{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4CEB55EWXTWZKR6YT3VK5PDYCV","short_pith_number":"pith:4CEB55EW","canonical_record":{"source":{"id":"1502.05708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-19T10:53:01Z","cross_cats_sorted":[],"title_canon_sha256":"44f38c0a330214302d2bdeccfca90444a2a1cdfee44e945ed9144eb5b43cef24","abstract_canon_sha256":"eb6ef576bf0593033af510aeae81293fbe5ee32dc3d9a9d40282f688deb505bb"},"schema_version":"1.0"},"canonical_sha256":"e0881ef496bced9547d89eeaaebc78155030e6e8ec8228bf96529d33d8d9d96d","source":{"kind":"arxiv","id":"1502.05708","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05708","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05708v2","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05708","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"4CEB55EWXTWZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4CEB55EWXTWZKR6Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4CEB55EW","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4CEB55EWXTWZKR6YT3VK5PDYCV","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-19T10:53:01Z","cross_cats_sorted":[],"title_canon_sha256":"44f38c0a330214302d2bdeccfca90444a2a1cdfee44e945ed9144eb5b43cef24","abstract_canon_sha256":"eb6ef576bf0593033af510aeae81293fbe5ee32dc3d9a9d40282f688deb505bb"},"schema_version":"1.0"},"canonical_sha256":"e0881ef496bced9547d89eeaaebc78155030e6e8ec8228bf96529d33d8d9d96d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:44.444095Z","signature_b64":"SyVR3tXnX8Vs7tAgDvqelairbRTYA9nbZ+br6DDYni1eF+VwlcwsClZGv/FPUTPlFoF7yQbYq3ZWvBapCLBIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0881ef496bced9547d89eeaaebc78155030e6e8ec8228bf96529d33d8d9d96d","last_reissued_at":"2026-05-18T00:57:44.443498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:44.443498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05708","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27awPiBfZ3leSo9gcGQ5NO0sNhBPB2P8w4DN114PFDvQ4s/ujkrASnbqzK7Ea1G2ppwBEBbZ6MGcui5f9byWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:42:11.281622Z"},"content_sha256":"7f8f16e10a72ba34f45f6211420de5591a14405cb411516798962e917ea35e70","schema_version":"1.0","event_id":"sha256:7f8f16e10a72ba34f45f6211420de5591a14405cb411516798962e917ea35e70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4CEB55EWXTWZKR6YT3VK5PDYCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Bour's theorem in Minkowski 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Erhan G\\\"uler, Yusuf Yayl{\\i}","submitted_at":"2015-02-19T10:53:01Z","abstract_excerpt":"We obtain isometric minimal helicoidal and rotational surfaces using generalized Bour's theorem in three dimensional Minkowski space. In addition, we show that the surfaces preserve minimality when their Gauss maps identically equal, choosing any diffentiable functions on the profile curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05708","kind":"arxiv","version":2},"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":"2026-05-18T00:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ykKW81Mk0lObqN7SPHJgi3ER7TinjZVinu7oBOKVKsA2ILyZzEKzJlDNdscIEOC1WZdljGiTEimmhUk6advBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:42:11.281965Z"},"content_sha256":"76bb0d944d9dd0bdb3fe35abcd945f5ee8bdfc7d60390c62a442027b16d07531","schema_version":"1.0","event_id":"sha256:76bb0d944d9dd0bdb3fe35abcd945f5ee8bdfc7d60390c62a442027b16d07531"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CEB55EWXTWZKR6YT3VK5PDYCV/bundle.json","state_url":"https://pith.science/pith/4CEB55EWXTWZKR6YT3VK5PDYCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CEB55EWXTWZKR6YT3VK5PDYCV/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":"2026-06-02T20:42:11Z","links":{"resolver":"https://pith.science/pith/4CEB55EWXTWZKR6YT3VK5PDYCV","bundle":"https://pith.science/pith/4CEB55EWXTWZKR6YT3VK5PDYCV/bundle.json","state":"https://pith.science/pith/4CEB55EWXTWZKR6YT3VK5PDYCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CEB55EWXTWZKR6YT3VK5PDYCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4CEB55EWXTWZKR6YT3VK5PDYCV","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":"eb6ef576bf0593033af510aeae81293fbe5ee32dc3d9a9d40282f688deb505bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-19T10:53:01Z","title_canon_sha256":"44f38c0a330214302d2bdeccfca90444a2a1cdfee44e945ed9144eb5b43cef24"},"schema_version":"1.0","source":{"id":"1502.05708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05708","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05708v2","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05708","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"4CEB55EWXTWZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4CEB55EWXTWZKR6Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4CEB55EW","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:76bb0d944d9dd0bdb3fe35abcd945f5ee8bdfc7d60390c62a442027b16d07531","target":"graph","created_at":"2026-05-18T00:57:44Z","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 isometric minimal helicoidal and rotational surfaces using generalized Bour's theorem in three dimensional Minkowski space. In addition, we show that the surfaces preserve minimality when their Gauss maps identically equal, choosing any diffentiable functions on the profile curve.","authors_text":"Erhan G\\\"uler, Yusuf Yayl{\\i}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-19T10:53:01Z","title":"Generalized Bour's theorem in Minkowski 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05708","kind":"arxiv","version":2},"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":"sha256:7f8f16e10a72ba34f45f6211420de5591a14405cb411516798962e917ea35e70","target":"record","created_at":"2026-05-18T00:57:44Z","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":"eb6ef576bf0593033af510aeae81293fbe5ee32dc3d9a9d40282f688deb505bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-19T10:53:01Z","title_canon_sha256":"44f38c0a330214302d2bdeccfca90444a2a1cdfee44e945ed9144eb5b43cef24"},"schema_version":"1.0","source":{"id":"1502.05708","kind":"arxiv","version":2}},"canonical_sha256":"e0881ef496bced9547d89eeaaebc78155030e6e8ec8228bf96529d33d8d9d96d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0881ef496bced9547d89eeaaebc78155030e6e8ec8228bf96529d33d8d9d96d","first_computed_at":"2026-05-18T00:57:44.443498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:44.443498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SyVR3tXnX8Vs7tAgDvqelairbRTYA9nbZ+br6DDYni1eF+VwlcwsClZGv/FPUTPlFoF7yQbYq3ZWvBapCLBIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:44.444095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f8f16e10a72ba34f45f6211420de5591a14405cb411516798962e917ea35e70","sha256:76bb0d944d9dd0bdb3fe35abcd945f5ee8bdfc7d60390c62a442027b16d07531"],"state_sha256":"052e65f96088f5ff1400fec2519507b43f4bfe6f088670f4bdcdf7160aa5cb66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iMgGGhspB3Ae3G1CKDsg5s+Nt+rkDMc1ly8RmKs6EEZLsVhgrv2j0xELefJM/6qgdCR1CascqZWVzbRwShuUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:42:11.284009Z","bundle_sha256":"cccbc29bfefe11764d8409779fad9d1bc3cff54da6cd58d51050754f4ec5a7c8"}}