{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:37M4ICIPV67U5AIV2USGZOVTDE","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":"8da88754f7cff1330ece53135e557921c310bc5284e1874a7e583617d22a8960","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2013-06-13T23:16:48Z","title_canon_sha256":"a5868e93d67f18205258c906da564d88f2abe0ff532834dfb63711c86cdab437"},"schema_version":"1.0","source":{"id":"1306.3272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3272","created_at":"2026-05-18T01:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3272v1","created_at":"2026-05-18T01:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3272","created_at":"2026-05-18T01:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"37M4ICIPV67U","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"37M4ICIPV67U5AIV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"37M4ICIP","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:1a9591cdcdd293c292923231b5f9485dcfd853f88f64f60c6535f01a206dc52c","target":"graph","created_at":"2026-05-18T01:49:22Z","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":"Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known properties of the power spectrum when the time series contains a periodic signal. The approach is also validated in general with numerical simulations. The method puts into evidence the importance that is played by the probability density function of the phases associated to each time stamp for a given frequency, and how this distribution can be perturbed by the","authors_text":"D. F. Torres, G. A. Caliandro, N. Rea","cross_cats":["astro-ph.IM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2013-06-13T23:16:48Z","title":"A method for evaluating the expectation value of a power spectrum using the probability density function of phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3272","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:ef4691f98a593c396273cf9084c798c6ab3900865e814e03737349d5fa608468","target":"record","created_at":"2026-05-18T01:49:22Z","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":"8da88754f7cff1330ece53135e557921c310bc5284e1874a7e583617d22a8960","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.HE","submitted_at":"2013-06-13T23:16:48Z","title_canon_sha256":"a5868e93d67f18205258c906da564d88f2abe0ff532834dfb63711c86cdab437"},"schema_version":"1.0","source":{"id":"1306.3272","kind":"arxiv","version":1}},"canonical_sha256":"dfd9c4090fafbf4e8115d5246cbab31916ebb248747b2e4d427533cb540811be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfd9c4090fafbf4e8115d5246cbab31916ebb248747b2e4d427533cb540811be","first_computed_at":"2026-05-18T01:49:22.527941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:22.527941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RIDV8IsF6/ZDL7NHHxKsTxVt7wPuvM4Etb2wHqjjviNzyotk2+aVIEhrjhL35JVic/gx2vue+SCoNOSbTX4hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:22.528392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef4691f98a593c396273cf9084c798c6ab3900865e814e03737349d5fa608468","sha256:1a9591cdcdd293c292923231b5f9485dcfd853f88f64f60c6535f01a206dc52c"],"state_sha256":"a638f996c9d0bfa634d92ccff37e201cf33841447f0e852d53811ff8fd44731a"}