{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NJWTC7QFYDLJGPLSR6JVKTRURZ","short_pith_number":"pith:NJWTC7QF","canonical_record":{"source":{"id":"1801.00241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-31T05:55:30Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5ee01016b0dbf64e13db0d7b7533c9c85c17c56c2c8c8f06a99b0d3ca87119ce","abstract_canon_sha256":"017c591786cf97612bdb0d93abeb9cc7440edbae2dae9d8c2d87395c68e6064f"},"schema_version":"1.0"},"canonical_sha256":"6a6d317e05c0d6933d728f93554e348e5eecf9e79d150112b51745f61d04020f","source":{"kind":"arxiv","id":"1801.00241","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00241","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00241v1","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00241","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"NJWTC7QFYDLJ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NJWTC7QFYDLJGPLS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NJWTC7QF","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NJWTC7QFYDLJGPLSR6JVKTRURZ","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-31T05:55:30Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5ee01016b0dbf64e13db0d7b7533c9c85c17c56c2c8c8f06a99b0d3ca87119ce","abstract_canon_sha256":"017c591786cf97612bdb0d93abeb9cc7440edbae2dae9d8c2d87395c68e6064f"},"schema_version":"1.0"},"canonical_sha256":"6a6d317e05c0d6933d728f93554e348e5eecf9e79d150112b51745f61d04020f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:58.979652Z","signature_b64":"LgNne9kLZIczabo9a8JFMMc7f166umhwvLmhBsS8r1QHUepnBjYfl6uLf9nf80hHIL9xFlHOql2PIK36CQedDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a6d317e05c0d6933d728f93554e348e5eecf9e79d150112b51745f61d04020f","last_reissued_at":"2026-05-18T00:26:58.979048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:58.979048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00241","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":"2026-05-18T00:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRbI/QZzicdPRck9tvgqbfXRVndpu5YkI8Pm8QEapecb/WSuUz2qpLMIIC7r7IVHCx/KEzskr90mPP0r/ZfkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T13:23:13.628160Z"},"content_sha256":"76ab23cdb7faf9560b445f376ebdc0c7501467563ee4d884ff15a6a787c2de43","schema_version":"1.0","event_id":"sha256:76ab23cdb7faf9560b445f376ebdc0c7501467563ee4d884ff15a6a787c2de43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NJWTC7QFYDLJGPLSR6JVKTRURZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometric Embedding and Darboux Integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jeanne Clelland, Naghmana Tehseen, Peter Vassiliou, Thomas Ivey","submitted_at":"2017-12-31T05:55:30Z","abstract_excerpt":"Given a smooth 2-dimensional Riemannian or pseudo-Riemannian manifold $(M, \\boldsymbol{g})$ and an ambient 3-dimensional Riemannian or pseudo-Riemannian manifold $(N, \\boldsymbol{h})$, one can ask under what circumstances does the exterior differential system $\\mathcal{I}$ for the isometric embedding $M\\hookrightarrow N$ have particularly nice solvability properties. In this paper we give a classification of all $2$-metrics $\\boldsymbol{g}$ whose local isometric embedding system into flat Riemannian or pseudo-Riemannian 3-manifolds $(N, \\boldsymbol{h})$ is Darboux integrable. As an illustratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00241","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":"2026-05-18T00:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9w5fhTbE79YQywPKZrV9CnTfIrVLhYqXr8enxHZ3tmc4mJbvwpQE27UQJAkSB60zfQN4kk/OMmVBg/PLIFhKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T13:23:13.628525Z"},"content_sha256":"97b5b45c5ca94d1865c6b35c168a9335cecfc690cd835935f98ebabfd85e5eeb","schema_version":"1.0","event_id":"sha256:97b5b45c5ca94d1865c6b35c168a9335cecfc690cd835935f98ebabfd85e5eeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ/bundle.json","state_url":"https://pith.science/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ/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":"2026-06-24T13:23:13Z","links":{"resolver":"https://pith.science/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ","bundle":"https://pith.science/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ/bundle.json","state":"https://pith.science/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJWTC7QFYDLJGPLSR6JVKTRURZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NJWTC7QFYDLJGPLSR6JVKTRURZ","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":"017c591786cf97612bdb0d93abeb9cc7440edbae2dae9d8c2d87395c68e6064f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-31T05:55:30Z","title_canon_sha256":"5ee01016b0dbf64e13db0d7b7533c9c85c17c56c2c8c8f06a99b0d3ca87119ce"},"schema_version":"1.0","source":{"id":"1801.00241","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00241","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00241v1","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00241","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"NJWTC7QFYDLJ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NJWTC7QFYDLJGPLS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NJWTC7QF","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:97b5b45c5ca94d1865c6b35c168a9335cecfc690cd835935f98ebabfd85e5eeb","target":"graph","created_at":"2026-05-18T00:26:58Z","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":"Given a smooth 2-dimensional Riemannian or pseudo-Riemannian manifold $(M, \\boldsymbol{g})$ and an ambient 3-dimensional Riemannian or pseudo-Riemannian manifold $(N, \\boldsymbol{h})$, one can ask under what circumstances does the exterior differential system $\\mathcal{I}$ for the isometric embedding $M\\hookrightarrow N$ have particularly nice solvability properties. In this paper we give a classification of all $2$-metrics $\\boldsymbol{g}$ whose local isometric embedding system into flat Riemannian or pseudo-Riemannian 3-manifolds $(N, \\boldsymbol{h})$ is Darboux integrable. As an illustratio","authors_text":"Jeanne Clelland, Naghmana Tehseen, Peter Vassiliou, Thomas Ivey","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-31T05:55:30Z","title":"Isometric Embedding and Darboux Integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00241","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":"sha256:76ab23cdb7faf9560b445f376ebdc0c7501467563ee4d884ff15a6a787c2de43","target":"record","created_at":"2026-05-18T00:26:58Z","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":"017c591786cf97612bdb0d93abeb9cc7440edbae2dae9d8c2d87395c68e6064f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-31T05:55:30Z","title_canon_sha256":"5ee01016b0dbf64e13db0d7b7533c9c85c17c56c2c8c8f06a99b0d3ca87119ce"},"schema_version":"1.0","source":{"id":"1801.00241","kind":"arxiv","version":1}},"canonical_sha256":"6a6d317e05c0d6933d728f93554e348e5eecf9e79d150112b51745f61d04020f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a6d317e05c0d6933d728f93554e348e5eecf9e79d150112b51745f61d04020f","first_computed_at":"2026-05-18T00:26:58.979048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:58.979048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LgNne9kLZIczabo9a8JFMMc7f166umhwvLmhBsS8r1QHUepnBjYfl6uLf9nf80hHIL9xFlHOql2PIK36CQedDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:58.979652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00241","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76ab23cdb7faf9560b445f376ebdc0c7501467563ee4d884ff15a6a787c2de43","sha256:97b5b45c5ca94d1865c6b35c168a9335cecfc690cd835935f98ebabfd85e5eeb"],"state_sha256":"35ffa28d0cbf08ad034dc5b156e63aab499451b22e97e5b9822a79540372b941"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ENJgqTEe19JckZQ++rc4sdlz8BBn1oEjAMANiuztov+kuA1/nbNPvQTKKSdvZbsXKnbN9z2WuDp5eeynvxfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T13:23:13.630494Z","bundle_sha256":"af7ee6d62205149ca4f2c9df1cf07c94731a21cd59c47aca498bec821319abd1"}}