{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:V2CUUK7MC4IKO7X6TIUA6WK2VM","short_pith_number":"pith:V2CUUK7M","schema_version":"1.0","canonical_sha256":"ae854a2bec1710a77efe9a280f595aab3569f20d71ab877445b0ebbfb13185e6","source":{"kind":"arxiv","id":"1610.05280","version":3},"attestation_state":"computed","paper":{"title":"Mitigating the Influence of the Boundary on PDE-based Covariance Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Georg Stadler, Yair Daon","submitted_at":"2016-10-17T19:27:48Z","abstract_excerpt":"Gaussian random fields over infinite-dimensional Hilbert spaces require the definition of appropriate covariance operators. The use of elliptic PDE operators to construct covariance operators allows to build on fast PDE solvers for manipulations with the resulting covariance and precision operators. However, PDE operators require a choice of boundary conditions, and this choice can have a strong and usually undesired influence on the Gaussian random field. We propose two techniques that allow to ameliorate these boundary effects for large-scale problems. The first approach combines the ellipti"},"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":"1610.05280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-17T19:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"0ecf5106ac0c0a7bf202c2775d6599c0009c928eb2e00e4ecd98c7075bee5df5","abstract_canon_sha256":"832da58d977687f426b7803e3ca0e1e3e40856875761cedb713d681f36424d95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:16.464391Z","signature_b64":"yWTHB0IRm9t0c17va+vznR0pS3fBlwLc+eL/c7jxPzYUlL/E0bN46SiRfdTrmW8yqADTlz3pIkVWslPfSKi/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae854a2bec1710a77efe9a280f595aab3569f20d71ab877445b0ebbfb13185e6","last_reissued_at":"2026-05-18T00:28:16.463414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:16.463414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mitigating the Influence of the Boundary on PDE-based Covariance Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Georg Stadler, Yair Daon","submitted_at":"2016-10-17T19:27:48Z","abstract_excerpt":"Gaussian random fields over infinite-dimensional Hilbert spaces require the definition of appropriate covariance operators. The use of elliptic PDE operators to construct covariance operators allows to build on fast PDE solvers for manipulations with the resulting covariance and precision operators. However, PDE operators require a choice of boundary conditions, and this choice can have a strong and usually undesired influence on the Gaussian random field. We propose two techniques that allow to ameliorate these boundary effects for large-scale problems. The first approach combines the ellipti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05280","kind":"arxiv","version":3},"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":"1610.05280","created_at":"2026-05-18T00:28:16.463600+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.05280v3","created_at":"2026-05-18T00:28:16.463600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05280","created_at":"2026-05-18T00:28:16.463600+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2CUUK7MC4IK","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2CUUK7MC4IKO7X6","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2CUUK7M","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.25075","citing_title":"Influence of Heterogeneity on the Response of Architected Metamaterials","ref_index":85,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM","json":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM.json","graph_json":"https://pith.science/api/pith-number/V2CUUK7MC4IKO7X6TIUA6WK2VM/graph.json","events_json":"https://pith.science/api/pith-number/V2CUUK7MC4IKO7X6TIUA6WK2VM/events.json","paper":"https://pith.science/paper/V2CUUK7M"},"agent_actions":{"view_html":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM","download_json":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM.json","view_paper":"https://pith.science/paper/V2CUUK7M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.05280&json=true","fetch_graph":"https://pith.science/api/pith-number/V2CUUK7MC4IKO7X6TIUA6WK2VM/graph.json","fetch_events":"https://pith.science/api/pith-number/V2CUUK7MC4IKO7X6TIUA6WK2VM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM/action/storage_attestation","attest_author":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM/action/author_attestation","sign_citation":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM/action/citation_signature","submit_replication":"https://pith.science/pith/V2CUUK7MC4IKO7X6TIUA6WK2VM/action/replication_record"}},"created_at":"2026-05-18T00:28:16.463600+00:00","updated_at":"2026-05-18T00:28:16.463600+00:00"}