{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C5VKWXKJJPCIWM4US4V3UH7LTT","short_pith_number":"pith:C5VKWXKJ","canonical_record":{"source":{"id":"1204.2890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-04-13T06:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"6c44512fc1e5b205be629b616826884b92719050c21793929750acacbf58d394","abstract_canon_sha256":"57624d70a1b4e8e771c177a3e28b006059f99c9f750949c1fc4daf4f4a9204a7"},"schema_version":"1.0"},"canonical_sha256":"176aab5d494bc48b3394972bba1feb9cc688b2e1fa5ace1bcaf14058fdfa7a0f","source":{"kind":"arxiv","id":"1204.2890","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2890","created_at":"2026-05-18T03:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2890v1","created_at":"2026-05-18T03:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2890","created_at":"2026-05-18T03:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"C5VKWXKJJPCI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C5VKWXKJJPCIWM4U","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C5VKWXKJ","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C5VKWXKJJPCIWM4US4V3UH7LTT","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-04-13T06:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"6c44512fc1e5b205be629b616826884b92719050c21793929750acacbf58d394","abstract_canon_sha256":"57624d70a1b4e8e771c177a3e28b006059f99c9f750949c1fc4daf4f4a9204a7"},"schema_version":"1.0"},"canonical_sha256":"176aab5d494bc48b3394972bba1feb9cc688b2e1fa5ace1bcaf14058fdfa7a0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:02.584737Z","signature_b64":"dqmZuVYLJFyaLOSqkIUIqN/Uib5vEP4C7itQ6lZEjLPuwb7SV34LrzaDPAaCiZclt8YZaOX0sRlEFSHzzwMAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"176aab5d494bc48b3394972bba1feb9cc688b2e1fa5ace1bcaf14058fdfa7a0f","last_reissued_at":"2026-05-18T03:58:02.584206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:02.584206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2890","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":"2026-05-18T03:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cksHLtw6nh6LPnCfW1RECepTe950LLSUdtUNYZiHvnjlP3SzKx3KEVVGFD4e1fSVVgLs67pnXqbtRlSS4W9XAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:27:48.780501Z"},"content_sha256":"e53893aa8283f7f6b28d36da84b26bbbd419bdcb3cf6bad1157690ed1095f13d","schema_version":"1.0","event_id":"sha256:e53893aa8283f7f6b28d36da84b26bbbd419bdcb3cf6bad1157690ed1095f13d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C5VKWXKJJPCIWM4US4V3UH7LTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The minimal surfaces over the slanted half-planes, vertical strips and single slit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Liulan Li, M. Vuorinen, S. Ponnusamy","submitted_at":"2012-04-13T06:28:31Z","abstract_excerpt":"In this paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings are obtained explicitly. Finally, we illustrate the harmonic mappings of each of these cases together with their minimal surfaces pictorially with the help of mathematica."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2890","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":"2026-05-18T03:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDATka9Cxt/FyvdZTh7UzuZbZKUzAtEChQkVTDUfwW9A6kjJvPDvTBkYlQ06xGkE8NKx5McilhB0vofSEHtHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:27:48.780845Z"},"content_sha256":"1ae2a4ee485abedb219d90ac9945fe473c9e302116374e4ccd049c6d027dc9a4","schema_version":"1.0","event_id":"sha256:1ae2a4ee485abedb219d90ac9945fe473c9e302116374e4ccd049c6d027dc9a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5VKWXKJJPCIWM4US4V3UH7LTT/bundle.json","state_url":"https://pith.science/pith/C5VKWXKJJPCIWM4US4V3UH7LTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5VKWXKJJPCIWM4US4V3UH7LTT/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":"2026-06-22T08:27:48Z","links":{"resolver":"https://pith.science/pith/C5VKWXKJJPCIWM4US4V3UH7LTT","bundle":"https://pith.science/pith/C5VKWXKJJPCIWM4US4V3UH7LTT/bundle.json","state":"https://pith.science/pith/C5VKWXKJJPCIWM4US4V3UH7LTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5VKWXKJJPCIWM4US4V3UH7LTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C5VKWXKJJPCIWM4US4V3UH7LTT","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":"57624d70a1b4e8e771c177a3e28b006059f99c9f750949c1fc4daf4f4a9204a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-04-13T06:28:31Z","title_canon_sha256":"6c44512fc1e5b205be629b616826884b92719050c21793929750acacbf58d394"},"schema_version":"1.0","source":{"id":"1204.2890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2890","created_at":"2026-05-18T03:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2890v1","created_at":"2026-05-18T03:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2890","created_at":"2026-05-18T03:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"C5VKWXKJJPCI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C5VKWXKJJPCIWM4U","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C5VKWXKJ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:1ae2a4ee485abedb219d90ac9945fe473c9e302116374e4ccd049c6d027dc9a4","target":"graph","created_at":"2026-05-18T03:58:02Z","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 paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings are obtained explicitly. Finally, we illustrate the harmonic mappings of each of these cases together with their minimal surfaces pictorially with the help of mathematica.","authors_text":"Liulan Li, M. Vuorinen, S. Ponnusamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-04-13T06:28:31Z","title":"The minimal surfaces over the slanted half-planes, vertical strips and single slit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2890","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:e53893aa8283f7f6b28d36da84b26bbbd419bdcb3cf6bad1157690ed1095f13d","target":"record","created_at":"2026-05-18T03:58:02Z","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":"57624d70a1b4e8e771c177a3e28b006059f99c9f750949c1fc4daf4f4a9204a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-04-13T06:28:31Z","title_canon_sha256":"6c44512fc1e5b205be629b616826884b92719050c21793929750acacbf58d394"},"schema_version":"1.0","source":{"id":"1204.2890","kind":"arxiv","version":1}},"canonical_sha256":"176aab5d494bc48b3394972bba1feb9cc688b2e1fa5ace1bcaf14058fdfa7a0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"176aab5d494bc48b3394972bba1feb9cc688b2e1fa5ace1bcaf14058fdfa7a0f","first_computed_at":"2026-05-18T03:58:02.584206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:02.584206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqmZuVYLJFyaLOSqkIUIqN/Uib5vEP4C7itQ6lZEjLPuwb7SV34LrzaDPAaCiZclt8YZaOX0sRlEFSHzzwMAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:02.584737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e53893aa8283f7f6b28d36da84b26bbbd419bdcb3cf6bad1157690ed1095f13d","sha256:1ae2a4ee485abedb219d90ac9945fe473c9e302116374e4ccd049c6d027dc9a4"],"state_sha256":"8bd372567b4b1db2b3292dca7baa8fa7e57901193d16b09ea1e1b982ae04edb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pn908JKRKjWoIqqL0VMRAw2rwdtRP0o6cTUs4k5g64AZWhzmi6MaxB0z90Ts9Ay1nrMQkae8CUg0laJOQ+nPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T08:27:48.782784Z","bundle_sha256":"7df232f05b04fb42eea9e22fb2b50b20f833a1f9f91668b3e6e51fba54c1fc26"}}