{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:P2S7WPQJMVNQ4S56ZE6DA5LCKW","short_pith_number":"pith:P2S7WPQJ","canonical_record":{"source":{"id":"0805.2433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-16T04:07:50Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"1ddc3f8cad8ffa924623c7c64dfe9dae1e331e808c26d0dd5094ea24deda6609","abstract_canon_sha256":"50144c5b229e3b575028cbdca2017c0fe40bb5d90ad9b4408ee3a6ecf7459c38"},"schema_version":"1.0"},"canonical_sha256":"7ea5fb3e09655b0e4bbec93c307562559bcd63d53d1812a8c7a575a2643b08f8","source":{"kind":"arxiv","id":"0805.2433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2433","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2433v1","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2433","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"P2S7WPQJMVNQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"P2S7WPQJMVNQ4S56","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"P2S7WPQJ","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:P2S7WPQJMVNQ4S56ZE6DA5LCKW","target":"record","payload":{"canonical_record":{"source":{"id":"0805.2433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-16T04:07:50Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"1ddc3f8cad8ffa924623c7c64dfe9dae1e331e808c26d0dd5094ea24deda6609","abstract_canon_sha256":"50144c5b229e3b575028cbdca2017c0fe40bb5d90ad9b4408ee3a6ecf7459c38"},"schema_version":"1.0"},"canonical_sha256":"7ea5fb3e09655b0e4bbec93c307562559bcd63d53d1812a8c7a575a2643b08f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:52.728202Z","signature_b64":"IDlMYGlF3louSUT8+z2NF1VvDFGsrBeKzB3UDpkPTj72ZBT0zrp+0gEC1uNwmJ4TWFd9/DE+SnCNejc2lHX1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ea5fb3e09655b0e4bbec93c307562559bcd63d53d1812a8c7a575a2643b08f8","last_reissued_at":"2026-05-18T02:15:52.727705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:52.727705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.2433","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":"2026-05-18T02:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I/H1f1vfjCFZiAoh9td+EiEHxE+UAzr7xg261mp9ju0jO7jsO16OTqRux8Mpup0ViCY2WDBlDc/+IbGiw0XlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:52:12.237043Z"},"content_sha256":"81fee4c9e9f4ed7c80a59fa5c81d4023951f4c49c9ae758a6878bf1d10d96833","schema_version":"1.0","event_id":"sha256:81fee4c9e9f4ed7c80a59fa5c81d4023951f4c49c9ae758a6878bf1d10d96833"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:P2S7WPQJMVNQ4S56ZE6DA5LCKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometric Immersions and Compensated Compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Dehua Wang, Gui-Qiang Chen, Marshall Slemrod","submitted_at":"2008-05-16T04:07:50Z","abstract_excerpt":"A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold ${\\mathcal M}^2$ which can be realized as isometric immersions into $\\R^3$. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type whose mathematical theory is largely incomplete. In this paper, we develop a general approach, which combines a fluid dynamic formulation of balance laws for the Gauss-Codazzi system with a compensated compactness framework, to deal wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2433","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":"2026-05-18T02:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZrIfwz5tBRg7xjNqvU4+po/Q3sSPBP7a5b4/piGjeW8NJghzYrkVrpkvisiu+mH40cWm25fstntM56fIIONuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:52:12.237708Z"},"content_sha256":"0e0fa8420995ee6e8d77de3450ad40a60867cad58c244438f091acfc00957dbe","schema_version":"1.0","event_id":"sha256:0e0fa8420995ee6e8d77de3450ad40a60867cad58c244438f091acfc00957dbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW/bundle.json","state_url":"https://pith.science/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW/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":"2026-05-28T16:52:12Z","links":{"resolver":"https://pith.science/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW","bundle":"https://pith.science/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW/bundle.json","state":"https://pith.science/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2S7WPQJMVNQ4S56ZE6DA5LCKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:P2S7WPQJMVNQ4S56ZE6DA5LCKW","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":"50144c5b229e3b575028cbdca2017c0fe40bb5d90ad9b4408ee3a6ecf7459c38","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-16T04:07:50Z","title_canon_sha256":"1ddc3f8cad8ffa924623c7c64dfe9dae1e331e808c26d0dd5094ea24deda6609"},"schema_version":"1.0","source":{"id":"0805.2433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2433","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2433v1","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2433","created_at":"2026-05-18T02:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"P2S7WPQJMVNQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"P2S7WPQJMVNQ4S56","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"P2S7WPQJ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0e0fa8420995ee6e8d77de3450ad40a60867cad58c244438f091acfc00957dbe","target":"graph","created_at":"2026-05-18T02:15:52Z","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":"A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold ${\\mathcal M}^2$ which can be realized as isometric immersions into $\\R^3$. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type whose mathematical theory is largely incomplete. In this paper, we develop a general approach, which combines a fluid dynamic formulation of balance laws for the Gauss-Codazzi system with a compensated compactness framework, to deal wi","authors_text":"Dehua Wang, Gui-Qiang Chen, Marshall Slemrod","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-16T04:07:50Z","title":"Isometric Immersions and Compensated Compactness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2433","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":"sha256:81fee4c9e9f4ed7c80a59fa5c81d4023951f4c49c9ae758a6878bf1d10d96833","target":"record","created_at":"2026-05-18T02:15:52Z","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":"50144c5b229e3b575028cbdca2017c0fe40bb5d90ad9b4408ee3a6ecf7459c38","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-05-16T04:07:50Z","title_canon_sha256":"1ddc3f8cad8ffa924623c7c64dfe9dae1e331e808c26d0dd5094ea24deda6609"},"schema_version":"1.0","source":{"id":"0805.2433","kind":"arxiv","version":1}},"canonical_sha256":"7ea5fb3e09655b0e4bbec93c307562559bcd63d53d1812a8c7a575a2643b08f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ea5fb3e09655b0e4bbec93c307562559bcd63d53d1812a8c7a575a2643b08f8","first_computed_at":"2026-05-18T02:15:52.727705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:52.727705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IDlMYGlF3louSUT8+z2NF1VvDFGsrBeKzB3UDpkPTj72ZBT0zrp+0gEC1uNwmJ4TWFd9/DE+SnCNejc2lHX1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:52.728202Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.2433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81fee4c9e9f4ed7c80a59fa5c81d4023951f4c49c9ae758a6878bf1d10d96833","sha256:0e0fa8420995ee6e8d77de3450ad40a60867cad58c244438f091acfc00957dbe"],"state_sha256":"e2fc15e8c55c2f61789c37ae0ef4b7264c01a1289e4bc18aab9f45bd4a75e5a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XqjVVDNTTKZkT+Hmn403a3d+A9ZS8lSmR8VSkw2QsnMMiJpm+f6GzrXKFc5Ds00tChFKRamcb6ZTy3Px1PXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:52:12.241369Z","bundle_sha256":"78e405101b96efba2c8567c81d4a56364adbb5abffc7b2c1a889eddb82479f35"}}