{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B4HUAGMQDFHL5LPRL3I7KTATJI","short_pith_number":"pith:B4HUAGMQ","canonical_record":{"source":{"id":"1402.6112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-25T10:04:21Z","cross_cats_sorted":[],"title_canon_sha256":"f9c68687805182bccea46671d59f145004723f3970637c4712362b141dc29d8e","abstract_canon_sha256":"eca8cf85ff9200b9233ce08629640b89346c9c5e02102baf54d1d1d6c9ab9415"},"schema_version":"1.0"},"canonical_sha256":"0f0f401990194ebeadf15ed1f54c134a1fd78afcfe63865c25f1937cce124c67","source":{"kind":"arxiv","id":"1402.6112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6112","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6112v1","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6112","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"pith_short_12","alias_value":"B4HUAGMQDFHL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4HUAGMQDFHL5LPR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4HUAGMQ","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B4HUAGMQDFHL5LPRL3I7KTATJI","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-25T10:04:21Z","cross_cats_sorted":[],"title_canon_sha256":"f9c68687805182bccea46671d59f145004723f3970637c4712362b141dc29d8e","abstract_canon_sha256":"eca8cf85ff9200b9233ce08629640b89346c9c5e02102baf54d1d1d6c9ab9415"},"schema_version":"1.0"},"canonical_sha256":"0f0f401990194ebeadf15ed1f54c134a1fd78afcfe63865c25f1937cce124c67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:05.367996Z","signature_b64":"XS0iJ/f5jAy9YsmZc+LSG5nodJGouMfaLhjbFfxcbXziCHTTaQZE0SNtacrKSIIdFdUn1l9Qa4gdH7D9OkYDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f0f401990194ebeadf15ed1f54c134a1fd78afcfe63865c25f1937cce124c67","last_reissued_at":"2026-05-18T01:11:05.367562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:05.367562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6112","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":"2026-05-18T01:11:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f4eE4EDgyFsTLdcrrWTYeP2fwLXLZx7C16wY+B/r1hfkVtPURFsgbcX7DVr+9l7/FCgiyAZZx41fukPIHi3UAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:42:25.772090Z"},"content_sha256":"7ceee37bd4efbd3fb06c07a8a36cf321c0207c3e3e0f3b3684ed7ca42ac3aa9a","schema_version":"1.0","event_id":"sha256:7ceee37bd4efbd3fb06c07a8a36cf321c0207c3e3e0f3b3684ed7ca42ac3aa9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B4HUAGMQDFHL5LPRL3I7KTATJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Meridian Surfaces of Elliptic or Hyperbolic Type in the Four-dimensional Minkowski Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Georgi Ganchev, Velichka Milousheva","submitted_at":"2014-02-25T10:04:21Z","abstract_excerpt":"We consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. We call these surfaces meridian surfaces of elliptic or hyperbolic type, respectively.\n  On the base of our invariant theory of surfaces we study meridian surfaces with special invariants and give the complete classification of the meridian surfaces with constant Gauss curvature or constant mean curvature. We also classify the Chen meridian surfaces and the meridian surfaces with parallel normal bundle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6112","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":"2026-05-18T01:11:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VdcemiCLh6L+lpaZYLfGFU64O691NDoqa8G2icG3Dg/V+txWjjEUZvKIue/2Fl0hvA6+0mCqXhFrsuV7MVu9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:42:25.772817Z"},"content_sha256":"0099dadffb42c602d81c74a95929965e837682b745a61c153a4487135061705a","schema_version":"1.0","event_id":"sha256:0099dadffb42c602d81c74a95929965e837682b745a61c153a4487135061705a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4HUAGMQDFHL5LPRL3I7KTATJI/bundle.json","state_url":"https://pith.science/pith/B4HUAGMQDFHL5LPRL3I7KTATJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4HUAGMQDFHL5LPRL3I7KTATJI/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":"2026-06-11T18:42:25Z","links":{"resolver":"https://pith.science/pith/B4HUAGMQDFHL5LPRL3I7KTATJI","bundle":"https://pith.science/pith/B4HUAGMQDFHL5LPRL3I7KTATJI/bundle.json","state":"https://pith.science/pith/B4HUAGMQDFHL5LPRL3I7KTATJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4HUAGMQDFHL5LPRL3I7KTATJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B4HUAGMQDFHL5LPRL3I7KTATJI","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":"eca8cf85ff9200b9233ce08629640b89346c9c5e02102baf54d1d1d6c9ab9415","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-25T10:04:21Z","title_canon_sha256":"f9c68687805182bccea46671d59f145004723f3970637c4712362b141dc29d8e"},"schema_version":"1.0","source":{"id":"1402.6112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6112","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6112v1","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6112","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"pith_short_12","alias_value":"B4HUAGMQDFHL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4HUAGMQDFHL5LPR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4HUAGMQ","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:0099dadffb42c602d81c74a95929965e837682b745a61c153a4487135061705a","target":"graph","created_at":"2026-05-18T01:11:05Z","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 a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. We call these surfaces meridian surfaces of elliptic or hyperbolic type, respectively.\n  On the base of our invariant theory of surfaces we study meridian surfaces with special invariants and give the complete classification of the meridian surfaces with constant Gauss curvature or constant mean curvature. We also classify the Chen meridian surfaces and the meridian surfaces with parallel normal bundle.","authors_text":"Georgi Ganchev, Velichka Milousheva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-25T10:04:21Z","title":"Meridian Surfaces of Elliptic or Hyperbolic Type in the Four-dimensional Minkowski Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6112","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":"sha256:7ceee37bd4efbd3fb06c07a8a36cf321c0207c3e3e0f3b3684ed7ca42ac3aa9a","target":"record","created_at":"2026-05-18T01:11:05Z","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":"eca8cf85ff9200b9233ce08629640b89346c9c5e02102baf54d1d1d6c9ab9415","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-25T10:04:21Z","title_canon_sha256":"f9c68687805182bccea46671d59f145004723f3970637c4712362b141dc29d8e"},"schema_version":"1.0","source":{"id":"1402.6112","kind":"arxiv","version":1}},"canonical_sha256":"0f0f401990194ebeadf15ed1f54c134a1fd78afcfe63865c25f1937cce124c67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f0f401990194ebeadf15ed1f54c134a1fd78afcfe63865c25f1937cce124c67","first_computed_at":"2026-05-18T01:11:05.367562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:05.367562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XS0iJ/f5jAy9YsmZc+LSG5nodJGouMfaLhjbFfxcbXziCHTTaQZE0SNtacrKSIIdFdUn1l9Qa4gdH7D9OkYDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:05.367996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ceee37bd4efbd3fb06c07a8a36cf321c0207c3e3e0f3b3684ed7ca42ac3aa9a","sha256:0099dadffb42c602d81c74a95929965e837682b745a61c153a4487135061705a"],"state_sha256":"c51d7dc3e263e59b6f2e4993b26555f0e5aca590419150ef28e20841dffc66ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uljNOfEEV26rS+6H8S3fYQzx1xTmfBF2wVKn/uNqSoWRLi+QVO+qjMlEOKzm9mT+vDvrwB4r1gP4I7w76kv9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T18:42:25.776714Z","bundle_sha256":"4cee9bac451b4517f84f866cef1e43cd617045dbbbf3fc8c0c339ce76552ff89"}}