{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SCSKWTEUIYH3N5LCCG2HZMRFZD","short_pith_number":"pith:SCSKWTEU","canonical_record":{"source":{"id":"2607.04833","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-06T09:08:00Z","cross_cats_sorted":["astro-ph.IM","gr-qc"],"title_canon_sha256":"33c4dc1dcc88bfdfa96da210ce3c8aa2066371a0c576931cc8c5e6a18e4a1405","abstract_canon_sha256":"e1c2a903666faf52f7122823d673ac07dc8b6a3dc81722bac6c29e4c98ab394b"},"schema_version":"1.0"},"canonical_sha256":"90a4ab4c94460fb6f56211b47cb225c8d0cc28f2b8266e83e803a40e5ef4f577","source":{"kind":"arxiv","id":"2607.04833","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04833","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04833v1","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04833","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"SCSKWTEUIYH3","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"pith_short_16","alias_value":"SCSKWTEUIYH3N5LC","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"pith_short_8","alias_value":"SCSKWTEU","created_at":"2026-07-07T02:20:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SCSKWTEUIYH3N5LCCG2HZMRFZD","target":"record","payload":{"canonical_record":{"source":{"id":"2607.04833","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-06T09:08:00Z","cross_cats_sorted":["astro-ph.IM","gr-qc"],"title_canon_sha256":"33c4dc1dcc88bfdfa96da210ce3c8aa2066371a0c576931cc8c5e6a18e4a1405","abstract_canon_sha256":"e1c2a903666faf52f7122823d673ac07dc8b6a3dc81722bac6c29e4c98ab394b"},"schema_version":"1.0"},"canonical_sha256":"90a4ab4c94460fb6f56211b47cb225c8d0cc28f2b8266e83e803a40e5ef4f577","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:20:06.192539Z","signature_b64":"00oln91d+Vws14VTsI1wRa1VwlJlYybPhq/sFLbpej4zgZ2o+m6/gOPRULaQVgS8YK81fYHB3ib5ClLhsekgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90a4ab4c94460fb6f56211b47cb225c8d0cc28f2b8266e83e803a40e5ef4f577","last_reissued_at":"2026-07-07T02:20:06.191955Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:20:06.191955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.04833","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":"2026-07-07T02:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aEUTVqxXzYZxQJeAuacBCoDO8VfaidZDOQmNb9glPaNmb7cPbEXO6eQKdhF3QX7uOd3+NU9nf4FuWqMWi55GAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T11:34:16.537237Z"},"content_sha256":"76410dac910a3de6dcc4db96cd37a91cf16a420759e781762f82a07747a2b2f8","schema_version":"1.0","event_id":"sha256:76410dac910a3de6dcc4db96cd37a91cf16a420759e781762f82a07747a2b2f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SCSKWTEUIYH3N5LCCG2HZMRFZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Bayesian P-spline estimation of spectral density matrices, with application to LISA TDI noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.IM","gr-qc"],"primary_cat":"stat.ME","authors_text":"Avi Vajpeyi, Jianan Liu, Patricio Maturana-Russell, Renate Meyer","submitted_at":"2026-07-06T09:08:00Z","abstract_excerpt":"We present a Bayesian P-spline method for estimating the frequency-dependent cross-spectral density matrix of stationary multivariate time series. The inverse spectral matrix is parametrised through its frequency-varying Cholesky decomposition, which guarantees Hermitian positive definiteness at every frequency. Each real log-diagonal entry and each real and imaginary off-diagonal entry is given an independent penalised B-spline prior that controls smoothness. Inference uses a blocked, coarse-grained Whittle likelihood with safe-Bayes $\\eta$-tempering to stabilise posterior calibration, sample"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04833","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04833/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":"2026-07-07T02:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1fa7i+CB2+wUHIgzBFijiF88EiPnS6QKl2LKE/R5zfjMOP3L2rDdLO1fBsc5v//Kkngh8/xgXgg7i9ja+JXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T11:34:16.538181Z"},"content_sha256":"da67efc3d89561ba2dfb54bbeb9324b9f6e1cc867f3512d87a16e2f6382774dc","schema_version":"1.0","event_id":"sha256:da67efc3d89561ba2dfb54bbeb9324b9f6e1cc867f3512d87a16e2f6382774dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD/bundle.json","state_url":"https://pith.science/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD/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":"2026-08-05T11:34:16Z","links":{"resolver":"https://pith.science/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD","bundle":"https://pith.science/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD/bundle.json","state":"https://pith.science/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCSKWTEUIYH3N5LCCG2HZMRFZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SCSKWTEUIYH3N5LCCG2HZMRFZD","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":"e1c2a903666faf52f7122823d673ac07dc8b6a3dc81722bac6c29e4c98ab394b","cross_cats_sorted":["astro-ph.IM","gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-06T09:08:00Z","title_canon_sha256":"33c4dc1dcc88bfdfa96da210ce3c8aa2066371a0c576931cc8c5e6a18e4a1405"},"schema_version":"1.0","source":{"id":"2607.04833","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04833","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04833v1","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04833","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"SCSKWTEUIYH3","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"pith_short_16","alias_value":"SCSKWTEUIYH3N5LC","created_at":"2026-07-07T02:20:06Z"},{"alias_kind":"pith_short_8","alias_value":"SCSKWTEU","created_at":"2026-07-07T02:20:06Z"}],"graph_snapshots":[{"event_id":"sha256:da67efc3d89561ba2dfb54bbeb9324b9f6e1cc867f3512d87a16e2f6382774dc","target":"graph","created_at":"2026-07-07T02:20:06Z","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/2607.04833/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a Bayesian P-spline method for estimating the frequency-dependent cross-spectral density matrix of stationary multivariate time series. The inverse spectral matrix is parametrised through its frequency-varying Cholesky decomposition, which guarantees Hermitian positive definiteness at every frequency. Each real log-diagonal entry and each real and imaginary off-diagonal entry is given an independent penalised B-spline prior that controls smoothness. Inference uses a blocked, coarse-grained Whittle likelihood with safe-Bayes $\\eta$-tempering to stabilise posterior calibration, sample","authors_text":"Avi Vajpeyi, Jianan Liu, Patricio Maturana-Russell, Renate Meyer","cross_cats":["astro-ph.IM","gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-06T09:08:00Z","title":"Multivariate Bayesian P-spline estimation of spectral density matrices, with application to LISA TDI noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04833","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":"sha256:76410dac910a3de6dcc4db96cd37a91cf16a420759e781762f82a07747a2b2f8","target":"record","created_at":"2026-07-07T02:20:06Z","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":"e1c2a903666faf52f7122823d673ac07dc8b6a3dc81722bac6c29e4c98ab394b","cross_cats_sorted":["astro-ph.IM","gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-06T09:08:00Z","title_canon_sha256":"33c4dc1dcc88bfdfa96da210ce3c8aa2066371a0c576931cc8c5e6a18e4a1405"},"schema_version":"1.0","source":{"id":"2607.04833","kind":"arxiv","version":1}},"canonical_sha256":"90a4ab4c94460fb6f56211b47cb225c8d0cc28f2b8266e83e803a40e5ef4f577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90a4ab4c94460fb6f56211b47cb225c8d0cc28f2b8266e83e803a40e5ef4f577","first_computed_at":"2026-07-07T02:20:06.191955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:20:06.191955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"00oln91d+Vws14VTsI1wRa1VwlJlYybPhq/sFLbpej4zgZ2o+m6/gOPRULaQVgS8YK81fYHB3ib5ClLhsekgAA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:20:06.192539Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04833","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76410dac910a3de6dcc4db96cd37a91cf16a420759e781762f82a07747a2b2f8","sha256:da67efc3d89561ba2dfb54bbeb9324b9f6e1cc867f3512d87a16e2f6382774dc"],"state_sha256":"ed7d530938345a5550fb2ec299c012aa9f8d1fb7e5572220aab6249cd0ace6eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jt0hlTbSFQbjmuIjix1RblMeSCkeycdcMEMmpheN+At8Vfl8wkdzNayDdd9S0kI1ClRocoSEKjb9P7xZkIdkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T11:34:16.590888Z","bundle_sha256":"486aa59566a6c7c1a2e44b558ba3b5cb1867b353bcd426eda9321c80b255bef4"}}