{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2OYLMDMETEDAPL6IQMHOEVI3BO","short_pith_number":"pith:2OYLMDME","schema_version":"1.0","canonical_sha256":"d3b0b60d84990607afc8830ee2551b0b94c3fff4c055c1c7e39f8e697f68c78d","source":{"kind":"arxiv","id":"1503.02211","version":1},"attestation_state":"computed","paper":{"title":"Isometric Immersions via Compensated Compactness for Slowly Decaying Negative Gauss Curvature and Rough Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Cleopatra Christoforou, Marshall Slemrod","submitted_at":"2015-03-07T20:45:25Z","abstract_excerpt":"In this paper the method of compensated compactness is applied to the problem of isometric immersion of a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Previous applications of the method to this problem have required decay of order $t^{-4}$ in the Gauss curvature. Here we show that the decay of Hong $t^{-2-\\delta/2}$ where $\\delta\\in(0,4)$ suffices."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.02211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-07T20:45:25Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6a93a08cd8229b89d6e17bee684c6e9761531f95a2e893a975b2e8be4309d32f","abstract_canon_sha256":"6e90380600ddf99ac3e955384752561e1f124d797fa16debdb02b918fcb44822"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:41.015379Z","signature_b64":"bjwBUfjRBi3ffPUyyRnahoXy98o1e/yqkSGzKa0hiiTtNAdZDHK00c6zAWtIGpBN6iJ2p5C7e2ZxNE3UcjZuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3b0b60d84990607afc8830ee2551b0b94c3fff4c055c1c7e39f8e697f68c78d","last_reissued_at":"2026-05-18T01:22:41.014940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:41.014940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric Immersions via Compensated Compactness for Slowly Decaying Negative Gauss Curvature and Rough Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Cleopatra Christoforou, Marshall Slemrod","submitted_at":"2015-03-07T20:45:25Z","abstract_excerpt":"In this paper the method of compensated compactness is applied to the problem of isometric immersion of a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Previous applications of the method to this problem have required decay of order $t^{-4}$ in the Gauss curvature. Here we show that the decay of Hong $t^{-2-\\delta/2}$ where $\\delta\\in(0,4)$ suffices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02211","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.02211","created_at":"2026-05-18T01:22:41.015013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02211v1","created_at":"2026-05-18T01:22:41.015013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02211","created_at":"2026-05-18T01:22:41.015013+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OYLMDMETEDA","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OYLMDMETEDAPL6I","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OYLMDME","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO","json":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO.json","graph_json":"https://pith.science/api/pith-number/2OYLMDMETEDAPL6IQMHOEVI3BO/graph.json","events_json":"https://pith.science/api/pith-number/2OYLMDMETEDAPL6IQMHOEVI3BO/events.json","paper":"https://pith.science/paper/2OYLMDME"},"agent_actions":{"view_html":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO","download_json":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO.json","view_paper":"https://pith.science/paper/2OYLMDME","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02211&json=true","fetch_graph":"https://pith.science/api/pith-number/2OYLMDMETEDAPL6IQMHOEVI3BO/graph.json","fetch_events":"https://pith.science/api/pith-number/2OYLMDMETEDAPL6IQMHOEVI3BO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO/action/storage_attestation","attest_author":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO/action/author_attestation","sign_citation":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO/action/citation_signature","submit_replication":"https://pith.science/pith/2OYLMDMETEDAPL6IQMHOEVI3BO/action/replication_record"}},"created_at":"2026-05-18T01:22:41.015013+00:00","updated_at":"2026-05-18T01:22:41.015013+00:00"}