMQ/bundle.json","state":"https://pith.science/pith/57Z73SBE3ROM246UHD5I3RNOMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57Z73SBE3ROM246UHD5I3RNOMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:57Z73SBE3ROM246UHD5I3RNOMQ","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":"f0f7cdeb10c73052cf2a589af1dd0493e7ac8292f6da24f0ecf7a3afc6282cac","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-20T16:25:24Z","title_canon_sha256":"bd3bf5314b2939687f8531debc9ef34a13e807e343e166b29abf6825e7d4f9e3"},"schema_version":"1.0","source":{"id":"1812.08676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08676","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08676v1","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08676","created_at":"2026-05-17T23:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"57Z73SBE3ROM","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"57Z73SBE3ROM246U","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"57Z73SBE","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:1a7add4dd4b3bca59c8c4cd3908c384c530e35dc70adc568b2bd564ba4a1ec17","target":"graph","created_at":"2026-05-17T23:57:49Z","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 an infinite family of complete non embedded rotational surfaces in $\\mathbb R^3$ whose second fundamental forms have length equal to one at any point. Also we prove that a complete rotational surface with second fundamental form of constant length is either a round sphere, a circular cylinder or, up to a homothety and a rigid motion, a member of that family. In particular, the round sphere and the circular cylinder are the only complete embedded rotational surfaces in $\\mathbb R^3$ with second fundamental form of constant length.","authors_text":"Alexandre P. Barreto, Francisco Fontenele, Luiz Hartmann","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-20T16:25:24Z","title":"Rotational Surfaces with second fundamental form of constant length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08676","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:bd6d28bcc0ec174914f720e1ea1031ae0dd83ef66b226accfb74092c3f6898e3","target":"record","created_at":"2026-05-17T23:57:49Z","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":"f0f7cdeb10c73052cf2a589af1dd0493e7ac8292f6da24f0ecf7a3afc6282cac","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-20T16:25:24Z","title_canon_sha256":"bd3bf5314b2939687f8531debc9ef34a13e807e343e166b29abf6825e7d4f9e3"},"schema_version":"1.0","source":{"id":"1812.08676","kind":"arxiv","version":1}},"canonical_sha256":"eff3fdc824dc5ccd73d438fa8dc5ae643ff47c3fe9b73af40d987f7a7a99dda0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eff3fdc824dc5ccd73d438fa8dc5ae643ff47c3fe9b73af40d987f7a7a99dda0","first_computed_at":"2026-05-17T23:57:49.399404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:49.399404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dgnDoLmPwJaOmbBJSFKk3JQ6tbzwEB2efBxi45v2T00MX9oN1iWM1PEYu8Wd7YGakdkUUXv3fEbp6+rsBBkrBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:49.399959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd6d28bcc0ec174914f720e1ea1031ae0dd83ef66b226accfb74092c3f6898e3","sha256:1a7add4dd4b3bca59c8c4cd3908c384c530e35dc70adc568b2bd564ba4a1ec17"],"state_sha256":"f51ac3ae7af3f1a9ccaa02067dc2ac451dbab365cf731479748ef94e523f66ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EY84F0q8KGavs5N6avhG64b4JBLCuno58J6MU0bPfLRZiUiMX57DjUyDgEOQlaDbKbDBr0TSnWzvFTl1gbmPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:53:31.556942Z","bundle_sha256":"4555c1110f0bbf1f9b9562ec7f005078204aa6dd4e4c3ea0e152c96d84cddc09"}}