{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KJLNDIKBWUR7UWOXZU6FR7U2XQ","short_pith_number":"pith:KJLNDIKB","canonical_record":{"source":{"id":"1404.0361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-01T19:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"5b4bcdfc99c316ab1a0b903d76a05040b03247574bea42fb0db4db18168fc608","abstract_canon_sha256":"457969c136cce4d0ce88648964a4adb682dc3525177a0b70e64e0231f9a70019"},"schema_version":"1.0"},"canonical_sha256":"5256d1a141b523fa59d7cd3c58fe9abc23edfbca56363ed04153af4e7476225e","source":{"kind":"arxiv","id":"1404.0361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0361","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0361v1","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0361","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"KJLNDIKBWUR7","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KJLNDIKBWUR7UWOX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KJLNDIKB","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KJLNDIKBWUR7UWOXZU6FR7U2XQ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-01T19:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"5b4bcdfc99c316ab1a0b903d76a05040b03247574bea42fb0db4db18168fc608","abstract_canon_sha256":"457969c136cce4d0ce88648964a4adb682dc3525177a0b70e64e0231f9a70019"},"schema_version":"1.0"},"canonical_sha256":"5256d1a141b523fa59d7cd3c58fe9abc23edfbca56363ed04153af4e7476225e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:04.573094Z","signature_b64":"heRZngw1xvdPe3zqrTBl0UAyNZ2pKttKJvgTrcylKx2tqsaG84lGcbOjyGe8chpWPY4eKwy7eCKPT5HzFHpqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5256d1a141b523fa59d7cd3c58fe9abc23edfbca56363ed04153af4e7476225e","last_reissued_at":"2026-05-18T02:55:04.572683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:04.572683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0361","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":"2026-05-18T02:55:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHIGe+Abo03xQ33zkkpoqjhfreduZdJQpOkQNpBrIQZWCI4Lhf6e9f59En+HqQ25r+8WGPsexpRMjrRDRWjYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:59:36.028267Z"},"content_sha256":"6e8c54900154be978ba0af0109d940d92a67a71e38d5a5878580c09b1dbcd190","schema_version":"1.0","event_id":"sha256:6e8c54900154be978ba0af0109d940d92a67a71e38d5a5878580c09b1dbcd190"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KJLNDIKBWUR7UWOXZU6FR7U2XQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Valery Ryzhikov","submitted_at":"2014-04-01T19:40:58Z","abstract_excerpt":"1. We answer Michael Gordin's question providing singular spectrum for transformations with homoclinic Bernoulli flows via Poisson suspensions induced by modified Sidon rank-one constructions.\n  2. We give homoclinic proof of Emmanuel Roy's theorem on multiple mixing of Poisson suspensions, adding new examples to Jonathan King's ergodic homoclinic groups of special zero-entropy transformations.\n  3. Sasha Prikhod'ko found the fast decay of correlations for some iceberg automorphisms. We get similar correlations for a class of infinite rank-one Sidon transformations.\n  This version is based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0361","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":"2026-05-18T02:55:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5CcQml2zu6g10hm6ly2H/7k4qD6B5B27WdZWReQhOJiK/zWeEmmtkArsxHkZsuICp2KNE+jmdQD+Eg52FlhZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:59:36.028739Z"},"content_sha256":"1973b0b8f2782a22799c614bbdf3a3dd396e60c0263de31f567c8913ad13e483","schema_version":"1.0","event_id":"sha256:1973b0b8f2782a22799c614bbdf3a3dd396e60c0263de31f567c8913ad13e483"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ/bundle.json","state_url":"https://pith.science/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ/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":"2026-06-25T12:59:36Z","links":{"resolver":"https://pith.science/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ","bundle":"https://pith.science/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ/bundle.json","state":"https://pith.science/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJLNDIKBWUR7UWOXZU6FR7U2XQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KJLNDIKBWUR7UWOXZU6FR7U2XQ","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":"457969c136cce4d0ce88648964a4adb682dc3525177a0b70e64e0231f9a70019","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-01T19:40:58Z","title_canon_sha256":"5b4bcdfc99c316ab1a0b903d76a05040b03247574bea42fb0db4db18168fc608"},"schema_version":"1.0","source":{"id":"1404.0361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0361","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0361v1","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0361","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"KJLNDIKBWUR7","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KJLNDIKBWUR7UWOX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KJLNDIKB","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:1973b0b8f2782a22799c614bbdf3a3dd396e60c0263de31f567c8913ad13e483","target":"graph","created_at":"2026-05-18T02:55:04Z","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":"1. We answer Michael Gordin's question providing singular spectrum for transformations with homoclinic Bernoulli flows via Poisson suspensions induced by modified Sidon rank-one constructions.\n  2. We give homoclinic proof of Emmanuel Roy's theorem on multiple mixing of Poisson suspensions, adding new examples to Jonathan King's ergodic homoclinic groups of special zero-entropy transformations.\n  3. Sasha Prikhod'ko found the fast decay of correlations for some iceberg automorphisms. We get similar correlations for a class of infinite rank-one Sidon transformations.\n  This version is based on ","authors_text":"Valery Ryzhikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-01T19:40:58Z","title":"Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson Suspensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0361","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":"sha256:6e8c54900154be978ba0af0109d940d92a67a71e38d5a5878580c09b1dbcd190","target":"record","created_at":"2026-05-18T02:55:04Z","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":"457969c136cce4d0ce88648964a4adb682dc3525177a0b70e64e0231f9a70019","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-01T19:40:58Z","title_canon_sha256":"5b4bcdfc99c316ab1a0b903d76a05040b03247574bea42fb0db4db18168fc608"},"schema_version":"1.0","source":{"id":"1404.0361","kind":"arxiv","version":1}},"canonical_sha256":"5256d1a141b523fa59d7cd3c58fe9abc23edfbca56363ed04153af4e7476225e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5256d1a141b523fa59d7cd3c58fe9abc23edfbca56363ed04153af4e7476225e","first_computed_at":"2026-05-18T02:55:04.572683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:04.572683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"heRZngw1xvdPe3zqrTBl0UAyNZ2pKttKJvgTrcylKx2tqsaG84lGcbOjyGe8chpWPY4eKwy7eCKPT5HzFHpqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:04.573094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e8c54900154be978ba0af0109d940d92a67a71e38d5a5878580c09b1dbcd190","sha256:1973b0b8f2782a22799c614bbdf3a3dd396e60c0263de31f567c8913ad13e483"],"state_sha256":"8b32422bd65cd19e776cccdf1855578055fe8272f32a8c55ead84d21715868ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bjaTxPa0yZ/1aRyG2PCdsDm/CqThGpwnfQleydzgEFVWU1vExju7dmScbCMeLA+og4spf+7FnCyjdwIxQeQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:59:36.031494Z","bundle_sha256":"9c68427f2bb5d95c0f2125762cd57488c4d81b9371bab56d1299f31502124bcb"}}