{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TQTGVM5XRVVVWFFFRYDBS6JUAE","short_pith_number":"pith:TQTGVM5X","canonical_record":{"source":{"id":"2409.12168","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-09-18T17:35:41Z","cross_cats_sorted":[],"title_canon_sha256":"52ffa45d5a4ddb514d10144d5d3106ae686d066fff3ef22b3a205a45c028070e","abstract_canon_sha256":"de03b0b905cb4a6c72f852fde08a42fb83b1dd22595c3082b329d75238e401ca"},"schema_version":"1.0"},"canonical_sha256":"9c266ab3b78d6b5b14a58e061979340104300e3698a5135367deb12ebfc8eec0","source":{"kind":"arxiv","id":"2409.12168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.12168","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2409.12168v1","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.12168","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"TQTGVM5XRVVV","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"TQTGVM5XRVVVWFFF","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"TQTGVM5X","created_at":"2026-07-05T09:08:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TQTGVM5XRVVVWFFFRYDBS6JUAE","target":"record","payload":{"canonical_record":{"source":{"id":"2409.12168","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-09-18T17:35:41Z","cross_cats_sorted":[],"title_canon_sha256":"52ffa45d5a4ddb514d10144d5d3106ae686d066fff3ef22b3a205a45c028070e","abstract_canon_sha256":"de03b0b905cb4a6c72f852fde08a42fb83b1dd22595c3082b329d75238e401ca"},"schema_version":"1.0"},"canonical_sha256":"9c266ab3b78d6b5b14a58e061979340104300e3698a5135367deb12ebfc8eec0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:08:43.753309Z","signature_b64":"rt2UXl+IHRr2CC1m1pqogmVqSRyER4P5PFX78fgV3htmOWQX4ewcX8GXqmfO+TYGsySwyvGOQlpXiSua5Y9SDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c266ab3b78d6b5b14a58e061979340104300e3698a5135367deb12ebfc8eec0","last_reissued_at":"2026-07-05T09:08:43.752831Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:08:43.752831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.12168","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":"2026-07-05T09:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R1vxwRmec/lyjXIvCzyZaMll4KKSkDDtWjCCrbBGAK59J5UHV4OYg2T0YmozGj5mLppTI6i8rHgbso8LI0PkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:21:00.333360Z"},"content_sha256":"bb8ea408bf27eb25db699153a77a3b494a0b05e4608c4797314aa43fd1c965d8","schema_version":"1.0","event_id":"sha256:bb8ea408bf27eb25db699153a77a3b494a0b05e4608c4797314aa43fd1c965d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TQTGVM5XRVVVWFFFRYDBS6JUAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic properties of infinite extension of symmetric interval exchange transformations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Frank Trujillo, Hao Wu, Przemys{\\l}aw Berk","submitted_at":"2024-09-18T17:35:41Z","abstract_excerpt":"We prove that skew products with the cocycle given by the function $f(x)=a(x-1/2)$ with $a\\neq 0$ are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in this family. Moreover, we prove that under an additional natural assumption of unique ergodicity on the IET, we can replace $f$ with any differentiable function with a non-zero sum of jumps. Finally, by considering weakly mixing IETs instead of just ergodic, we show that the skew products with cocycle given by $f$ have infinite ergodic index."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.12168","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.12168/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJD8K2mySDnbiRePxKU8PHapaG3+zaiUAhXzH+RasqSrNx+N/HSmNjtYtKUivuN8vWLpnqjKahEhM+sSdmWkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:21:00.333767Z"},"content_sha256":"2abee74551216d5dea0b688ef2e039613ad060a14cfe5a620f4529e25b4d480d","schema_version":"1.0","event_id":"sha256:2abee74551216d5dea0b688ef2e039613ad060a14cfe5a620f4529e25b4d480d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE/bundle.json","state_url":"https://pith.science/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE/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":"2026-08-06T00:21:00Z","links":{"resolver":"https://pith.science/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE","bundle":"https://pith.science/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE/bundle.json","state":"https://pith.science/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQTGVM5XRVVVWFFFRYDBS6JUAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TQTGVM5XRVVVWFFFRYDBS6JUAE","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":"de03b0b905cb4a6c72f852fde08a42fb83b1dd22595c3082b329d75238e401ca","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-09-18T17:35:41Z","title_canon_sha256":"52ffa45d5a4ddb514d10144d5d3106ae686d066fff3ef22b3a205a45c028070e"},"schema_version":"1.0","source":{"id":"2409.12168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.12168","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2409.12168v1","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.12168","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"TQTGVM5XRVVV","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"TQTGVM5XRVVVWFFF","created_at":"2026-07-05T09:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"TQTGVM5X","created_at":"2026-07-05T09:08:43Z"}],"graph_snapshots":[{"event_id":"sha256:2abee74551216d5dea0b688ef2e039613ad060a14cfe5a620f4529e25b4d480d","target":"graph","created_at":"2026-07-05T09:08:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.12168/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that skew products with the cocycle given by the function $f(x)=a(x-1/2)$ with $a\\neq 0$ are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in this family. Moreover, we prove that under an additional natural assumption of unique ergodicity on the IET, we can replace $f$ with any differentiable function with a non-zero sum of jumps. Finally, by considering weakly mixing IETs instead of just ergodic, we show that the skew products with cocycle given by $f$ have infinite ergodic index.","authors_text":"Frank Trujillo, Hao Wu, Przemys{\\l}aw Berk","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-09-18T17:35:41Z","title":"Ergodic properties of infinite extension of symmetric interval exchange transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.12168","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:bb8ea408bf27eb25db699153a77a3b494a0b05e4608c4797314aa43fd1c965d8","target":"record","created_at":"2026-07-05T09:08:43Z","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":"de03b0b905cb4a6c72f852fde08a42fb83b1dd22595c3082b329d75238e401ca","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-09-18T17:35:41Z","title_canon_sha256":"52ffa45d5a4ddb514d10144d5d3106ae686d066fff3ef22b3a205a45c028070e"},"schema_version":"1.0","source":{"id":"2409.12168","kind":"arxiv","version":1}},"canonical_sha256":"9c266ab3b78d6b5b14a58e061979340104300e3698a5135367deb12ebfc8eec0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c266ab3b78d6b5b14a58e061979340104300e3698a5135367deb12ebfc8eec0","first_computed_at":"2026-07-05T09:08:43.752831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:08:43.752831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rt2UXl+IHRr2CC1m1pqogmVqSRyER4P5PFX78fgV3htmOWQX4ewcX8GXqmfO+TYGsySwyvGOQlpXiSua5Y9SDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:08:43.753309Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.12168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb8ea408bf27eb25db699153a77a3b494a0b05e4608c4797314aa43fd1c965d8","sha256:2abee74551216d5dea0b688ef2e039613ad060a14cfe5a620f4529e25b4d480d"],"state_sha256":"0f45bd010472f13d9cb2857afad69b827f52602e2af9a789e9f1cc6a97faf23b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYAUxh2dGc0Jh7lbALDF0jlD4+/jInRWICwpkcgPegdadiACGTdO5rc2wfW7UUPFHKpjc2YCbpB7fideAgh/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T00:21:00.336319Z","bundle_sha256":"a357aff3d7fbfbe82801c8b59a0cd74049dc0719b97d69f382285b3401f2184d"}}