{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:76TPUMPA3W7MUCCUNFYNUN5W52","short_pith_number":"pith:76TPUMPA","canonical_record":{"source":{"id":"math/0104027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2001-04-02T19:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"ea852dd8ee5970ac21fc5bb716eb9f74009cdfeaa429dc56cc05482852bf8221","abstract_canon_sha256":"b18bcdfe07ac07710726b06e2ec113879a24b51c34389c2dfdfc4a095d839e37"},"schema_version":"1.0"},"canonical_sha256":"ffa6fa31e0ddbeca08546970da37b6ee805aeaef59d81f32402fac5a7180b210","source":{"kind":"arxiv","id":"math/0104027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0104027","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0104027v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0104027","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"76TPUMPA3W7M","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"76TPUMPA3W7MUCCU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"76TPUMPA","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:76TPUMPA3W7MUCCUNFYNUN5W52","target":"record","payload":{"canonical_record":{"source":{"id":"math/0104027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2001-04-02T19:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"ea852dd8ee5970ac21fc5bb716eb9f74009cdfeaa429dc56cc05482852bf8221","abstract_canon_sha256":"b18bcdfe07ac07710726b06e2ec113879a24b51c34389c2dfdfc4a095d839e37"},"schema_version":"1.0"},"canonical_sha256":"ffa6fa31e0ddbeca08546970da37b6ee805aeaef59d81f32402fac5a7180b210","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.978908Z","signature_b64":"Rff+oGywZs9fulZTwuR8s5NmcA1ycVGbGZNUtUOOEfzKl4dZ3kvi585dwISFTThOPCBz3aER9qqLwIgou8GDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffa6fa31e0ddbeca08546970da37b6ee805aeaef59d81f32402fac5a7180b210","last_reissued_at":"2026-05-18T01:38:29.978454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.978454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0104027","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9yTAtD83weoFbzBBYRV14/bUmHEm4zh8toJYmS8j6ShZn/4w58WaFDMU1LkNeAus1pLSbvAEiJ6PdJDiQKhKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:37:12.149698Z"},"content_sha256":"a4c42e264fa32228789d44e0e0dc3a80446e39c34b39a54c350a038314ebbacc","schema_version":"1.0","event_id":"sha256:a4c42e264fa32228789d44e0e0dc3a80446e39c34b39a54c350a038314ebbacc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:76TPUMPA3W7MUCCUNFYNUN5W52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral densities describing off-white noises","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Boris Tsirelson","submitted_at":"2001-04-02T19:56:01Z","abstract_excerpt":"For the white noise, the spectral density is constant, and the past (restriction to (-\\infty,0)) is independent from the future (restriction to (0,+\\infty)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change; that is called an off-white noise. I derive from well-known results a necessary and sufficient condition for a spectral density to describe an off-white noise."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104027","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRHAaca0ZmAJtAPb37ssBlfOI0L5D5s9ZHg1arFTkcE5bkXKDW03uC8qwqio6Nil3k/CyUp5ypADL+U4shTYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:37:12.150041Z"},"content_sha256":"50f49b620090324595d81d8e5fa461e941fa8190735a8758822afeab8d5120ed","schema_version":"1.0","event_id":"sha256:50f49b620090324595d81d8e5fa461e941fa8190735a8758822afeab8d5120ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/76TPUMPA3W7MUCCUNFYNUN5W52/bundle.json","state_url":"https://pith.science/pith/76TPUMPA3W7MUCCUNFYNUN5W52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/76TPUMPA3W7MUCCUNFYNUN5W52/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":"2026-06-02T21:37:12Z","links":{"resolver":"https://pith.science/pith/76TPUMPA3W7MUCCUNFYNUN5W52","bundle":"https://pith.science/pith/76TPUMPA3W7MUCCUNFYNUN5W52/bundle.json","state":"https://pith.science/pith/76TPUMPA3W7MUCCUNFYNUN5W52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/76TPUMPA3W7MUCCUNFYNUN5W52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:76TPUMPA3W7MUCCUNFYNUN5W52","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":"b18bcdfe07ac07710726b06e2ec113879a24b51c34389c2dfdfc4a095d839e37","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-04-02T19:56:01Z","title_canon_sha256":"ea852dd8ee5970ac21fc5bb716eb9f74009cdfeaa429dc56cc05482852bf8221"},"schema_version":"1.0","source":{"id":"math/0104027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0104027","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0104027v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0104027","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"76TPUMPA3W7M","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"76TPUMPA3W7MUCCU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"76TPUMPA","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:50f49b620090324595d81d8e5fa461e941fa8190735a8758822afeab8d5120ed","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"For the white noise, the spectral density is constant, and the past (restriction to (-\\infty,0)) is independent from the future (restriction to (0,+\\infty)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change; that is called an off-white noise. I derive from well-known results a necessary and sufficient condition for a spectral density to describe an off-white noise.","authors_text":"Boris Tsirelson","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2001-04-02T19:56:01Z","title":"Spectral densities describing off-white noises"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104027","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:a4c42e264fa32228789d44e0e0dc3a80446e39c34b39a54c350a038314ebbacc","target":"record","created_at":"2026-05-18T01:38:29Z","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":"b18bcdfe07ac07710726b06e2ec113879a24b51c34389c2dfdfc4a095d839e37","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2001-04-02T19:56:01Z","title_canon_sha256":"ea852dd8ee5970ac21fc5bb716eb9f74009cdfeaa429dc56cc05482852bf8221"},"schema_version":"1.0","source":{"id":"math/0104027","kind":"arxiv","version":1}},"canonical_sha256":"ffa6fa31e0ddbeca08546970da37b6ee805aeaef59d81f32402fac5a7180b210","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffa6fa31e0ddbeca08546970da37b6ee805aeaef59d81f32402fac5a7180b210","first_computed_at":"2026-05-18T01:38:29.978454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.978454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rff+oGywZs9fulZTwuR8s5NmcA1ycVGbGZNUtUOOEfzKl4dZ3kvi585dwISFTThOPCBz3aER9qqLwIgou8GDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.978908Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0104027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4c42e264fa32228789d44e0e0dc3a80446e39c34b39a54c350a038314ebbacc","sha256:50f49b620090324595d81d8e5fa461e941fa8190735a8758822afeab8d5120ed"],"state_sha256":"8a3bbd87d15ad711fb16d5252dd569eb74e6c5a5081d8ac68db70a31ea9f6087"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32FeTCf19rG15kGXxgR8xgXcQrw9iQePR0tZHswzqM9K+GINsaLB4QMo2kiCcEw5Q4FjQ50e+1+5cyArct8yBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:37:12.152006Z","bundle_sha256":"ea8014dc918e6f8c6db18eabcb12b7638c77ce75b9c1c00d3ad7af37fcaf1d4c"}}