{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:DOPKSANFH2FNHBYROZWOMQNUUR","short_pith_number":"pith:DOPKSANF","canonical_record":{"source":{"id":"2311.18454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-11-30T10:55:56Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a9ac3cf571102cc32fc3597be3451d443fae68c19e21c8a3b9902a09af6fbb99","abstract_canon_sha256":"73cd724ddd559791d56a338098fc531ed303fa74f2b0464922812918a8a38bd0"},"schema_version":"1.0"},"canonical_sha256":"1b9ea901a53e8ad38711766ce641b4a469daff39b6e52c8f756fac50928fa7a1","source":{"kind":"arxiv","id":"2311.18454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.18454","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"2311.18454v2","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.18454","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"DOPKSANFH2FN","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOPKSANFH2FNHBYR","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOPKSANF","created_at":"2026-07-05T11:06:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:DOPKSANFH2FNHBYROZWOMQNUUR","target":"record","payload":{"canonical_record":{"source":{"id":"2311.18454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-11-30T10:55:56Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a9ac3cf571102cc32fc3597be3451d443fae68c19e21c8a3b9902a09af6fbb99","abstract_canon_sha256":"73cd724ddd559791d56a338098fc531ed303fa74f2b0464922812918a8a38bd0"},"schema_version":"1.0"},"canonical_sha256":"1b9ea901a53e8ad38711766ce641b4a469daff39b6e52c8f756fac50928fa7a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:19.625224Z","signature_b64":"vpb1D5fhEcGAnUif+U+IbnsTU//Oc/Vge4c6Rt5K8IaKhjxvLSxYrIN8qwmfuO+lHxffFjN5bcEcem1dVM6DBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b9ea901a53e8ad38711766ce641b4a469daff39b6e52c8f756fac50928fa7a1","last_reissued_at":"2026-07-05T11:06:19.624772Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:19.624772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.18454","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":"2026-07-05T11:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVpJW+aeSciAMBUpOOqD5E1/ZgLOxtaaOT9WQjc66z4wQ2Uf12zGls+V8aBtaQy20S7ovp8MN55aQM8mPv8WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:33:57.516297Z"},"content_sha256":"cc7f897394e451723c75e111452ec207ccf2ca1aaa9312d8f36bcc07379d7481","schema_version":"1.0","event_id":"sha256:cc7f897394e451723c75e111452ec207ccf2ca1aaa9312d8f36bcc07379d7481"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:DOPKSANFH2FNHBYROZWOMQNUUR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $k$-free numbers in cyclotomic fields: entropy, symmetries and topological invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Alvaro Bustos, Andreas Nickel, Michael Baake","submitted_at":"2023-11-30T10:55:56Z","abstract_excerpt":"Point sets of number-theoretic origin, such as the visible lattice points or the $k$-th power free integers, have interesting geometric and spectral properties and give rise to topological dynamical systems that belong to a large class of subshifts with positive topological entropy. Among them are $\\cB$-free systems in one dimension and their higher-dimensional generalisations, most prominently the $k$-free integers in algebraic number fields. Here, we extend previous work on quadratic fields to the class of cyclotomic fields. In particular, we discuss their entropy and extended symmetries, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.18454","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.18454/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":"2026-07-05T11:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rdEHuxNTgstz8apB5DQom03NGvWIltSu+nkNOW/OKzkbCzt3DfmIDk6SNG69yp6HAXflYcSd/Q4TF026XVa4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:33:57.517126Z"},"content_sha256":"cc795167284d096c598c67050a8a8008bebd5617706fdfaf4842f7a7fea4d556","schema_version":"1.0","event_id":"sha256:cc795167284d096c598c67050a8a8008bebd5617706fdfaf4842f7a7fea4d556"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOPKSANFH2FNHBYROZWOMQNUUR/bundle.json","state_url":"https://pith.science/pith/DOPKSANFH2FNHBYROZWOMQNUUR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOPKSANFH2FNHBYROZWOMQNUUR/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":"2026-08-20T23:33:57Z","links":{"resolver":"https://pith.science/pith/DOPKSANFH2FNHBYROZWOMQNUUR","bundle":"https://pith.science/pith/DOPKSANFH2FNHBYROZWOMQNUUR/bundle.json","state":"https://pith.science/pith/DOPKSANFH2FNHBYROZWOMQNUUR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOPKSANFH2FNHBYROZWOMQNUUR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DOPKSANFH2FNHBYROZWOMQNUUR","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":"73cd724ddd559791d56a338098fc531ed303fa74f2b0464922812918a8a38bd0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-11-30T10:55:56Z","title_canon_sha256":"a9ac3cf571102cc32fc3597be3451d443fae68c19e21c8a3b9902a09af6fbb99"},"schema_version":"1.0","source":{"id":"2311.18454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.18454","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"2311.18454v2","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.18454","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"DOPKSANFH2FN","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOPKSANFH2FNHBYR","created_at":"2026-07-05T11:06:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOPKSANF","created_at":"2026-07-05T11:06:19Z"}],"graph_snapshots":[{"event_id":"sha256:cc795167284d096c598c67050a8a8008bebd5617706fdfaf4842f7a7fea4d556","target":"graph","created_at":"2026-07-05T11:06:19Z","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/2311.18454/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Point sets of number-theoretic origin, such as the visible lattice points or the $k$-th power free integers, have interesting geometric and spectral properties and give rise to topological dynamical systems that belong to a large class of subshifts with positive topological entropy. Among them are $\\cB$-free systems in one dimension and their higher-dimensional generalisations, most prominently the $k$-free integers in algebraic number fields. Here, we extend previous work on quadratic fields to the class of cyclotomic fields. In particular, we discuss their entropy and extended symmetries, wi","authors_text":"Alvaro Bustos, Andreas Nickel, Michael Baake","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-11-30T10:55:56Z","title":"On $k$-free numbers in cyclotomic fields: entropy, symmetries and topological invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.18454","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:cc7f897394e451723c75e111452ec207ccf2ca1aaa9312d8f36bcc07379d7481","target":"record","created_at":"2026-07-05T11:06:19Z","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":"73cd724ddd559791d56a338098fc531ed303fa74f2b0464922812918a8a38bd0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-11-30T10:55:56Z","title_canon_sha256":"a9ac3cf571102cc32fc3597be3451d443fae68c19e21c8a3b9902a09af6fbb99"},"schema_version":"1.0","source":{"id":"2311.18454","kind":"arxiv","version":2}},"canonical_sha256":"1b9ea901a53e8ad38711766ce641b4a469daff39b6e52c8f756fac50928fa7a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b9ea901a53e8ad38711766ce641b4a469daff39b6e52c8f756fac50928fa7a1","first_computed_at":"2026-07-05T11:06:19.624772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:19.624772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vpb1D5fhEcGAnUif+U+IbnsTU//Oc/Vge4c6Rt5K8IaKhjxvLSxYrIN8qwmfuO+lHxffFjN5bcEcem1dVM6DBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:19.625224Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.18454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc7f897394e451723c75e111452ec207ccf2ca1aaa9312d8f36bcc07379d7481","sha256:cc795167284d096c598c67050a8a8008bebd5617706fdfaf4842f7a7fea4d556"],"state_sha256":"1f5b4a428234eac5f5e3d2d257363311febfffd26b414c07bdbeb1ef0a308c94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZ2XO26UkC7s/KH1VKRd++xV3gtCHAacRFbCwFfP4/9B4FqdjNFo4Wx+DU0h7ux3E0mvYnR2TZYbrrrdiDOEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T23:33:57.524447Z","bundle_sha256":"ed9fff91eada77b59e0269bf8824e3af3d8743ac3a642e6bde26ea8361034c38"}}