{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MJONXDE62UC2I3V2Z6LVKF6AMI","short_pith_number":"pith:MJONXDE6","canonical_record":{"source":{"id":"1508.06886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-27T14:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"f7dfe6fd2a69c6061f52cde5675a87ee3661e6430aa16ef693eaac19adc904f7","abstract_canon_sha256":"169e294aa4fda58e3d2724343221faef38ad2c58bceb0b6346f93c06ffd24ed8"},"schema_version":"1.0"},"canonical_sha256":"625cdb8c9ed505a46ebacf975517c062032f800f0ea060c05820aa89b0f66ff1","source":{"kind":"arxiv","id":"1508.06886","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06886","created_at":"2026-05-18T01:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06886v1","created_at":"2026-05-18T01:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06886","created_at":"2026-05-18T01:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"MJONXDE62UC2","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJONXDE62UC2I3V2","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJONXDE6","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MJONXDE62UC2I3V2Z6LVKF6AMI","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-27T14:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"f7dfe6fd2a69c6061f52cde5675a87ee3661e6430aa16ef693eaac19adc904f7","abstract_canon_sha256":"169e294aa4fda58e3d2724343221faef38ad2c58bceb0b6346f93c06ffd24ed8"},"schema_version":"1.0"},"canonical_sha256":"625cdb8c9ed505a46ebacf975517c062032f800f0ea060c05820aa89b0f66ff1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:17.498828Z","signature_b64":"x+/8jj3idGg1wwWjE1EL1+TNSSKbP5yu/5EwLWdXcEqdWlCFjj3DkZaD6no8QBsW3BmFgjXBFCYtDFU+5I6pBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"625cdb8c9ed505a46ebacf975517c062032f800f0ea060c05820aa89b0f66ff1","last_reissued_at":"2026-05-18T01:00:17.498012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:17.498012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06886","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":"2026-05-18T01:00:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rm7FlXuycQuAxp1trr6DnYNL5txonNX0jEtuveqEZQ8ig0d00E07pjcdwullCxODvCynSKE8dOkEcy/21G/IBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:29:50.161224Z"},"content_sha256":"d7700a452a194a7c66c44e1d7b847aff86d50a21dc8d839ebdbaed6db75cd30d","schema_version":"1.0","event_id":"sha256:d7700a452a194a7c66c44e1d7b847aff86d50a21dc8d839ebdbaed6db75cd30d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MJONXDE62UC2I3V2Z6LVKF6AMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semiparametric estimation of spectral density function for irregular spatial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Shu Yang, Zhengyuan Zhu","submitted_at":"2015-08-27T14:53:21Z","abstract_excerpt":"Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure based on the spectral representation of covariance functions. However,they either ignore the high frequency properties of the spectral density, which are essential to determine the performance of interpolation procedures such as Kriging, or lack of theoretical justification. We propose a new semi-parametric method to estimate spectral densities of isotropic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06886","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":"2026-05-18T01:00:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWUkHbDskIi3STdiNKI+uJdU7xuJ9hMNFR8Y2wEPNw+SenyE9wZquybWHppxnqIkEhVAuesqRfwUsFM/Ik4uCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:29:50.161584Z"},"content_sha256":"57b325da3e5d754df86d6efd4c1b9122994bf035889b9a3720c56a0c9bdbb459","schema_version":"1.0","event_id":"sha256:57b325da3e5d754df86d6efd4c1b9122994bf035889b9a3720c56a0c9bdbb459"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJONXDE62UC2I3V2Z6LVKF6AMI/bundle.json","state_url":"https://pith.science/pith/MJONXDE62UC2I3V2Z6LVKF6AMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJONXDE62UC2I3V2Z6LVKF6AMI/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":"2026-06-23T17:29:50Z","links":{"resolver":"https://pith.science/pith/MJONXDE62UC2I3V2Z6LVKF6AMI","bundle":"https://pith.science/pith/MJONXDE62UC2I3V2Z6LVKF6AMI/bundle.json","state":"https://pith.science/pith/MJONXDE62UC2I3V2Z6LVKF6AMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJONXDE62UC2I3V2Z6LVKF6AMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MJONXDE62UC2I3V2Z6LVKF6AMI","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":"169e294aa4fda58e3d2724343221faef38ad2c58bceb0b6346f93c06ffd24ed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-27T14:53:21Z","title_canon_sha256":"f7dfe6fd2a69c6061f52cde5675a87ee3661e6430aa16ef693eaac19adc904f7"},"schema_version":"1.0","source":{"id":"1508.06886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06886","created_at":"2026-05-18T01:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06886v1","created_at":"2026-05-18T01:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06886","created_at":"2026-05-18T01:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"MJONXDE62UC2","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJONXDE62UC2I3V2","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJONXDE6","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:57b325da3e5d754df86d6efd4c1b9122994bf035889b9a3720c56a0c9bdbb459","target":"graph","created_at":"2026-05-18T01:00:17Z","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":"Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure based on the spectral representation of covariance functions. However,they either ignore the high frequency properties of the spectral density, which are essential to determine the performance of interpolation procedures such as Kriging, or lack of theoretical justification. We propose a new semi-parametric method to estimate spectral densities of isotropic s","authors_text":"Shu Yang, Zhengyuan Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-27T14:53:21Z","title":"Semiparametric estimation of spectral density function for irregular spatial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06886","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:d7700a452a194a7c66c44e1d7b847aff86d50a21dc8d839ebdbaed6db75cd30d","target":"record","created_at":"2026-05-18T01:00:17Z","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":"169e294aa4fda58e3d2724343221faef38ad2c58bceb0b6346f93c06ffd24ed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-08-27T14:53:21Z","title_canon_sha256":"f7dfe6fd2a69c6061f52cde5675a87ee3661e6430aa16ef693eaac19adc904f7"},"schema_version":"1.0","source":{"id":"1508.06886","kind":"arxiv","version":1}},"canonical_sha256":"625cdb8c9ed505a46ebacf975517c062032f800f0ea060c05820aa89b0f66ff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"625cdb8c9ed505a46ebacf975517c062032f800f0ea060c05820aa89b0f66ff1","first_computed_at":"2026-05-18T01:00:17.498012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:17.498012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+/8jj3idGg1wwWjE1EL1+TNSSKbP5yu/5EwLWdXcEqdWlCFjj3DkZaD6no8QBsW3BmFgjXBFCYtDFU+5I6pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:17.498828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7700a452a194a7c66c44e1d7b847aff86d50a21dc8d839ebdbaed6db75cd30d","sha256:57b325da3e5d754df86d6efd4c1b9122994bf035889b9a3720c56a0c9bdbb459"],"state_sha256":"1bd79dd8a3f849499b69b573e0b9511806cab7dbf3adcac4b4c350619cdd676b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrm3wR4khzzGEjw524d+Y7gGTrRsD5w2k93nbuVt1g2rpI1B10nj6onGyR4F0Aww8hzInc6BMUujCmE+Ok0IAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:29:50.163500Z","bundle_sha256":"1e30a6e823e102e6b203a71432a3d5c3bc1ddc051ca99423141e7fd899ffe8f8"}}