{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NIP5HVCVH7RKAUZBKEYOJHXYWD","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":"c4c8f0f6c7cb623e022946b5717006189c29268038982de421fef9384a9fcbf1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-01-21T16:11:29Z","title_canon_sha256":"883bfb4308181f00f04111d8a5cc992ca429023e1e0f2390bba2b9f8c2e68e69"},"schema_version":"1.0","source":{"id":"0901.3304","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3304","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3304v2","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3304","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"NIP5HVCVH7RK","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NIP5HVCVH7RKAUZB","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NIP5HVCV","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:bf35bb3af02229ca3908a6b5cec8968db363cf85ea078d7ffdad4d4dea30fc79","target":"graph","created_at":"2026-05-18T04:26:54Z","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":"In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor sets introduced by Per Larsson.","authors_text":"Bal\\'azs Sz\\'ekely, K\\'aroly Simon, Michel Dekking","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-01-21T16:11:29Z","title":"The algebraic difference of two random Cantor sets: The Larsson family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3304","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":"sha256:2712b92314ad070878fa64f0a1c7eb28ae4294a6d7dc6cdfe8d803a5e06bafbf","target":"record","created_at":"2026-05-18T04:26:54Z","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":"c4c8f0f6c7cb623e022946b5717006189c29268038982de421fef9384a9fcbf1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-01-21T16:11:29Z","title_canon_sha256":"883bfb4308181f00f04111d8a5cc992ca429023e1e0f2390bba2b9f8c2e68e69"},"schema_version":"1.0","source":{"id":"0901.3304","kind":"arxiv","version":2}},"canonical_sha256":"6a1fd3d4553fe2a053215130e49ef8b0d1e8ebf3593c6e3c7b384960bb6cf82d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a1fd3d4553fe2a053215130e49ef8b0d1e8ebf3593c6e3c7b384960bb6cf82d","first_computed_at":"2026-05-18T04:26:54.814757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:54.814757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djlPPIVlPw0ieFSubh/iQPvSO3hdDOYnFDsVOWX8oxVVk4epmrMiBhWV7hba8N95Dy3W343pvKE1YjX70PYWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:54.815128Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.3304","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2712b92314ad070878fa64f0a1c7eb28ae4294a6d7dc6cdfe8d803a5e06bafbf","sha256:bf35bb3af02229ca3908a6b5cec8968db363cf85ea078d7ffdad4d4dea30fc79"],"state_sha256":"bd0bab8aa982bc4b2bffb74bd5ddf1bffa229e17e71559e1dae1837becf5e68e"}