{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DR7JSM4XJARXQZXZCUU3FTX6UU","short_pith_number":"pith:DR7JSM4X","schema_version":"1.0","canonical_sha256":"1c7e99339748237866f91529b2cefea53f7517a014b2f26741b8ba5968977d71","source":{"kind":"arxiv","id":"1102.5136","version":2},"attestation_state":"computed","paper":{"title":"Hausdorff dimension for fractals invariant under the multiplicative integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Boris Solomyak, Richard Kenyon, Yuval Peres","submitted_at":"2011-02-25T01:38:46Z","abstract_excerpt":"We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences $(x_k)$ such that $x_k x_{2k}=0$ for all $k$. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.5136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-25T01:38:46Z","cross_cats_sorted":[],"title_canon_sha256":"176fc398b8a8c2738e790823c3152c4386a4ee850ddfaa60fa02c4f19e0e51b4","abstract_canon_sha256":"ed0ba23fcfe7d4ea162b6893e6b74aaa1af751eecef0ce8e5b3b1c15b63b2461"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:10.764099Z","signature_b64":"bwXuPJTYwTk2ts6X1a199kUZzBRaPyQ27fqvVXwO30tfSqmwQXRhzygt3qBlS4E6OGRSG5NSy+Nqjkbh0u5oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c7e99339748237866f91529b2cefea53f7517a014b2f26741b8ba5968977d71","last_reissued_at":"2026-05-18T00:24:10.763387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:10.763387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hausdorff dimension for fractals invariant under the multiplicative integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Boris Solomyak, Richard Kenyon, Yuval Peres","submitted_at":"2011-02-25T01:38:46Z","abstract_excerpt":"We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences $(x_k)$ such that $x_k x_{2k}=0$ for all $k$. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5136","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.5136","created_at":"2026-05-18T00:24:10.763508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.5136v2","created_at":"2026-05-18T00:24:10.763508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5136","created_at":"2026-05-18T00:24:10.763508+00:00"},{"alias_kind":"pith_short_12","alias_value":"DR7JSM4XJARX","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DR7JSM4XJARXQZXZ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DR7JSM4X","created_at":"2026-05-18T12:26:26.731475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU","json":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU.json","graph_json":"https://pith.science/api/pith-number/DR7JSM4XJARXQZXZCUU3FTX6UU/graph.json","events_json":"https://pith.science/api/pith-number/DR7JSM4XJARXQZXZCUU3FTX6UU/events.json","paper":"https://pith.science/paper/DR7JSM4X"},"agent_actions":{"view_html":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU","download_json":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU.json","view_paper":"https://pith.science/paper/DR7JSM4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.5136&json=true","fetch_graph":"https://pith.science/api/pith-number/DR7JSM4XJARXQZXZCUU3FTX6UU/graph.json","fetch_events":"https://pith.science/api/pith-number/DR7JSM4XJARXQZXZCUU3FTX6UU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU/action/storage_attestation","attest_author":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU/action/author_attestation","sign_citation":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU/action/citation_signature","submit_replication":"https://pith.science/pith/DR7JSM4XJARXQZXZCUU3FTX6UU/action/replication_record"}},"created_at":"2026-05-18T00:24:10.763508+00:00","updated_at":"2026-05-18T00:24:10.763508+00:00"}