{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MJZD4KCFM23HQEQFOMV5ZL6MEC","short_pith_number":"pith:MJZD4KCF","canonical_record":{"source":{"id":"1205.6649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-30T12:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"694702be34a623da08c4b53c8a67f1538288873916585fae14f537257cb28530","abstract_canon_sha256":"b6d561305c6cc996de6f96a392ee1fd31318fcdc2962baa82f129c1904e0f4d3"},"schema_version":"1.0"},"canonical_sha256":"62723e284566b6781205732bdcafcc2096810b7a55ceb3e2fc4d9ee7a91629c6","source":{"kind":"arxiv","id":"1205.6649","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6649","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6649v1","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6649","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"MJZD4KCFM23H","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MJZD4KCFM23HQEQF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MJZD4KCF","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MJZD4KCFM23HQEQFOMV5ZL6MEC","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-30T12:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"694702be34a623da08c4b53c8a67f1538288873916585fae14f537257cb28530","abstract_canon_sha256":"b6d561305c6cc996de6f96a392ee1fd31318fcdc2962baa82f129c1904e0f4d3"},"schema_version":"1.0"},"canonical_sha256":"62723e284566b6781205732bdcafcc2096810b7a55ceb3e2fc4d9ee7a91629c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:38.314724Z","signature_b64":"Y2Tu9q7GF64jqfo5SRwVj+RJz1DcMZxaOVOduTSxjgN6L9pMd2muDw+forq05zbKhZVG0YL6gslJaKwoh2ojAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62723e284566b6781205732bdcafcc2096810b7a55ceb3e2fc4d9ee7a91629c6","last_reissued_at":"2026-05-18T03:54:38.314009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:38.314009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6649","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":"2026-05-18T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+b7Hyrg0J09+THINMJNoSIeSaBot/YUpO8AECrcXLrncCH6CuqT88fTawjrn0mGwRcb/DnC2PEejTFExRT9uAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:38:20.188731Z"},"content_sha256":"8641c8b16e56472c533e4bdac913635a5a9990c2bc54c76227c6572cd9455214","schema_version":"1.0","event_id":"sha256:8641c8b16e56472c533e4bdac913635a5a9990c2bc54c76227c6572cd9455214"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MJZD4KCFM23HQEQFOMV5ZL6MEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Similar Ruled Surfaces with Variable Transformations in Minkowski 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mehmet \\\"Onder","submitted_at":"2012-05-30T12:49:10Z","abstract_excerpt":"In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3 form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curves with variable transformation. Moreover, we obtain that cylindrical surfaces and conoids form two families of similar ruled surfaces in E_1^3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6649","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":"2026-05-18T03:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3o39faNzBF4m6eFkXRpEiQtPVw0Wn5mBpELmvA3IvJnZywKqecEfa9wVY2B9BOxa6cL6vkr5vvpedkbvYCQ1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:38:20.189074Z"},"content_sha256":"fb45b16e4e56632daf9c2fbdf4b2158c058b380b358fa0e2fe313817778ab68e","schema_version":"1.0","event_id":"sha256:fb45b16e4e56632daf9c2fbdf4b2158c058b380b358fa0e2fe313817778ab68e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC/bundle.json","state_url":"https://pith.science/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC/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":"2026-06-23T14:38:20Z","links":{"resolver":"https://pith.science/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC","bundle":"https://pith.science/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC/bundle.json","state":"https://pith.science/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJZD4KCFM23HQEQFOMV5ZL6MEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MJZD4KCFM23HQEQFOMV5ZL6MEC","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":"b6d561305c6cc996de6f96a392ee1fd31318fcdc2962baa82f129c1904e0f4d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-30T12:49:10Z","title_canon_sha256":"694702be34a623da08c4b53c8a67f1538288873916585fae14f537257cb28530"},"schema_version":"1.0","source":{"id":"1205.6649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6649","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6649v1","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6649","created_at":"2026-05-18T03:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"MJZD4KCFM23H","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MJZD4KCFM23HQEQF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MJZD4KCF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:fb45b16e4e56632daf9c2fbdf4b2158c058b380b358fa0e2fe313817778ab68e","target":"graph","created_at":"2026-05-18T03:54:38Z","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 study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3 form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curves with variable transformation. Moreover, we obtain that cylindrical surfaces and conoids form two families of similar ruled surfaces in E_1^3.","authors_text":"Mehmet \\\"Onder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-30T12:49:10Z","title":"Similar Ruled Surfaces with Variable Transformations in Minkowski 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6649","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":"sha256:8641c8b16e56472c533e4bdac913635a5a9990c2bc54c76227c6572cd9455214","target":"record","created_at":"2026-05-18T03:54:38Z","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":"b6d561305c6cc996de6f96a392ee1fd31318fcdc2962baa82f129c1904e0f4d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-30T12:49:10Z","title_canon_sha256":"694702be34a623da08c4b53c8a67f1538288873916585fae14f537257cb28530"},"schema_version":"1.0","source":{"id":"1205.6649","kind":"arxiv","version":1}},"canonical_sha256":"62723e284566b6781205732bdcafcc2096810b7a55ceb3e2fc4d9ee7a91629c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62723e284566b6781205732bdcafcc2096810b7a55ceb3e2fc4d9ee7a91629c6","first_computed_at":"2026-05-18T03:54:38.314009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:38.314009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y2Tu9q7GF64jqfo5SRwVj+RJz1DcMZxaOVOduTSxjgN6L9pMd2muDw+forq05zbKhZVG0YL6gslJaKwoh2ojAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:38.314724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8641c8b16e56472c533e4bdac913635a5a9990c2bc54c76227c6572cd9455214","sha256:fb45b16e4e56632daf9c2fbdf4b2158c058b380b358fa0e2fe313817778ab68e"],"state_sha256":"928d660b82a5a759b777ba5503283ef5366d84c32d78fe5a2ac687491b7d3ecb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HKEUc5J5BJ39BG0b+m0Xqv9Bm1MQVU7UM1mRAMJ252x6lfGh6k7MVyqkEOs1MmvtMq6HeWOOqdsFOFwp7Y60CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:38:20.191020Z","bundle_sha256":"a09a43a95647e7c77a52e91d3c2588b9ebfedb776d5404655ddb5fe196a14442"}}