{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:OS3RGAYOMX2L72DBC3TTU744OR","short_pith_number":"pith:OS3RGAYO","schema_version":"1.0","canonical_sha256":"74b713030e65f4bfe86116e73a7f9c7455f151c46a6a756353b60e82b96a0b72","source":{"kind":"arxiv","id":"2606.13827","version":2},"attestation_state":"computed","paper":{"title":"Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Srinivas Nambirajan","submitted_at":"2026-06-11T18:58:55Z","abstract_excerpt":"Markovian Whittle-Mat\\'ern fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \\[ (\\kappa^2 - \\Delta)^{\\alpha/2} u = \\mathcal{W}, \\;\\; \\kappa \\in \\mathbb{R}, \\; \\alpha \\in \\mathbb{N}. \\] of SPDEs. Using recent developements in the analysis of Discrete Exterior Calculus (DEC), we present a different, yet closely related, convergent GMRF approximation to these Mat\\'ern fields over complete, boundaryless Riemannian manifolds discretized as well-centered simplicial"},"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":"2606.13827","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-11T18:58:55Z","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"title_canon_sha256":"fb68d11568e339a97203976c5b6c15eb250fee00d638ba548a5105cc088df8c2","abstract_canon_sha256":"750e6a8c25009fa5eef4e618663bd24b318612bdafcf620cc84563de8ec6e1b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:00.614377Z","signature_b64":"huxkknUWhHXk2thTuuohH3u3JanjFtR/XqEcLemkm/DTHiJklg7/ZphAWMzOB2T+QfSRg+gJsBog8Hrvt8yRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74b713030e65f4bfe86116e73a7f9c7455f151c46a6a756353b60e82b96a0b72","last_reissued_at":"2026-06-19T16:10:00.613951Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:00.613951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Srinivas Nambirajan","submitted_at":"2026-06-11T18:58:55Z","abstract_excerpt":"Markovian Whittle-Mat\\'ern fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \\[ (\\kappa^2 - \\Delta)^{\\alpha/2} u = \\mathcal{W}, \\;\\; \\kappa \\in \\mathbb{R}, \\; \\alpha \\in \\mathbb{N}. \\] of SPDEs. Using recent developements in the analysis of Discrete Exterior Calculus (DEC), we present a different, yet closely related, convergent GMRF approximation to these Mat\\'ern fields over complete, boundaryless Riemannian manifolds discretized as well-centered simplicial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13827","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13827/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.13827","created_at":"2026-06-19T16:10:00.614007+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.13827v2","created_at":"2026-06-19T16:10:00.614007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13827","created_at":"2026-06-19T16:10:00.614007+00:00"},{"alias_kind":"pith_short_12","alias_value":"OS3RGAYOMX2L","created_at":"2026-06-19T16:10:00.614007+00:00"},{"alias_kind":"pith_short_16","alias_value":"OS3RGAYOMX2L72DB","created_at":"2026-06-19T16:10:00.614007+00:00"},{"alias_kind":"pith_short_8","alias_value":"OS3RGAYO","created_at":"2026-06-19T16:10:00.614007+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/OS3RGAYOMX2L72DBC3TTU744OR","json":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR.json","graph_json":"https://pith.science/api/pith-number/OS3RGAYOMX2L72DBC3TTU744OR/graph.json","events_json":"https://pith.science/api/pith-number/OS3RGAYOMX2L72DBC3TTU744OR/events.json","paper":"https://pith.science/paper/OS3RGAYO"},"agent_actions":{"view_html":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR","download_json":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR.json","view_paper":"https://pith.science/paper/OS3RGAYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.13827&json=true","fetch_graph":"https://pith.science/api/pith-number/OS3RGAYOMX2L72DBC3TTU744OR/graph.json","fetch_events":"https://pith.science/api/pith-number/OS3RGAYOMX2L72DBC3TTU744OR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR/action/storage_attestation","attest_author":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR/action/author_attestation","sign_citation":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR/action/citation_signature","submit_replication":"https://pith.science/pith/OS3RGAYOMX2L72DBC3TTU744OR/action/replication_record"}},"created_at":"2026-06-19T16:10:00.614007+00:00","updated_at":"2026-06-19T16:10:00.614007+00:00"}