{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EMPKD4BTXVN5ITS2QEA3MLIRWK","short_pith_number":"pith:EMPKD4BT","canonical_record":{"source":{"id":"1710.06826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-10-18T16:56:45Z","cross_cats_sorted":[],"title_canon_sha256":"43efc1d499b2bd8389959a68339cffbacdde4a39d3b3e2fade4b08a89a128f3a","abstract_canon_sha256":"7847fccd685c42df5a092ff72fccde8489b96c9aa27671e5d42148867e266098"},"schema_version":"1.0"},"canonical_sha256":"231ea1f033bd5bd44e5a8101b62d11b299282a6b9cf03ffbff96beb5f4c29e44","source":{"kind":"arxiv","id":"1710.06826","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06826","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06826v1","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06826","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"EMPKD4BTXVN5","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EMPKD4BTXVN5ITS2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EMPKD4BT","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EMPKD4BTXVN5ITS2QEA3MLIRWK","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-10-18T16:56:45Z","cross_cats_sorted":[],"title_canon_sha256":"43efc1d499b2bd8389959a68339cffbacdde4a39d3b3e2fade4b08a89a128f3a","abstract_canon_sha256":"7847fccd685c42df5a092ff72fccde8489b96c9aa27671e5d42148867e266098"},"schema_version":"1.0"},"canonical_sha256":"231ea1f033bd5bd44e5a8101b62d11b299282a6b9cf03ffbff96beb5f4c29e44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:32.018763Z","signature_b64":"N2alS9U3wso4GLcUB1Ws9UQl+9IpY8vmkMsTn+9/0aNwGxxF9tkQ/Xrh9RYKbI7Y6acIlg6ruI2/+bjYLOd5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"231ea1f033bd5bd44e5a8101b62d11b299282a6b9cf03ffbff96beb5f4c29e44","last_reissued_at":"2026-05-18T00:32:32.018066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:32.018066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06826","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BhvmsKASweZnpGEO66W0QFdAo/IwjgK2GRBO7lsqJOGXmNKVZPuBXaYzMD48nemT8GE6nEemUtWGtSsCCsR5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:22:27.675862Z"},"content_sha256":"2b74d136ee8c7224313e97713f9648ba9ca08cea802f3d28174e2b3e2591a246","schema_version":"1.0","event_id":"sha256:2b74d136ee8c7224313e97713f9648ba9ca08cea802f3d28174e2b3e2591a246"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EMPKD4BTXVN5ITS2QEA3MLIRWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial random field models based on L\\'evy indicator convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Thomas Opitz","submitted_at":"2017-10-18T16:56:45Z","abstract_excerpt":"Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may be prohibitively computer-intensive. We here remedy such issues through a class of process convolutions based on smoothing a (d+1)-dimensional L\\'evy basis with an indicator function kernel to construct a d-dimensional convolution process. Indicator kernels ensure univariate distributions in the L\\'evy basis family, which provides a sound basis for interpre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06826","kind":"arxiv","version":1},"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":"2026-05-18T00:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EBJ3Y7i5+TxePVLgH4lMHLCcL2tiEtSCTOrw5Hs7VQRFo3NTcNTE5/zyq5e3EhbyDGGxgf7UwNx9gjyAiNmkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:22:27.676370Z"},"content_sha256":"e095f02aa1a5299f0ed676bbf6d061aa0f625429fd7d1af0819db30f241d8eab","schema_version":"1.0","event_id":"sha256:e095f02aa1a5299f0ed676bbf6d061aa0f625429fd7d1af0819db30f241d8eab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK/bundle.json","state_url":"https://pith.science/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK/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":"2026-05-30T13:22:27Z","links":{"resolver":"https://pith.science/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK","bundle":"https://pith.science/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK/bundle.json","state":"https://pith.science/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMPKD4BTXVN5ITS2QEA3MLIRWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EMPKD4BTXVN5ITS2QEA3MLIRWK","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":"7847fccd685c42df5a092ff72fccde8489b96c9aa27671e5d42148867e266098","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-10-18T16:56:45Z","title_canon_sha256":"43efc1d499b2bd8389959a68339cffbacdde4a39d3b3e2fade4b08a89a128f3a"},"schema_version":"1.0","source":{"id":"1710.06826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06826","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06826v1","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06826","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"EMPKD4BTXVN5","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EMPKD4BTXVN5ITS2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EMPKD4BT","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:e095f02aa1a5299f0ed676bbf6d061aa0f625429fd7d1af0819db30f241d8eab","target":"graph","created_at":"2026-05-18T00:32:32Z","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":"Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may be prohibitively computer-intensive. We here remedy such issues through a class of process convolutions based on smoothing a (d+1)-dimensional L\\'evy basis with an indicator function kernel to construct a d-dimensional convolution process. Indicator kernels ensure univariate distributions in the L\\'evy basis family, which provides a sound basis for interpre","authors_text":"Thomas Opitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-10-18T16:56:45Z","title":"Spatial random field models based on L\\'evy indicator convolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06826","kind":"arxiv","version":1},"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":"sha256:2b74d136ee8c7224313e97713f9648ba9ca08cea802f3d28174e2b3e2591a246","target":"record","created_at":"2026-05-18T00:32:32Z","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":"7847fccd685c42df5a092ff72fccde8489b96c9aa27671e5d42148867e266098","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-10-18T16:56:45Z","title_canon_sha256":"43efc1d499b2bd8389959a68339cffbacdde4a39d3b3e2fade4b08a89a128f3a"},"schema_version":"1.0","source":{"id":"1710.06826","kind":"arxiv","version":1}},"canonical_sha256":"231ea1f033bd5bd44e5a8101b62d11b299282a6b9cf03ffbff96beb5f4c29e44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"231ea1f033bd5bd44e5a8101b62d11b299282a6b9cf03ffbff96beb5f4c29e44","first_computed_at":"2026-05-18T00:32:32.018066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:32.018066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N2alS9U3wso4GLcUB1Ws9UQl+9IpY8vmkMsTn+9/0aNwGxxF9tkQ/Xrh9RYKbI7Y6acIlg6ruI2/+bjYLOd5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:32.018763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b74d136ee8c7224313e97713f9648ba9ca08cea802f3d28174e2b3e2591a246","sha256:e095f02aa1a5299f0ed676bbf6d061aa0f625429fd7d1af0819db30f241d8eab"],"state_sha256":"8dd9630a8aa1a2b5dd034be595b5b4b0c8f11b48b47fe58045f18ce02c3cf821"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Idhw++Brgmh4ENrb29u4VmaSmhK9od94yr6uZ3UIWPcy0IIOPUbKgvlwEuCOaX9FGegcIFg8jrQuNrcGu1XdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:22:27.681664Z","bundle_sha256":"46bc0d0618214fbcfdb606a0b8062864f93aab9a23367c2bd0ccb5db20a8dd61"}}