{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:J4RJXMV6HGGXOC3UEOBKEK767W","short_pith_number":"pith:J4RJXMV6","canonical_record":{"source":{"id":"1310.4794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-10-17T18:43:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"108dd72235f9f7fa290d47d84d750be7e8720b2d8e0f403c7b971c0fb20f22d8","abstract_canon_sha256":"fa4e8f8b5c2e10e97d75944aacf6e656359520814f640f36dcfcda831c433282"},"schema_version":"1.0"},"canonical_sha256":"4f229bb2be398d770b742382a22bfefdb5e833a178b40b710d92f3850d752142","source":{"kind":"arxiv","id":"1310.4794","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4794","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4794v2","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4794","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"pith_short_12","alias_value":"J4RJXMV6HGGX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J4RJXMV6HGGXOC3U","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J4RJXMV6","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:J4RJXMV6HGGXOC3UEOBKEK767W","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-10-17T18:43:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"108dd72235f9f7fa290d47d84d750be7e8720b2d8e0f403c7b971c0fb20f22d8","abstract_canon_sha256":"fa4e8f8b5c2e10e97d75944aacf6e656359520814f640f36dcfcda831c433282"},"schema_version":"1.0"},"canonical_sha256":"4f229bb2be398d770b742382a22bfefdb5e833a178b40b710d92f3850d752142","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:32.349841Z","signature_b64":"vEfQ2hEk6kVeIOswRwbIclIdkZv4f2B+mx9hmW4Rr7kyJgunTjZiYODwqW+9OaQVpep8nCZ+N1Koixrpp8hsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f229bb2be398d770b742382a22bfefdb5e833a178b40b710d92f3850d752142","last_reissued_at":"2026-05-18T02:56:32.349115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:32.349115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4794","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":"2026-05-18T02:56:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+nBACAgZxO0Wl7Bmuz5o0CkSP3E/SpQo4O0l+aLEtmpLUFpK0mNVZtSq9Fq1xCZpEOqtTbp2FdtA+vUbzBxPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:37:43.323184Z"},"content_sha256":"6b5784c2c659894748c99727484362d7528e87afb4320ee0e9d4f6ce2546eeb4","schema_version":"1.0","event_id":"sha256:6b5784c2c659894748c99727484362d7528e87afb4320ee0e9d4f6ce2546eeb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:J4RJXMV6HGGXOC3UEOBKEK767W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Gaussian Radon Transform and Machine Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"stat.ML","authors_text":"Ambar Sengupta, Irina Holmes","submitted_at":"2013-10-17T18:43:40Z","abstract_excerpt":"There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle for such stochastic models. We propose an estimation model for the ridge regression problem within the framework of abstract Wiener spaces and show how the support vector machine solution to such problems can be interpreted in terms of the Gaussian Radon transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4794","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":""},"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":"2026-05-18T02:56:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RFJDnb+VwcNK/bfHbmoDnHSbEPBIH5EdhSb6LVIK5yUEVF3fctxfGiP5z9o1P6g3CkHGV/aKNzCT8i7egcdYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:37:43.324003Z"},"content_sha256":"b2d9012a34b703bea02683ec8c5034a5d6b2b698a7faca4fa6fbc8d4966e75e0","schema_version":"1.0","event_id":"sha256:b2d9012a34b703bea02683ec8c5034a5d6b2b698a7faca4fa6fbc8d4966e75e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4RJXMV6HGGXOC3UEOBKEK767W/bundle.json","state_url":"https://pith.science/pith/J4RJXMV6HGGXOC3UEOBKEK767W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4RJXMV6HGGXOC3UEOBKEK767W/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":"2026-05-28T23:37:43Z","links":{"resolver":"https://pith.science/pith/J4RJXMV6HGGXOC3UEOBKEK767W","bundle":"https://pith.science/pith/J4RJXMV6HGGXOC3UEOBKEK767W/bundle.json","state":"https://pith.science/pith/J4RJXMV6HGGXOC3UEOBKEK767W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4RJXMV6HGGXOC3UEOBKEK767W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J4RJXMV6HGGXOC3UEOBKEK767W","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":"fa4e8f8b5c2e10e97d75944aacf6e656359520814f640f36dcfcda831c433282","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-10-17T18:43:40Z","title_canon_sha256":"108dd72235f9f7fa290d47d84d750be7e8720b2d8e0f403c7b971c0fb20f22d8"},"schema_version":"1.0","source":{"id":"1310.4794","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4794","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4794v2","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4794","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"pith_short_12","alias_value":"J4RJXMV6HGGX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J4RJXMV6HGGXOC3U","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J4RJXMV6","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:b2d9012a34b703bea02683ec8c5034a5d6b2b698a7faca4fa6fbc8d4966e75e0","target":"graph","created_at":"2026-05-18T02:56:32Z","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":"There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle for such stochastic models. We propose an estimation model for the ridge regression problem within the framework of abstract Wiener spaces and show how the support vector machine solution to such problems can be interpreted in terms of the Gaussian Radon transform.","authors_text":"Ambar Sengupta, Irina Holmes","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-10-17T18:43:40Z","title":"The Gaussian Radon Transform and Machine Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4794","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":"sha256:6b5784c2c659894748c99727484362d7528e87afb4320ee0e9d4f6ce2546eeb4","target":"record","created_at":"2026-05-18T02:56:32Z","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":"fa4e8f8b5c2e10e97d75944aacf6e656359520814f640f36dcfcda831c433282","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-10-17T18:43:40Z","title_canon_sha256":"108dd72235f9f7fa290d47d84d750be7e8720b2d8e0f403c7b971c0fb20f22d8"},"schema_version":"1.0","source":{"id":"1310.4794","kind":"arxiv","version":2}},"canonical_sha256":"4f229bb2be398d770b742382a22bfefdb5e833a178b40b710d92f3850d752142","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f229bb2be398d770b742382a22bfefdb5e833a178b40b710d92f3850d752142","first_computed_at":"2026-05-18T02:56:32.349115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:32.349115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vEfQ2hEk6kVeIOswRwbIclIdkZv4f2B+mx9hmW4Rr7kyJgunTjZiYODwqW+9OaQVpep8nCZ+N1Koixrpp8hsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:32.349841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4794","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b5784c2c659894748c99727484362d7528e87afb4320ee0e9d4f6ce2546eeb4","sha256:b2d9012a34b703bea02683ec8c5034a5d6b2b698a7faca4fa6fbc8d4966e75e0"],"state_sha256":"4b9571ec8b9c427234a9a8d1785d1107e89e3bf7a2b854f89a24cb3d09d8fc24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gM9s6JNeF/aRie4boDe48DyCFfh5A330ZSJUNqatoK9UTj7aEsymgAAIeCpSm0v/8tRmIp9fHdst/Y9FFShFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:37:43.326823Z","bundle_sha256":"394b60890cbf98bd52ea797daf7bd5e688072eb7744788887a15c5966c19750d"}}