{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HCWJ3XCCJHC456UXKOZBJTJQ72","short_pith_number":"pith:HCWJ3XCC","canonical_record":{"source":{"id":"1111.3148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T09:20:36Z","cross_cats_sorted":[],"title_canon_sha256":"1973ae26504dd421916a7b108952deaf37d708a17d966c2c3db16f84c1793a91","abstract_canon_sha256":"ba8b3ba558f4b2ac10a06441d2527e2394271c305c4e600a9e0d5f94d1237a2f"},"schema_version":"1.0"},"canonical_sha256":"38ac9ddc4249c5cefa9753b214cd30feb81756aa73889a6b4308d0458cc1275e","source":{"kind":"arxiv","id":"1111.3148","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3148","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3148v1","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3148","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"HCWJ3XCCJHC4","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCWJ3XCCJHC456UX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCWJ3XCC","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HCWJ3XCCJHC456UXKOZBJTJQ72","target":"record","payload":{"canonical_record":{"source":{"id":"1111.3148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T09:20:36Z","cross_cats_sorted":[],"title_canon_sha256":"1973ae26504dd421916a7b108952deaf37d708a17d966c2c3db16f84c1793a91","abstract_canon_sha256":"ba8b3ba558f4b2ac10a06441d2527e2394271c305c4e600a9e0d5f94d1237a2f"},"schema_version":"1.0"},"canonical_sha256":"38ac9ddc4249c5cefa9753b214cd30feb81756aa73889a6b4308d0458cc1275e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:22.904475Z","signature_b64":"RbJhWxv0rS+8AhyNTk7t0MpAlTpL4F7Ru1e6whYs0xGQX6p3zH3o/1taWwFq5d3+5cEiG1f02lMO/SnMD9dvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38ac9ddc4249c5cefa9753b214cd30feb81756aa73889a6b4308d0458cc1275e","last_reissued_at":"2026-05-18T04:08:22.903907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:22.903907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.3148","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":"2026-05-18T04:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"voKHHQafZI6zAmQtwc3qbxWzk/R1dh4Q7xnmjujLwvlrgOCSCi87tlRwqqFhw/s/2A8q/SxhIPxu6J9TC7hECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:10:33.776644Z"},"content_sha256":"fffbde5268d6971c3d696ad49b4b598b2c81d1e3080e5c91aa4b4e39d7c04d81","schema_version":"1.0","event_id":"sha256:fffbde5268d6971c3d696ad49b4b598b2c81d1e3080e5c91aa4b4e39d7c04d81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HCWJ3XCCJHC456UXKOZBJTJQ72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Dual Timelike Mannheim Partner Curves in D3 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ozcan Bektas, Suleyman Senyurt","submitted_at":"2011-11-14T09:20:36Z","abstract_excerpt":"The first aim of this paper is to define the dual timelike Mannheim partner curves in Dual Lorentzian Space D3 1, the second aim of this paper is to obtain the relationships between the curvatures and the torsions of the dual timelike Mannheim partner curves with respect to each other and the final aim of this paper is to get the necessary and sufficient conditions for the dual timelike Mannheim partner curves in D3 1 ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3148","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":"2026-05-18T04:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vOCnQxE1YTNmuSnhKpLxjq6gm3OXTIHO7TAOFW1WyJC4NEE9hhIayJw1ENNkcUkZvThIOrYvort7i15nKwxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:10:33.776982Z"},"content_sha256":"e58d23713798d9f2796fa387ce3c4365ff8ebb999652879bc9429a0a239ddde0","schema_version":"1.0","event_id":"sha256:e58d23713798d9f2796fa387ce3c4365ff8ebb999652879bc9429a0a239ddde0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCWJ3XCCJHC456UXKOZBJTJQ72/bundle.json","state_url":"https://pith.science/pith/HCWJ3XCCJHC456UXKOZBJTJQ72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCWJ3XCCJHC456UXKOZBJTJQ72/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":"2026-07-04T13:10:33Z","links":{"resolver":"https://pith.science/pith/HCWJ3XCCJHC456UXKOZBJTJQ72","bundle":"https://pith.science/pith/HCWJ3XCCJHC456UXKOZBJTJQ72/bundle.json","state":"https://pith.science/pith/HCWJ3XCCJHC456UXKOZBJTJQ72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCWJ3XCCJHC456UXKOZBJTJQ72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HCWJ3XCCJHC456UXKOZBJTJQ72","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":"ba8b3ba558f4b2ac10a06441d2527e2394271c305c4e600a9e0d5f94d1237a2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T09:20:36Z","title_canon_sha256":"1973ae26504dd421916a7b108952deaf37d708a17d966c2c3db16f84c1793a91"},"schema_version":"1.0","source":{"id":"1111.3148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3148","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3148v1","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3148","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"HCWJ3XCCJHC4","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCWJ3XCCJHC456UX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCWJ3XCC","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e58d23713798d9f2796fa387ce3c4365ff8ebb999652879bc9429a0a239ddde0","target":"graph","created_at":"2026-05-18T04:08:22Z","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":"The first aim of this paper is to define the dual timelike Mannheim partner curves in Dual Lorentzian Space D3 1, the second aim of this paper is to obtain the relationships between the curvatures and the torsions of the dual timelike Mannheim partner curves with respect to each other and the final aim of this paper is to get the necessary and sufficient conditions for the dual timelike Mannheim partner curves in D3 1 .","authors_text":"Ozcan Bektas, Suleyman Senyurt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T09:20:36Z","title":"On Dual Timelike Mannheim Partner Curves in D3 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3148","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:fffbde5268d6971c3d696ad49b4b598b2c81d1e3080e5c91aa4b4e39d7c04d81","target":"record","created_at":"2026-05-18T04:08:22Z","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":"ba8b3ba558f4b2ac10a06441d2527e2394271c305c4e600a9e0d5f94d1237a2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T09:20:36Z","title_canon_sha256":"1973ae26504dd421916a7b108952deaf37d708a17d966c2c3db16f84c1793a91"},"schema_version":"1.0","source":{"id":"1111.3148","kind":"arxiv","version":1}},"canonical_sha256":"38ac9ddc4249c5cefa9753b214cd30feb81756aa73889a6b4308d0458cc1275e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38ac9ddc4249c5cefa9753b214cd30feb81756aa73889a6b4308d0458cc1275e","first_computed_at":"2026-05-18T04:08:22.903907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:22.903907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RbJhWxv0rS+8AhyNTk7t0MpAlTpL4F7Ru1e6whYs0xGQX6p3zH3o/1taWwFq5d3+5cEiG1f02lMO/SnMD9dvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:22.904475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fffbde5268d6971c3d696ad49b4b598b2c81d1e3080e5c91aa4b4e39d7c04d81","sha256:e58d23713798d9f2796fa387ce3c4365ff8ebb999652879bc9429a0a239ddde0"],"state_sha256":"9ae57d48d45421c6ff989c0c119df7b01844cf3e472370f4d0b03cfe57e63e41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkRiF3dRwjvRXYrgdM7jZ9VGJjIpXK156LhaL+N08bytkyLMSEdt7PlIqfXwMmlpTrPFdjc9cClodUOMRs7TDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T13:10:33.778809Z","bundle_sha256":"4019e251e67a98fa7f725bc596f036500c2bb429a27a63796d3b08e2ee2a54f9"}}