{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SXJH3CIQFUERXOHRL7JPZWCCNI","short_pith_number":"pith:SXJH3CIQ","canonical_record":{"source":{"id":"1704.03506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T19:30:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"62ffcbabe087ff57803ed5b41da7f1b5120767b9ca843e649bc9a86f033273ee","abstract_canon_sha256":"11d4931d03466a6ebc2dde6bc18803333ebc069204e91ef0db6d3ac16bad0fee"},"schema_version":"1.0"},"canonical_sha256":"95d27d89102d091bb8f15fd2fcd8426a0df41f0c239cae4f87f0c0ad8c3d3fa6","source":{"kind":"arxiv","id":"1704.03506","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03506","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03506v2","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03506","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"SXJH3CIQFUER","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SXJH3CIQFUERXOHR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SXJH3CIQ","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SXJH3CIQFUERXOHRL7JPZWCCNI","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T19:30:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"62ffcbabe087ff57803ed5b41da7f1b5120767b9ca843e649bc9a86f033273ee","abstract_canon_sha256":"11d4931d03466a6ebc2dde6bc18803333ebc069204e91ef0db6d3ac16bad0fee"},"schema_version":"1.0"},"canonical_sha256":"95d27d89102d091bb8f15fd2fcd8426a0df41f0c239cae4f87f0c0ad8c3d3fa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:23.300057Z","signature_b64":"7GGD55iZhLY2PYuPw+1qqnMqdL+QFMo/nJj3iupz4fJ8fb/vteeC/LkDeVIQNY/o04aj05P76wvGT/VLJALoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95d27d89102d091bb8f15fd2fcd8426a0df41f0c239cae4f87f0c0ad8c3d3fa6","last_reissued_at":"2026-05-18T00:23:23.299293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:23.299293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03506","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":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRBOUScdo0byuJ87MdL5YeG+x+DboiGVb+3SiXxALN9X6acGWoELG7+db0ZqUnWPpNB1qkTAtWZkfC3w8WlRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:29:04.962789Z"},"content_sha256":"3c83bc086bc4da3fe4d60b63b420be50a1346580ed643c0ae065cc62484b8ad7","schema_version":"1.0","event_id":"sha256:3c83bc086bc4da3fe4d60b63b420be50a1346580ed643c0ae065cc62484b8ad7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SXJH3CIQFUERXOHRL7JPZWCCNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"M\\\"obius disjointness for models of an ergodic system and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"el Houcein el Abdalaoui, Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk, Thierry de la Rue","submitted_at":"2017-04-11T19:30:32Z","abstract_excerpt":"Given a topological dynamical system $(X,T)$ and an arithmetic function $\\boldsymbol{u}\\colon\\mathbb{N}\\to\\mathbb{C}$, we study the strong MOMO property (relatively to $\\boldsymbol{u}$) which is a strong version of $\\boldsymbol{u}$-disjointness with all observable sequences in $(X,T)$. It is proved that, given an ergodic measure-preserving system $(Z,\\mathcal{D},\\kappa,R)$, the strong MOMO property (relatively to $\\boldsymbol{u}$) of a uniquely ergodic model $(X,T)$ of $R$ yields all other uniquely ergodic models of $R$ to be $\\boldsymbol{u}$-disjoint. It follows that all uniquely ergodic mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03506","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":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GvRsG32TM2INh9/x35eJKdMcXfVws+J0Y1zqNYlU6JRBlg7PxhEzEaNY+5FI+i+DID5KxynORvzNzp9RXccOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:29:04.963140Z"},"content_sha256":"955cedca4cbd2b95480b296e67f768f52e9945c19b065d0e18a7525c50a8010a","schema_version":"1.0","event_id":"sha256:955cedca4cbd2b95480b296e67f768f52e9945c19b065d0e18a7525c50a8010a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXJH3CIQFUERXOHRL7JPZWCCNI/bundle.json","state_url":"https://pith.science/pith/SXJH3CIQFUERXOHRL7JPZWCCNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXJH3CIQFUERXOHRL7JPZWCCNI/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":"2026-06-01T22:29:04Z","links":{"resolver":"https://pith.science/pith/SXJH3CIQFUERXOHRL7JPZWCCNI","bundle":"https://pith.science/pith/SXJH3CIQFUERXOHRL7JPZWCCNI/bundle.json","state":"https://pith.science/pith/SXJH3CIQFUERXOHRL7JPZWCCNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXJH3CIQFUERXOHRL7JPZWCCNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SXJH3CIQFUERXOHRL7JPZWCCNI","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":"11d4931d03466a6ebc2dde6bc18803333ebc069204e91ef0db6d3ac16bad0fee","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T19:30:32Z","title_canon_sha256":"62ffcbabe087ff57803ed5b41da7f1b5120767b9ca843e649bc9a86f033273ee"},"schema_version":"1.0","source":{"id":"1704.03506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03506","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03506v2","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03506","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"SXJH3CIQFUER","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SXJH3CIQFUERXOHR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SXJH3CIQ","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:955cedca4cbd2b95480b296e67f768f52e9945c19b065d0e18a7525c50a8010a","target":"graph","created_at":"2026-05-18T00:23:23Z","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":"Given a topological dynamical system $(X,T)$ and an arithmetic function $\\boldsymbol{u}\\colon\\mathbb{N}\\to\\mathbb{C}$, we study the strong MOMO property (relatively to $\\boldsymbol{u}$) which is a strong version of $\\boldsymbol{u}$-disjointness with all observable sequences in $(X,T)$. It is proved that, given an ergodic measure-preserving system $(Z,\\mathcal{D},\\kappa,R)$, the strong MOMO property (relatively to $\\boldsymbol{u}$) of a uniquely ergodic model $(X,T)$ of $R$ yields all other uniquely ergodic models of $R$ to be $\\boldsymbol{u}$-disjoint. It follows that all uniquely ergodic mode","authors_text":"el Houcein el Abdalaoui, Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk, Thierry de la Rue","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T19:30:32Z","title":"M\\\"obius disjointness for models of an ergodic system and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03506","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":"sha256:3c83bc086bc4da3fe4d60b63b420be50a1346580ed643c0ae065cc62484b8ad7","target":"record","created_at":"2026-05-18T00:23:23Z","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":"11d4931d03466a6ebc2dde6bc18803333ebc069204e91ef0db6d3ac16bad0fee","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T19:30:32Z","title_canon_sha256":"62ffcbabe087ff57803ed5b41da7f1b5120767b9ca843e649bc9a86f033273ee"},"schema_version":"1.0","source":{"id":"1704.03506","kind":"arxiv","version":2}},"canonical_sha256":"95d27d89102d091bb8f15fd2fcd8426a0df41f0c239cae4f87f0c0ad8c3d3fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95d27d89102d091bb8f15fd2fcd8426a0df41f0c239cae4f87f0c0ad8c3d3fa6","first_computed_at":"2026-05-18T00:23:23.299293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:23.299293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7GGD55iZhLY2PYuPw+1qqnMqdL+QFMo/nJj3iupz4fJ8fb/vteeC/LkDeVIQNY/o04aj05P76wvGT/VLJALoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:23.300057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c83bc086bc4da3fe4d60b63b420be50a1346580ed643c0ae065cc62484b8ad7","sha256:955cedca4cbd2b95480b296e67f768f52e9945c19b065d0e18a7525c50a8010a"],"state_sha256":"0d5bc4cf3720f689f646a516fecf468613395a7ee4e0d9bd5b4f5d0fbf4cad56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVQpoOzZPqqbci3CvAKqpGnILLnURRSpvGFHUBvmGIReZLhPETkGdn/JPyLw0UrDGhmVtOm4b5AaHK+qXbWhAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:29:04.965193Z","bundle_sha256":"834a6bf92b372a7f2fa3def7f035a4d4991cb318fcc1de63af44dc6049fe85f1"}}