{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6U3Q6EVFF7DIFA6QG4UJPMQHIB","short_pith_number":"pith:6U3Q6EVF","canonical_record":{"source":{"id":"1705.10090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T09:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"1befb3073e6512b956234e5879348fae1829ec41e1a799c8329ec605204f2922","abstract_canon_sha256":"10de198be4305e425508359d1c3ae955c62abf8e9219623d58794eb715a94be2"},"schema_version":"1.0"},"canonical_sha256":"f5370f12a52fc68283d0372897b2074041bea04aeb92a32b9e768f4f013ba890","source":{"kind":"arxiv","id":"1705.10090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10090","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10090v1","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10090","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"6U3Q6EVFF7DI","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6U3Q6EVFF7DIFA6Q","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6U3Q6EVF","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6U3Q6EVFF7DIFA6QG4UJPMQHIB","target":"record","payload":{"canonical_record":{"source":{"id":"1705.10090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T09:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"1befb3073e6512b956234e5879348fae1829ec41e1a799c8329ec605204f2922","abstract_canon_sha256":"10de198be4305e425508359d1c3ae955c62abf8e9219623d58794eb715a94be2"},"schema_version":"1.0"},"canonical_sha256":"f5370f12a52fc68283d0372897b2074041bea04aeb92a32b9e768f4f013ba890","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:31.984692Z","signature_b64":"N56BWI09EvH9n9wNcvL3U52fjtrFCjDvzoI0OMW9Ro9+yo4keGfmjeZ3Hzp0ksJr0qswBG1SsS25317Ay5D6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5370f12a52fc68283d0372897b2074041bea04aeb92a32b9e768f4f013ba890","last_reissued_at":"2026-05-18T00:43:31.984229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:31.984229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.10090","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":"2026-05-18T00:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UckHTZ5rUZoJxMuGLzkzydYhiPNXmfADL6vv2vuhbmBFZbd+C5KthIaUB7dtOmTgE1bdzWwC+tuHpnhMcAHTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:31:35.304883Z"},"content_sha256":"4fd0c7430def5f3496720ec3a6a9418f98a89d400b513bb8f5da90e8913870f2","schema_version":"1.0","event_id":"sha256:4fd0c7430def5f3496720ec3a6a9418f98a89d400b513bb8f5da90e8913870f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6U3Q6EVFF7DIFA6QG4UJPMQHIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant angle surfaces in Lorentzian Berger spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Apoena Passos Passamani, Irene I. Onnis, Paola Piu","submitted_at":"2017-05-29T09:38:03Z","abstract_excerpt":"In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere $\\s_{\\varepsilon}^3$, that is the three-dimensional sphere endowed with a $1$-parameter family of Lorentzian metrics, obtained by deforming the round metric on $\\s^3$ along the fibers of the Hopf fibration $\\s^3\\to \\s^2({1}/{2})$ by $-\\varepsilon^2$. Our main result provides a characterization of the helix surfaces in $\\s_{\\varepsilon}^3$ using the symmetries of the ambient space and a general helix in $\\s_{\\varepsilon}^3$, with axis the infinitesimal generator of the Hopf fibers. Also, we construct so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10090","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":"2026-05-18T00:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GWuSnqusfieHBs/E8tSSVBw/DaQGxSotlOKxjCOvdbl7uTU+wuCCigXD7rQDHke0PrxPFIDh8Yah2OLF5AdaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:31:35.305614Z"},"content_sha256":"b520dd69b21d95fe2acf90b21385ee72709430a4fd9501b0bee753af386187be","schema_version":"1.0","event_id":"sha256:b520dd69b21d95fe2acf90b21385ee72709430a4fd9501b0bee753af386187be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB/bundle.json","state_url":"https://pith.science/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB/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":"2026-06-06T20:31:35Z","links":{"resolver":"https://pith.science/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB","bundle":"https://pith.science/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB/bundle.json","state":"https://pith.science/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6U3Q6EVFF7DIFA6QG4UJPMQHIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6U3Q6EVFF7DIFA6QG4UJPMQHIB","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":"10de198be4305e425508359d1c3ae955c62abf8e9219623d58794eb715a94be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T09:38:03Z","title_canon_sha256":"1befb3073e6512b956234e5879348fae1829ec41e1a799c8329ec605204f2922"},"schema_version":"1.0","source":{"id":"1705.10090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10090","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10090v1","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10090","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"6U3Q6EVFF7DI","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6U3Q6EVFF7DIFA6Q","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6U3Q6EVF","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:b520dd69b21d95fe2acf90b21385ee72709430a4fd9501b0bee753af386187be","target":"graph","created_at":"2026-05-18T00:43:31Z","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 helix spacelike and timelike surfaces in the Lorentzian Berger sphere $\\s_{\\varepsilon}^3$, that is the three-dimensional sphere endowed with a $1$-parameter family of Lorentzian metrics, obtained by deforming the round metric on $\\s^3$ along the fibers of the Hopf fibration $\\s^3\\to \\s^2({1}/{2})$ by $-\\varepsilon^2$. Our main result provides a characterization of the helix surfaces in $\\s_{\\varepsilon}^3$ using the symmetries of the ambient space and a general helix in $\\s_{\\varepsilon}^3$, with axis the infinitesimal generator of the Hopf fibers. Also, we construct so","authors_text":"Apoena Passos Passamani, Irene I. Onnis, Paola Piu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T09:38:03Z","title":"Constant angle surfaces in Lorentzian Berger spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10090","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":"sha256:4fd0c7430def5f3496720ec3a6a9418f98a89d400b513bb8f5da90e8913870f2","target":"record","created_at":"2026-05-18T00:43:31Z","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":"10de198be4305e425508359d1c3ae955c62abf8e9219623d58794eb715a94be2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-29T09:38:03Z","title_canon_sha256":"1befb3073e6512b956234e5879348fae1829ec41e1a799c8329ec605204f2922"},"schema_version":"1.0","source":{"id":"1705.10090","kind":"arxiv","version":1}},"canonical_sha256":"f5370f12a52fc68283d0372897b2074041bea04aeb92a32b9e768f4f013ba890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5370f12a52fc68283d0372897b2074041bea04aeb92a32b9e768f4f013ba890","first_computed_at":"2026-05-18T00:43:31.984229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:31.984229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N56BWI09EvH9n9wNcvL3U52fjtrFCjDvzoI0OMW9Ro9+yo4keGfmjeZ3Hzp0ksJr0qswBG1SsS25317Ay5D6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:31.984692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fd0c7430def5f3496720ec3a6a9418f98a89d400b513bb8f5da90e8913870f2","sha256:b520dd69b21d95fe2acf90b21385ee72709430a4fd9501b0bee753af386187be"],"state_sha256":"e0596b7a405e1e68eb62ec20cfb19a3d9795a3740a14b8f7e33fbfbbffc10099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dbPLNZMPoKceawFh8Q0w6mGlzeif8vynGGCCivTpjqUtoWR1CpAEjfZM4reLZttKqvVUOSihtervuJNBM6lgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:31:35.309993Z","bundle_sha256":"e521b09c4b3b315bb195d78486ece79a8013b7cabce56fb8b832e7e201f6444b"}}