{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IY6LTM73XTDWR5BMZTZ735KFFE","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":"347a2d9f324ba3310b3480493dd106149df1f88fed13e3f1235c53cf4e8db28c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2012-02-21T20:48:23Z","title_canon_sha256":"c3a233810a6cc2a2ab0a8191175caceec78a6bc87ce94c73eae19396c8e1b642"},"schema_version":"1.0","source":{"id":"1202.4746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4746","created_at":"2026-05-18T04:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4746v1","created_at":"2026-05-18T04:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4746","created_at":"2026-05-18T04:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"IY6LTM73XTDW","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IY6LTM73XTDWR5BM","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IY6LTM73","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:30b239a870c97a9991542fc984e576b240e6c3b66d0799afaa6b42ac75984377","target":"graph","created_at":"2026-05-18T04:01:49Z","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":"A long memory process has self-similarity or scale-invariant properties in low frequencies. We prove that the log of the scale-dependent wavelet variance for a long memory process is asymptotically proportional to scales by using the Taylor expansion of wavelet variances.","authors_text":"Wojciech Kordecki, Wonsang You","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2012-02-21T20:48:23Z","title":"A Proof on Asymptotics of Wavelet Variance of a Long Memory Process by Using Taylor Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4746","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:e03e817f866b9b8b333432bd576017325b81c3d0b929b87505ff69d0e3ac325f","target":"record","created_at":"2026-05-18T04:01:49Z","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":"347a2d9f324ba3310b3480493dd106149df1f88fed13e3f1235c53cf4e8db28c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2012-02-21T20:48:23Z","title_canon_sha256":"c3a233810a6cc2a2ab0a8191175caceec78a6bc87ce94c73eae19396c8e1b642"},"schema_version":"1.0","source":{"id":"1202.4746","kind":"arxiv","version":1}},"canonical_sha256":"463cb9b3fbbcc768f42cccf3fdf5452929c7f1c9ba8189f3c3361fccf1d7f7cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463cb9b3fbbcc768f42cccf3fdf5452929c7f1c9ba8189f3c3361fccf1d7f7cb","first_computed_at":"2026-05-18T04:01:49.958096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:49.958096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nh5i3sIrt690uV71ZlZvHvGnDaDnAUtqgI/E7ZlpgNpORlFGrIzmZRzPpmfDPQGI/IyjStYUS4GYAISGryb9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:49.958591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e03e817f866b9b8b333432bd576017325b81c3d0b929b87505ff69d0e3ac325f","sha256:30b239a870c97a9991542fc984e576b240e6c3b66d0799afaa6b42ac75984377"],"state_sha256":"7ed5c9a18f508329e22712e6f5e99a1cb6e05c0b61a335129ace7129427f95a2"}