{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BSJMPTUVVHPV726TFQSATN4O7S","short_pith_number":"pith:BSJMPTUV","canonical_record":{"source":{"id":"1405.4919","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-19T23:27:36Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"770eb5b018c61d9c1d8c0af62a6af2c877f9b40b19620d367693693183bdbcab","abstract_canon_sha256":"a3921096d4f6320780040f4bb93a0987d3b73eab536b0337b8b6052614d452a0"},"schema_version":"1.0"},"canonical_sha256":"0c92c7ce95a9df5febd32c2409b78efc957157423c43a945a5280d14fed87d50","source":{"kind":"arxiv","id":"1405.4919","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4919","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4919v3","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4919","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"BSJMPTUVVHPV","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BSJMPTUVVHPV726T","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BSJMPTUV","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BSJMPTUVVHPV726TFQSATN4O7S","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4919","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-19T23:27:36Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"770eb5b018c61d9c1d8c0af62a6af2c877f9b40b19620d367693693183bdbcab","abstract_canon_sha256":"a3921096d4f6320780040f4bb93a0987d3b73eab536b0337b8b6052614d452a0"},"schema_version":"1.0"},"canonical_sha256":"0c92c7ce95a9df5febd32c2409b78efc957157423c43a945a5280d14fed87d50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:43.451465Z","signature_b64":"KyDiHO5rf2DF4UY3GFqgqwr4P/mGGJtXjIDgkPCuBC7vfEH2RoAG+qLAbqyo995b1iW5TEo9qQ6dKBgNB/J1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c92c7ce95a9df5febd32c2409b78efc957157423c43a945a5280d14fed87d50","last_reissued_at":"2026-05-18T00:47:43.450739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:43.450739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4919","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z1rbpf6jnf3TqmUPEut9jaL4cndMDcTbclubabQPo/Urgi5jRNH44P3vo/9yitQRwRFR6XdzCALmMMoq5+VjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:41:58.416869Z"},"content_sha256":"d80305f2ab25015c265ad244b3a7ee94eee0fe87c1ea33d1895747bf62165cd7","schema_version":"1.0","event_id":"sha256:d80305f2ab25015c265ad244b3a7ee94eee0fe87c1ea33d1895747bf62165cd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BSJMPTUVVHPV726TFQSATN4O7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the dimensions of a family of overlapping self-affine carpets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Jonathan Fraser, Pablo Shmerkin","submitted_at":"2014-05-19T23:27:36Z","abstract_excerpt":"We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4919","kind":"arxiv","version":3},"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":"2026-05-18T00:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKJ52ft6hBbOUS303rnvyRCG0ySMmAve4iZBL0XlIFWkMz0GxkBbAVXh3oZtjw2puyngBL1XLNB1VmSlorLuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:41:58.417206Z"},"content_sha256":"cc4276f7c550a8d42cd0fc62816676702f525682670c9d2e94d6d24b14d0d220","schema_version":"1.0","event_id":"sha256:cc4276f7c550a8d42cd0fc62816676702f525682670c9d2e94d6d24b14d0d220"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSJMPTUVVHPV726TFQSATN4O7S/bundle.json","state_url":"https://pith.science/pith/BSJMPTUVVHPV726TFQSATN4O7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSJMPTUVVHPV726TFQSATN4O7S/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":"2026-06-20T13:41:58Z","links":{"resolver":"https://pith.science/pith/BSJMPTUVVHPV726TFQSATN4O7S","bundle":"https://pith.science/pith/BSJMPTUVVHPV726TFQSATN4O7S/bundle.json","state":"https://pith.science/pith/BSJMPTUVVHPV726TFQSATN4O7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSJMPTUVVHPV726TFQSATN4O7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BSJMPTUVVHPV726TFQSATN4O7S","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":"a3921096d4f6320780040f4bb93a0987d3b73eab536b0337b8b6052614d452a0","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-19T23:27:36Z","title_canon_sha256":"770eb5b018c61d9c1d8c0af62a6af2c877f9b40b19620d367693693183bdbcab"},"schema_version":"1.0","source":{"id":"1405.4919","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4919","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4919v3","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4919","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"BSJMPTUVVHPV","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BSJMPTUVVHPV726T","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BSJMPTUV","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:cc4276f7c550a8d42cd0fc62816676702f525682670c9d2e94d6d24b14d0d220","target":"graph","created_at":"2026-05-18T00:47:43Z","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":"We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results r","authors_text":"Jonathan Fraser, Pablo Shmerkin","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-19T23:27:36Z","title":"On the dimensions of a family of overlapping self-affine carpets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4919","kind":"arxiv","version":3},"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:d80305f2ab25015c265ad244b3a7ee94eee0fe87c1ea33d1895747bf62165cd7","target":"record","created_at":"2026-05-18T00:47:43Z","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":"a3921096d4f6320780040f4bb93a0987d3b73eab536b0337b8b6052614d452a0","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-19T23:27:36Z","title_canon_sha256":"770eb5b018c61d9c1d8c0af62a6af2c877f9b40b19620d367693693183bdbcab"},"schema_version":"1.0","source":{"id":"1405.4919","kind":"arxiv","version":3}},"canonical_sha256":"0c92c7ce95a9df5febd32c2409b78efc957157423c43a945a5280d14fed87d50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c92c7ce95a9df5febd32c2409b78efc957157423c43a945a5280d14fed87d50","first_computed_at":"2026-05-18T00:47:43.450739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:43.450739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KyDiHO5rf2DF4UY3GFqgqwr4P/mGGJtXjIDgkPCuBC7vfEH2RoAG+qLAbqyo995b1iW5TEo9qQ6dKBgNB/J1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:43.451465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4919","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d80305f2ab25015c265ad244b3a7ee94eee0fe87c1ea33d1895747bf62165cd7","sha256:cc4276f7c550a8d42cd0fc62816676702f525682670c9d2e94d6d24b14d0d220"],"state_sha256":"d479c0387f2e513c7601091edf5ecfe2c8367209c8bc00bc573fb218678356b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8pWXqwi9EsEtDMdr/wf+SMxxS0BF8+pIqtIylWIjCMINXXhcwMPc2CA7OF5PtZkhxIP+Ay2qGRmH+dBAyovCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T13:41:58.419050Z","bundle_sha256":"31c2bedb2efdfaf59655b30bbdaa10a31ad53afb4802b7bb68baad93d935b93c"}}