{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:FZN7LDLB6Y6FPMHZ4B7T4EMWUA","short_pith_number":"pith:FZN7LDLB","canonical_record":{"source":{"id":"2109.02777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2021-09-06T23:49:21Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"74e084b65cf119cbc3935c37a4a6611035c5606c9b29da5f3e4f6f136388ad50","abstract_canon_sha256":"cfb56e5846e0980820722751d33f84dbc8ae2a6ef0461147ce65ee50b0f81ba7"},"schema_version":"1.0"},"canonical_sha256":"2e5bf58d61f63c57b0f9e07f3e1196a001aaaba2116967dae2323e3004e5e91d","source":{"kind":"arxiv","id":"2109.02777","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.02777","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"2109.02777v2","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.02777","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"FZN7LDLB6Y6F","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"pith_short_16","alias_value":"FZN7LDLB6Y6FPMHZ","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"pith_short_8","alias_value":"FZN7LDLB","created_at":"2026-07-05T04:12:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:FZN7LDLB6Y6FPMHZ4B7T4EMWUA","target":"record","payload":{"canonical_record":{"source":{"id":"2109.02777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2021-09-06T23:49:21Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"74e084b65cf119cbc3935c37a4a6611035c5606c9b29da5f3e4f6f136388ad50","abstract_canon_sha256":"cfb56e5846e0980820722751d33f84dbc8ae2a6ef0461147ce65ee50b0f81ba7"},"schema_version":"1.0"},"canonical_sha256":"2e5bf58d61f63c57b0f9e07f3e1196a001aaaba2116967dae2323e3004e5e91d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:12:35.984216Z","signature_b64":"Y2sBGM/2o1lHuDkUQQ5B4Fol2Elr5Z6Uc9akrMAZXhoOrlNhP4zqIoPeU608/XVWp7lanQ3b28Wq0mUp1h4eAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e5bf58d61f63c57b0f9e07f3e1196a001aaaba2116967dae2323e3004e5e91d","last_reissued_at":"2026-07-05T04:12:35.983801Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:12:35.983801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.02777","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbBmYXRuqF4RNzQLrbvfC3oYM5PwjcH/zosXJDk9jEIriWirkmJiGYYwjwIw4s+YS97fcnrZ/DAKvbAod1r7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:05:15.779627Z"},"content_sha256":"cf960f85067e0257d18278f5900f0e13910d15fd84f283d05497e4da90cb5e5e","schema_version":"1.0","event_id":"sha256:cf960f85067e0257d18278f5900f0e13910d15fd84f283d05497e4da90cb5e5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:FZN7LDLB6Y6FPMHZ4B7T4EMWUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"stat.CO","authors_text":"Daniel Sanz-Alonso, Ruiyi Yang","submitted_at":"2021-09-06T23:49:21Z","abstract_excerpt":"The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations enhance the scalability of GP regression and classification to datasets of large size $N$ by setting $n\\approx N$ and exploiting sparsity. In this paper we reconsider the standard choice $n \\approx N$ through an analysis of the estimation performance. Our theory implies that, under certain smoothness assumptions, one can reduce the computation and memory cost wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.02777","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/2109.02777/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HnNKFkUJH2f+52YwlXu6P85AZyKL2BB9PwXqdUtCW0FKdQL2qJuEExS3YH+uzIzr6QjBiNiqyaFXfRULTwxYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:05:15.780128Z"},"content_sha256":"deef68536ce0599a613fd67a5bca3d29c39552e638a594b8e3cc788c6ce1f955","schema_version":"1.0","event_id":"sha256:deef68536ce0599a613fd67a5bca3d29c39552e638a594b8e3cc788c6ce1f955"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA/bundle.json","state_url":"https://pith.science/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA/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":"2026-08-05T14:05:15Z","links":{"resolver":"https://pith.science/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA","bundle":"https://pith.science/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA/bundle.json","state":"https://pith.science/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZN7LDLB6Y6FPMHZ4B7T4EMWUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FZN7LDLB6Y6FPMHZ4B7T4EMWUA","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":"cfb56e5846e0980820722751d33f84dbc8ae2a6ef0461147ce65ee50b0f81ba7","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2021-09-06T23:49:21Z","title_canon_sha256":"74e084b65cf119cbc3935c37a4a6611035c5606c9b29da5f3e4f6f136388ad50"},"schema_version":"1.0","source":{"id":"2109.02777","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.02777","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"2109.02777v2","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.02777","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"FZN7LDLB6Y6F","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"pith_short_16","alias_value":"FZN7LDLB6Y6FPMHZ","created_at":"2026-07-05T04:12:35Z"},{"alias_kind":"pith_short_8","alias_value":"FZN7LDLB","created_at":"2026-07-05T04:12:35Z"}],"graph_snapshots":[{"event_id":"sha256:deef68536ce0599a613fd67a5bca3d29c39552e638a594b8e3cc788c6ce1f955","target":"graph","created_at":"2026-07-05T04:12:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.02777/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations enhance the scalability of GP regression and classification to datasets of large size $N$ by setting $n\\approx N$ and exploiting sparsity. In this paper we reconsider the standard choice $n \\approx N$ through an analysis of the estimation performance. Our theory implies that, under certain smoothness assumptions, one can reduce the computation and memory cost wi","authors_text":"Daniel Sanz-Alonso, Ruiyi Yang","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2021-09-06T23:49:21Z","title":"Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.02777","kind":"arxiv","version":2},"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:cf960f85067e0257d18278f5900f0e13910d15fd84f283d05497e4da90cb5e5e","target":"record","created_at":"2026-07-05T04:12:35Z","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":"cfb56e5846e0980820722751d33f84dbc8ae2a6ef0461147ce65ee50b0f81ba7","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2021-09-06T23:49:21Z","title_canon_sha256":"74e084b65cf119cbc3935c37a4a6611035c5606c9b29da5f3e4f6f136388ad50"},"schema_version":"1.0","source":{"id":"2109.02777","kind":"arxiv","version":2}},"canonical_sha256":"2e5bf58d61f63c57b0f9e07f3e1196a001aaaba2116967dae2323e3004e5e91d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e5bf58d61f63c57b0f9e07f3e1196a001aaaba2116967dae2323e3004e5e91d","first_computed_at":"2026-07-05T04:12:35.983801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:12:35.983801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y2sBGM/2o1lHuDkUQQ5B4Fol2Elr5Z6Uc9akrMAZXhoOrlNhP4zqIoPeU608/XVWp7lanQ3b28Wq0mUp1h4eAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:12:35.984216Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.02777","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf960f85067e0257d18278f5900f0e13910d15fd84f283d05497e4da90cb5e5e","sha256:deef68536ce0599a613fd67a5bca3d29c39552e638a594b8e3cc788c6ce1f955"],"state_sha256":"c77f26de90bb192d8333abefde2d25288fcce515eda673eb0aa780b58a4a3a03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VynEJibbBqQgpiIAKU9bHrmkrJrTtKImE2v42Tk4CGB45uwx6v90MDZ9uQt16xFL85HzWkJjG+2HYPuHLIeNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:05:15.818616Z","bundle_sha256":"d515e5864cf19352724b0aad0d600ccf51754fe03ec030ff7384f20952c11e74"}}