{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2VHXMCZPDQHDR5HLBJMJGNSRMV","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":"1fea3d678da0730f1a52e583260a970820003086c8225b2f2ba643f43b777d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-16T10:52:40Z","title_canon_sha256":"0f4eaee2a4ac23bb9dd77fabe0e699be71109f9c11ea99a4b4f23c1bccd3c3ba"},"schema_version":"1.0","source":{"id":"1309.3896","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3896","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3896v3","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3896","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"2VHXMCZPDQHD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2VHXMCZPDQHDR5HL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2VHXMCZP","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:973442a217f2b5e4b28b94fa408a545a58d468cdf592a6b24d008a58d10e4c7c","target":"graph","created_at":"2026-05-18T01:21:38Z","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 $K \\subset \\mathbb{R}^{2}$ be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension $\\dim K = s > 1$. Intersecting $K$ with translates of a fixed line, one can study the $(s - 1)$-dimensional Hausdorff and packing measures of the generic non-empty line sections. In a recent article, T. Kempton gave a necessary and sufficient condition for the Hausdorff measures of the sections to be positive. In this paper, I consider the packing measures: it turns out that the generic section has infinite $(s - 1)$-dimensional packing measure under rela","authors_text":"Tuomas Orponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-16T10:52:40Z","title":"On the packing measure of slices of self-similar sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3896","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":"sha256:30376dd552dfe5778000194b3da70d0fcdab35d7a9a73d8d16388c33e4e598c1","target":"record","created_at":"2026-05-18T01:21:38Z","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":"1fea3d678da0730f1a52e583260a970820003086c8225b2f2ba643f43b777d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-16T10:52:40Z","title_canon_sha256":"0f4eaee2a4ac23bb9dd77fabe0e699be71109f9c11ea99a4b4f23c1bccd3c3ba"},"schema_version":"1.0","source":{"id":"1309.3896","kind":"arxiv","version":3}},"canonical_sha256":"d54f760b2f1c0e38f4eb0a589336516577af671a3cee7cd4446a6b82952acfb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d54f760b2f1c0e38f4eb0a589336516577af671a3cee7cd4446a6b82952acfb8","first_computed_at":"2026-05-18T01:21:38.256904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:38.256904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZucMq8EUGodOBCDnI0JOIYp5kJEEKh4XTvq2Q7fKl8ms6nwlYapxD8qA7yKVTyLVzLgVA5pcb3r4KXBHamzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:38.257472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3896","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30376dd552dfe5778000194b3da70d0fcdab35d7a9a73d8d16388c33e4e598c1","sha256:973442a217f2b5e4b28b94fa408a545a58d468cdf592a6b24d008a58d10e4c7c"],"state_sha256":"7c45547d5765c29a1591408f00ac7d83e89004981786e1ecbc33596a66aa33c8"}