{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5Z5SNKWCAWVFMPA2JT63SMIVCT","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":"84211348ce6db705e40f340fe03624b883bd04664d3622e67e16f24fbf7b6e8e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-28T20:37:30Z","title_canon_sha256":"c2648c89d392c0e2693977919e6cf025956242edbe7c0f6b20c63eca78782873"},"schema_version":"1.0","source":{"id":"1506.08450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08450","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08450v2","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08450","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"5Z5SNKWCAWVF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5Z5SNKWCAWVFMPA2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5Z5SNKWC","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:d894dc718a64bca1a57c519d29730dc41d9c2d6ef4bf1cc8719328389b05aa11","target":"graph","created_at":"2026-05-18T00:48:55Z","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":"Establishing the convergence of splines can be cast as a variational problem which is amenable to a $\\Gamma$-convergence approach. We consider the case in which the regularization coefficient scales with the number of observations, $n$, as $\\lambda_n=n^{-p}$. Using standard theorems from the $\\Gamma$-convergence literature, we prove that the general spline model is consistent in that estimators converge in a sense slightly weaker than weak convergence in probability for $p\\leq \\frac{1}{2}$. Without further assumptions we show this rate is sharp. This differs from rates for strong convergence u","authors_text":"Adam M. Johansen, Matthew Thorpe","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-28T20:37:30Z","title":"Pointwise Convergence in Probability of General Smoothing Splines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08450","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":"sha256:3200f315e67b393320cc5dc0b8a6c317d382a068c1a0363e9e3932777f552871","target":"record","created_at":"2026-05-18T00:48:55Z","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":"84211348ce6db705e40f340fe03624b883bd04664d3622e67e16f24fbf7b6e8e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-28T20:37:30Z","title_canon_sha256":"c2648c89d392c0e2693977919e6cf025956242edbe7c0f6b20c63eca78782873"},"schema_version":"1.0","source":{"id":"1506.08450","kind":"arxiv","version":2}},"canonical_sha256":"ee7b26aac205aa563c1a4cfdb9311514fceaed1b9e830e79db19db01fddeba23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7b26aac205aa563c1a4cfdb9311514fceaed1b9e830e79db19db01fddeba23","first_computed_at":"2026-05-18T00:48:55.030797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:55.030797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MON1gJaXLyVOkzb+SFgQaxAT2hsK+pNcZAWbr7t97Mhp8OshpBtAaE0bFX8JZ6+2vMlSqR88Lo3ZbDaT9MQYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:55.031585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3200f315e67b393320cc5dc0b8a6c317d382a068c1a0363e9e3932777f552871","sha256:d894dc718a64bca1a57c519d29730dc41d9c2d6ef4bf1cc8719328389b05aa11"],"state_sha256":"9cb783cb0b8434f17455094598e6851564b2e2bd21abe2d1b7de7544b99822f6"}