{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T4WQ7LNOH7BM5LIKMDI435OAUN","short_pith_number":"pith:T4WQ7LNO","canonical_record":{"source":{"id":"1901.09432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-27T20:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"9f1722b11014c9b967d5156cabea98e4007932c4a4aa896e2966025c8fe38642","abstract_canon_sha256":"1d89523de3149ac3c5dc377a15d875c8807f641188e034b7cb5afe7fce891444"},"schema_version":"1.0"},"canonical_sha256":"9f2d0fadae3fc2cead0a60d1cdf5c0a371fa9d39b7626f677fdc53b9aba69724","source":{"kind":"arxiv","id":"1901.09432","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09432","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09432v1","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09432","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"T4WQ7LNOH7BM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T4WQ7LNOH7BM5LIK","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T4WQ7LNO","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T4WQ7LNOH7BM5LIKMDI435OAUN","target":"record","payload":{"canonical_record":{"source":{"id":"1901.09432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-27T20:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"9f1722b11014c9b967d5156cabea98e4007932c4a4aa896e2966025c8fe38642","abstract_canon_sha256":"1d89523de3149ac3c5dc377a15d875c8807f641188e034b7cb5afe7fce891444"},"schema_version":"1.0"},"canonical_sha256":"9f2d0fadae3fc2cead0a60d1cdf5c0a371fa9d39b7626f677fdc53b9aba69724","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:24.769097Z","signature_b64":"pnC0MJKXhg3+LmjrrBly8C7906XJGuncWaqEqqm1JkeAHddAKnPu2Lv4yt5NQKOpWNCax7f7lWqN5kyiq9VkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f2d0fadae3fc2cead0a60d1cdf5c0a371fa9d39b7626f677fdc53b9aba69724","last_reissued_at":"2026-05-17T23:55:24.768369Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:24.768369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.09432","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":"2026-05-17T23:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2VCWQP7t1g2lQES3mMvznvKhAKMXliUUfHgRIOAvWNeffZqs0ipCbtQeQUErBoVDVnDBwMFUQ2IbNvYUoWGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:35:45.791941Z"},"content_sha256":"fda1a3849bf3f772d3a27117ae38d52fdffdfb5ea5d9348ef167154cf0251b93","schema_version":"1.0","event_id":"sha256:fda1a3849bf3f772d3a27117ae38d52fdffdfb5ea5d9348ef167154cf0251b93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T4WQ7LNOH7BM5LIKMDI435OAUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding Conformal and Isometric Immersions of Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Albert Chern, Felix Kn\\\"oppel, Franz Pedit, Peter Schr\\\"oder, Ulrich Pinkall","submitted_at":"2019-01-27T20:10:29Z","abstract_excerpt":"We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical experiments indicate that, by taking suitable limits, minimization of these functionals can also yield piecewise smooth isometric immersions of a prescribed Riemannian metric on $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09432","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":"2026-05-17T23:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hk48KzqMrC0Pfp5Bzb//VE8h7c1iUzgBTAxYv4Yj8qgBqT43oWN2l7a43aEYGhKsWqDUG15kiq1Q7dCmFVTtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:35:45.792270Z"},"content_sha256":"49396cfa8ef7d64a41c9c237fe17488a33d4b8ba92b7fa0289f200634dfa87b5","schema_version":"1.0","event_id":"sha256:49396cfa8ef7d64a41c9c237fe17488a33d4b8ba92b7fa0289f200634dfa87b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4WQ7LNOH7BM5LIKMDI435OAUN/bundle.json","state_url":"https://pith.science/pith/T4WQ7LNOH7BM5LIKMDI435OAUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4WQ7LNOH7BM5LIKMDI435OAUN/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":"2026-06-26T18:35:45Z","links":{"resolver":"https://pith.science/pith/T4WQ7LNOH7BM5LIKMDI435OAUN","bundle":"https://pith.science/pith/T4WQ7LNOH7BM5LIKMDI435OAUN/bundle.json","state":"https://pith.science/pith/T4WQ7LNOH7BM5LIKMDI435OAUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4WQ7LNOH7BM5LIKMDI435OAUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T4WQ7LNOH7BM5LIKMDI435OAUN","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":"1d89523de3149ac3c5dc377a15d875c8807f641188e034b7cb5afe7fce891444","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-27T20:10:29Z","title_canon_sha256":"9f1722b11014c9b967d5156cabea98e4007932c4a4aa896e2966025c8fe38642"},"schema_version":"1.0","source":{"id":"1901.09432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09432","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09432v1","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09432","created_at":"2026-05-17T23:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"T4WQ7LNOH7BM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T4WQ7LNOH7BM5LIK","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T4WQ7LNO","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:49396cfa8ef7d64a41c9c237fe17488a33d4b8ba92b7fa0289f200634dfa87b5","target":"graph","created_at":"2026-05-17T23:55:24Z","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 introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical experiments indicate that, by taking suitable limits, minimization of these functionals can also yield piecewise smooth isometric immersions of a prescribed Riemannian metric on $M$.","authors_text":"Albert Chern, Felix Kn\\\"oppel, Franz Pedit, Peter Schr\\\"oder, Ulrich Pinkall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-27T20:10:29Z","title":"Finding Conformal and Isometric Immersions of Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09432","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:fda1a3849bf3f772d3a27117ae38d52fdffdfb5ea5d9348ef167154cf0251b93","target":"record","created_at":"2026-05-17T23:55:24Z","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":"1d89523de3149ac3c5dc377a15d875c8807f641188e034b7cb5afe7fce891444","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-27T20:10:29Z","title_canon_sha256":"9f1722b11014c9b967d5156cabea98e4007932c4a4aa896e2966025c8fe38642"},"schema_version":"1.0","source":{"id":"1901.09432","kind":"arxiv","version":1}},"canonical_sha256":"9f2d0fadae3fc2cead0a60d1cdf5c0a371fa9d39b7626f677fdc53b9aba69724","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f2d0fadae3fc2cead0a60d1cdf5c0a371fa9d39b7626f677fdc53b9aba69724","first_computed_at":"2026-05-17T23:55:24.768369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:24.768369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pnC0MJKXhg3+LmjrrBly8C7906XJGuncWaqEqqm1JkeAHddAKnPu2Lv4yt5NQKOpWNCax7f7lWqN5kyiq9VkAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:24.769097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.09432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fda1a3849bf3f772d3a27117ae38d52fdffdfb5ea5d9348ef167154cf0251b93","sha256:49396cfa8ef7d64a41c9c237fe17488a33d4b8ba92b7fa0289f200634dfa87b5"],"state_sha256":"074aeac430fe5b3c20423c09413f1a920de9a3bf518d00bcebba37914087be19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kms50K+vWeSBdTgXu4bANqWI7UIb72EJhrgHbrVl35lxic4s/a4MVI+jjSxXVVLszEENmKJU3wYGzXX6U18nBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T18:35:45.794103Z","bundle_sha256":"48e7878fad3dfa638e7398e832418d1ff5cfcd5f8c91af7e67054a6342c4d5ea"}}