{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2PIW3KAE2WNR36H3R5ZIZ6K4GA","short_pith_number":"pith:2PIW3KAE","canonical_record":{"source":{"id":"1709.01575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T19:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"4924b1ce3b1e28e758e05e00f7c668b6bba5d184cc49cd83cb82ed66e080e0bf","abstract_canon_sha256":"89cd99e063d3c47b7bf6d1d1ee5cfc5e4ac411632e9602e8e722e0be086a63d1"},"schema_version":"1.0"},"canonical_sha256":"d3d16da804d59b1df8fb8f728cf95c302a19c83cc6a92f7b28557778ac384091","source":{"kind":"arxiv","id":"1709.01575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01575","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01575v2","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01575","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"pith_short_12","alias_value":"2PIW3KAE2WNR","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PIW3KAE2WNR36H3","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PIW3KAE","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2PIW3KAE2WNR36H3R5ZIZ6K4GA","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T19:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"4924b1ce3b1e28e758e05e00f7c668b6bba5d184cc49cd83cb82ed66e080e0bf","abstract_canon_sha256":"89cd99e063d3c47b7bf6d1d1ee5cfc5e4ac411632e9602e8e722e0be086a63d1"},"schema_version":"1.0"},"canonical_sha256":"d3d16da804d59b1df8fb8f728cf95c302a19c83cc6a92f7b28557778ac384091","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:33.820554Z","signature_b64":"qZAnGIZUOuAMBbRzIYJH/Y1kwq7+hAqjCa2PlXUT49Ay42GCx5GtZZTvNj2bAa2SleRVp5pBmpg47le7JMoBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3d16da804d59b1df8fb8f728cf95c302a19c83cc6a92f7b28557778ac384091","last_reissued_at":"2026-05-17T23:53:33.820088Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:33.820088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtwAy7Bzm7WuuTmJXlWMGczkaWIxYdN8Q2BE89nCmbW6UJQBKGwVoHw2qi3SnBV039LEpdM9aMDvB/KxcuSaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T22:29:21.971602Z"},"content_sha256":"9340910738a6cd077ae878be8d8aefc8c5f1855aeebae540a90988b861780700","schema_version":"1.0","event_id":"sha256:9340910738a6cd077ae878be8d8aefc8c5f1855aeebae540a90988b861780700"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2PIW3KAE2WNR36H3R5ZIZ6K4GA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodicity of skew products over linearly recurrent IETs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Donald Robertson, Jon Chaika","submitted_at":"2017-09-05T19:57:55Z","abstract_excerpt":"We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01575","kind":"arxiv","version":2},"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":"2026-05-17T23:53:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"atOzclCXqKl6ENy5OmHFUzLaoLW9kV2fRy9mJSbIvjQ2XTWumDMOYvphP78JQdHbNAsNWOkqlKHYQ2ozCu6WCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T22:29:21.972239Z"},"content_sha256":"a126dd4c8b0f8fd8ffde3ab8924272bd6ebea696aad540df72a598d246f00800","schema_version":"1.0","event_id":"sha256:a126dd4c8b0f8fd8ffde3ab8924272bd6ebea696aad540df72a598d246f00800"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA/bundle.json","state_url":"https://pith.science/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA/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":"2026-05-21T22:29:21Z","links":{"resolver":"https://pith.science/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA","bundle":"https://pith.science/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA/bundle.json","state":"https://pith.science/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2PIW3KAE2WNR36H3R5ZIZ6K4GA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2PIW3KAE2WNR36H3R5ZIZ6K4GA","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":"89cd99e063d3c47b7bf6d1d1ee5cfc5e4ac411632e9602e8e722e0be086a63d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T19:57:55Z","title_canon_sha256":"4924b1ce3b1e28e758e05e00f7c668b6bba5d184cc49cd83cb82ed66e080e0bf"},"schema_version":"1.0","source":{"id":"1709.01575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01575","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01575v2","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01575","created_at":"2026-05-17T23:53:33Z"},{"alias_kind":"pith_short_12","alias_value":"2PIW3KAE2WNR","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PIW3KAE2WNR36H3","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PIW3KAE","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:a126dd4c8b0f8fd8ffde3ab8924272bd6ebea696aad540df72a598d246f00800","target":"graph","created_at":"2026-05-17T23:53:33Z","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":"We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure.","authors_text":"Donald Robertson, Jon Chaika","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T19:57:55Z","title":"Ergodicity of skew products over linearly recurrent IETs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01575","kind":"arxiv","version":2},"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":"sha256:9340910738a6cd077ae878be8d8aefc8c5f1855aeebae540a90988b861780700","target":"record","created_at":"2026-05-17T23:53:33Z","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":"89cd99e063d3c47b7bf6d1d1ee5cfc5e4ac411632e9602e8e722e0be086a63d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T19:57:55Z","title_canon_sha256":"4924b1ce3b1e28e758e05e00f7c668b6bba5d184cc49cd83cb82ed66e080e0bf"},"schema_version":"1.0","source":{"id":"1709.01575","kind":"arxiv","version":2}},"canonical_sha256":"d3d16da804d59b1df8fb8f728cf95c302a19c83cc6a92f7b28557778ac384091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3d16da804d59b1df8fb8f728cf95c302a19c83cc6a92f7b28557778ac384091","first_computed_at":"2026-05-17T23:53:33.820088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:33.820088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZAnGIZUOuAMBbRzIYJH/Y1kwq7+hAqjCa2PlXUT49Ay42GCx5GtZZTvNj2bAa2SleRVp5pBmpg47le7JMoBAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:33.820554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9340910738a6cd077ae878be8d8aefc8c5f1855aeebae540a90988b861780700","sha256:a126dd4c8b0f8fd8ffde3ab8924272bd6ebea696aad540df72a598d246f00800"],"state_sha256":"b4eaedbf0de9636d97b7749c90522dfb64eb432f315eeff8ccc472eaf8afd247"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uad9j4ACj7DlY28YZNr9naP2WsvDQrOWKhQ6rwjkYyX9YOmeIP+236ZDgA00YGtV0EGpYqG7t7jos7G8PqhSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T22:29:21.975367Z","bundle_sha256":"3535bed868f94e3afb115352961493b58bc5dced8bfa6f3b9b1a6f1a2243d6bc"}}