{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FXGW24VHBS5MZ2ZMPMOQCQ7BVB","short_pith_number":"pith:FXGW24VH","canonical_record":{"source":{"id":"1304.0214","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-31T15:02:24Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8b428d41495d18c0881c32aa91562f57998bed4d0d0d2cf1260043288a44d832","abstract_canon_sha256":"994aa4f2183b1a87b7081603cc5000f08608663efdc14bc4f8907c078a1bd540"},"schema_version":"1.0"},"canonical_sha256":"2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c","source":{"kind":"arxiv","id":"1304.0214","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0214","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0214v4","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0214","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"FXGW24VHBS5M","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FXGW24VHBS5MZ2ZM","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FXGW24VH","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FXGW24VHBS5MZ2ZMPMOQCQ7BVB","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0214","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-31T15:02:24Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8b428d41495d18c0881c32aa91562f57998bed4d0d0d2cf1260043288a44d832","abstract_canon_sha256":"994aa4f2183b1a87b7081603cc5000f08608663efdc14bc4f8907c078a1bd540"},"schema_version":"1.0"},"canonical_sha256":"2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:23.938017Z","signature_b64":"E6rQIV1zJYo+1NjlVVuERYZgZD0Z0LAA5Uc8KIRBcZ+7kCT3Bm/c6XlE5c7pbtmkL2ZfftXzEQ8PqZ+TIgjHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c","last_reissued_at":"2026-05-18T03:11:23.937322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:23.937322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0214","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXvKhtH2FI1fn2fUwvGQzSZGT45ptzJz8S8xE5BY1/GhRTPQIZF2KtjThJx+7EqoOtt3liY0H6Z/bhHIAxXHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:52:37.592104Z"},"content_sha256":"9bc3b7d00c0b6124ed457feb4625a1cda9125f1e4f41fbf89dffd5b1b516794b","schema_version":"1.0","event_id":"sha256:9bc3b7d00c0b6124ed457feb4625a1cda9125f1e4f41fbf89dffd5b1b516794b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FXGW24VHBS5MZ2ZMPMOQCQ7BVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic Properties of $k$-Free Integers in Number Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Francesco Cellarosi, Ilya Vinogradov","submitted_at":"2013-03-31T15:02:24Z","abstract_excerpt":"Let $K/\\mathbf Q$ be a degree $d$ extension. Inside the ring of integers $\\mathcal O_K$ we define the set of $k$-free integers $\\mathcal F_k$ and a natural $\\mathcal O_K$-action on the space of binary $\\mathcal O_K$-indexed sequences, equipped with an $\\mathcal O_K$-invariant probability measure associated to $\\mathcal F_k$. We prove that this action is ergodic, has pure point spectrum and is isomorphic to a $\\mathbf Z^d$-action on a compact abelian group. In particular, it is not weakly mixing and has zero measure-theoretical entropy. This work generalizes the paper by the first author and Si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0214","kind":"arxiv","version":4},"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":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWVLd/YMydnFrWE3dDIb2mz3rM2GHooIm6qJtQeS3H05RTWCGDXuyOng1NI6C0dy8FURnPoDZk3rHWSxHlLUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:52:37.592674Z"},"content_sha256":"8eced68e40693b113ab6e454b581243ff943536187bf9812274dd8baa03a8ad1","schema_version":"1.0","event_id":"sha256:8eced68e40693b113ab6e454b581243ff943536187bf9812274dd8baa03a8ad1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB/bundle.json","state_url":"https://pith.science/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB/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":"2026-05-30T23:52:37Z","links":{"resolver":"https://pith.science/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB","bundle":"https://pith.science/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB/bundle.json","state":"https://pith.science/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXGW24VHBS5MZ2ZMPMOQCQ7BVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FXGW24VHBS5MZ2ZMPMOQCQ7BVB","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":"994aa4f2183b1a87b7081603cc5000f08608663efdc14bc4f8907c078a1bd540","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-31T15:02:24Z","title_canon_sha256":"8b428d41495d18c0881c32aa91562f57998bed4d0d0d2cf1260043288a44d832"},"schema_version":"1.0","source":{"id":"1304.0214","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0214","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0214v4","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0214","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"FXGW24VHBS5M","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FXGW24VHBS5MZ2ZM","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FXGW24VH","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:8eced68e40693b113ab6e454b581243ff943536187bf9812274dd8baa03a8ad1","target":"graph","created_at":"2026-05-18T03:11:23Z","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":"Let $K/\\mathbf Q$ be a degree $d$ extension. Inside the ring of integers $\\mathcal O_K$ we define the set of $k$-free integers $\\mathcal F_k$ and a natural $\\mathcal O_K$-action on the space of binary $\\mathcal O_K$-indexed sequences, equipped with an $\\mathcal O_K$-invariant probability measure associated to $\\mathcal F_k$. We prove that this action is ergodic, has pure point spectrum and is isomorphic to a $\\mathbf Z^d$-action on a compact abelian group. In particular, it is not weakly mixing and has zero measure-theoretical entropy. This work generalizes the paper by the first author and Si","authors_text":"Francesco Cellarosi, Ilya Vinogradov","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-31T15:02:24Z","title":"Ergodic Properties of $k$-Free Integers in Number Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0214","kind":"arxiv","version":4},"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":"sha256:9bc3b7d00c0b6124ed457feb4625a1cda9125f1e4f41fbf89dffd5b1b516794b","target":"record","created_at":"2026-05-18T03:11:23Z","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":"994aa4f2183b1a87b7081603cc5000f08608663efdc14bc4f8907c078a1bd540","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-31T15:02:24Z","title_canon_sha256":"8b428d41495d18c0881c32aa91562f57998bed4d0d0d2cf1260043288a44d832"},"schema_version":"1.0","source":{"id":"1304.0214","kind":"arxiv","version":4}},"canonical_sha256":"2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dcd6d72a70cbacceb2c7b1d0143e1a8521fae738970040a7b62534931b5151c","first_computed_at":"2026-05-18T03:11:23.937322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:23.937322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E6rQIV1zJYo+1NjlVVuERYZgZD0Z0LAA5Uc8KIRBcZ+7kCT3Bm/c6XlE5c7pbtmkL2ZfftXzEQ8PqZ+TIgjHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:23.938017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0214","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bc3b7d00c0b6124ed457feb4625a1cda9125f1e4f41fbf89dffd5b1b516794b","sha256:8eced68e40693b113ab6e454b581243ff943536187bf9812274dd8baa03a8ad1"],"state_sha256":"fcfc33ffc8d23035ac9206d064a889eb3f85f916747c2afd3ff96fb2d5d9b6c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7G+JxmOhws8VbcWEfDPtdoQr3KDjCuQiwYCgpADVb1tOl7njGRXdjCyPQsoTpJqFp0IsyUaiX14eNj9+gAvEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:52:37.595996Z","bundle_sha256":"d332c29ec735094569556ab062f2e40ea61850a45de8779817048a6c002c7c5b"}}