{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:YBGYXTWVBJU7WQPSTHHKB5ZKHV","short_pith_number":"pith:YBGYXTWV","canonical_record":{"source":{"id":"math/0001189","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2000-01-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"9dcdb2e960ebb2672c81306e3150baa1c664d945f720699c27e3a3ba1f3716ac","abstract_canon_sha256":"c2d24a76f3d99b81ae831824932bc23a28ade73ef20d36829c7bc475de1f3abd"},"schema_version":"1.0"},"canonical_sha256":"c04d8bced50a69fb41f299cea0f72a3d5f2d54e365045d8eff2bbe2e8aef526d","source":{"kind":"arxiv","id":"math/0001189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0001189","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0001189v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0001189","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"YBGYXTWVBJU7","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"YBGYXTWVBJU7WQPS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"YBGYXTWV","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:YBGYXTWVBJU7WQPSTHHKB5ZKHV","target":"record","payload":{"canonical_record":{"source":{"id":"math/0001189","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2000-01-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"9dcdb2e960ebb2672c81306e3150baa1c664d945f720699c27e3a3ba1f3716ac","abstract_canon_sha256":"c2d24a76f3d99b81ae831824932bc23a28ade73ef20d36829c7bc475de1f3abd"},"schema_version":"1.0"},"canonical_sha256":"c04d8bced50a69fb41f299cea0f72a3d5f2d54e365045d8eff2bbe2e8aef526d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:30.395564Z","signature_b64":"Q91VeaojnrPo5+Dhn7XgIQpPekMLlCAQsKlAw5YYtSsc8rduccUa6zHR0wKVR2efKpChxSOOA1cMQ1Rg8xRqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c04d8bced50a69fb41f299cea0f72a3d5f2d54e365045d8eff2bbe2e8aef526d","last_reissued_at":"2026-05-18T01:38:30.395018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:30.395018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0001189","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":"2026-05-18T01:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HctFuxAm6smiZVJVzN1qG0OoKdUdQWPWzJgJMYFgGTHYmYz7T6taVR96JE+p7ydD0+35i81L56DRmKwAJGzSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:33:08.450462Z"},"content_sha256":"90934d33fc05b6061acc13e68bd58cd68f965ab8a0b016d991da03e28577a010","schema_version":"1.0","event_id":"sha256:90934d33fc05b6061acc13e68bd58cd68f965ab8a0b016d991da03e28577a010"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:YBGYXTWVBJU7WQPSTHHKB5ZKHV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Links between different analytic descriptions of constant mean curvature surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfred M. Grundland, Eugene V. Ferapontov","submitted_at":"2000-01-01T00:00:00Z","abstract_excerpt":"Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system \\[ \\begin{split} &\\partial \\psi_{1} = (|\\psi_{1}|^{2} + |\\psi_{2}|^{2}) \\psi_{2} \\\\ &\\bar{\\partial} \\psi_{2} =- (|\\psi_{1}|^{2} + |\\psi_{2}|^{2}) \\psi_{1} \\end{split} \\] descriptive of CMC surfaces within the framework of the generalized Weierstrass representation, decouples into a direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this system with the sigma model equations are established. It is pointed out"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001189","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":"2026-05-18T01:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Zy7SQ3z4GXKp4bDYr52kzVfE4H8tDYudLuRLLLwYtmtqCrXK6d8s78EH/eV0HvPOLcuUCFaL1mketVrWrfdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:33:08.450807Z"},"content_sha256":"2a8b3e384a0dd67e4b99e38d16d90cfc90d3959c5292473a93041b59b9a76d62","schema_version":"1.0","event_id":"sha256:2a8b3e384a0dd67e4b99e38d16d90cfc90d3959c5292473a93041b59b9a76d62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV/bundle.json","state_url":"https://pith.science/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV/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":"2026-06-26T09:33:08Z","links":{"resolver":"https://pith.science/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV","bundle":"https://pith.science/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV/bundle.json","state":"https://pith.science/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBGYXTWVBJU7WQPSTHHKB5ZKHV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:YBGYXTWVBJU7WQPSTHHKB5ZKHV","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":"c2d24a76f3d99b81ae831824932bc23a28ade73ef20d36829c7bc475de1f3abd","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2000-01-01T00:00:00Z","title_canon_sha256":"9dcdb2e960ebb2672c81306e3150baa1c664d945f720699c27e3a3ba1f3716ac"},"schema_version":"1.0","source":{"id":"math/0001189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0001189","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0001189v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0001189","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"YBGYXTWVBJU7","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"YBGYXTWVBJU7WQPS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"YBGYXTWV","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:2a8b3e384a0dd67e4b99e38d16d90cfc90d3959c5292473a93041b59b9a76d62","target":"graph","created_at":"2026-05-18T01:38:30Z","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":"Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system \\[ \\begin{split} &\\partial \\psi_{1} = (|\\psi_{1}|^{2} + |\\psi_{2}|^{2}) \\psi_{2} \\\\ &\\bar{\\partial} \\psi_{2} =- (|\\psi_{1}|^{2} + |\\psi_{2}|^{2}) \\psi_{1} \\end{split} \\] descriptive of CMC surfaces within the framework of the generalized Weierstrass representation, decouples into a direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this system with the sigma model equations are established. It is pointed out","authors_text":"Alfred M. Grundland, Eugene V. Ferapontov","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2000-01-01T00:00:00Z","title":"Links between different analytic descriptions of constant mean curvature surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001189","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":"sha256:90934d33fc05b6061acc13e68bd58cd68f965ab8a0b016d991da03e28577a010","target":"record","created_at":"2026-05-18T01:38:30Z","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":"c2d24a76f3d99b81ae831824932bc23a28ade73ef20d36829c7bc475de1f3abd","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2000-01-01T00:00:00Z","title_canon_sha256":"9dcdb2e960ebb2672c81306e3150baa1c664d945f720699c27e3a3ba1f3716ac"},"schema_version":"1.0","source":{"id":"math/0001189","kind":"arxiv","version":1}},"canonical_sha256":"c04d8bced50a69fb41f299cea0f72a3d5f2d54e365045d8eff2bbe2e8aef526d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c04d8bced50a69fb41f299cea0f72a3d5f2d54e365045d8eff2bbe2e8aef526d","first_computed_at":"2026-05-18T01:38:30.395018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.395018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q91VeaojnrPo5+Dhn7XgIQpPekMLlCAQsKlAw5YYtSsc8rduccUa6zHR0wKVR2efKpChxSOOA1cMQ1Rg8xRqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.395564Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0001189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90934d33fc05b6061acc13e68bd58cd68f965ab8a0b016d991da03e28577a010","sha256:2a8b3e384a0dd67e4b99e38d16d90cfc90d3959c5292473a93041b59b9a76d62"],"state_sha256":"01b44a9e2c8a2f16f936c52ea7bfb9c8e56ba0c14183a0e1dfe4fbc6f274a505"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qX6G646jXYLYjuVuWG2C49ztod24oELz/tuus85FbyLwL5POnY7jMbi8YXrd2Gv12zFk0atKXAObywSh5y01AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:33:08.452737Z","bundle_sha256":"f63d645fc78b197e4029fa77b3cd25a65bdc05fd5f20fb33af5e4d8289b56b72"}}