{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WQODRAJ6ZNRGRAOE6W7RJHDSCY","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":"65b320913e078245db2e20882ac7b2aac556bba4724eb1ef587fa92fd10e2e9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-23T16:02:40Z","title_canon_sha256":"d25129a4b983bd149d78ceb68208d7af9a33025fce6dbfb5324a9bcbad4c5b4a"},"schema_version":"1.0","source":{"id":"1906.09600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09600","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09600v1","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09600","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"WQODRAJ6ZNRG","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WQODRAJ6ZNRGRAOE","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WQODRAJ6","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:f2e3bd451001cde0654ca0e22305f0b7457b7dbf0c7ed3abfde2f3d63ea43af5","target":"graph","created_at":"2026-05-17T23:42:37Z","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 deal with the so-called Ahlfors regular sets (also known as $s$-regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: under which conditions does the limit $\\lim_{\\varepsilon\\to 0+} \\varepsilon^s N(\\varepsilon,K)$ exist, where $K$ is an $s$-regular set and $N(\\varepsilon,K)$ is for instance the $\\varepsilon$-packing number of $K$?","authors_text":"Du\\v{s}an Pokorn\\'y, Marc Rauch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-23T16:02:40Z","title":"On the asymptotics of counting functions for Ahlfors regular sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09600","kind":"arxiv","version":1},"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:d305268fefff849d16214cdf5d460f9871dd8c6232b0e8eba6336a0b51103331","target":"record","created_at":"2026-05-17T23:42:37Z","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":"65b320913e078245db2e20882ac7b2aac556bba4724eb1ef587fa92fd10e2e9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-23T16:02:40Z","title_canon_sha256":"d25129a4b983bd149d78ceb68208d7af9a33025fce6dbfb5324a9bcbad4c5b4a"},"schema_version":"1.0","source":{"id":"1906.09600","kind":"arxiv","version":1}},"canonical_sha256":"b41c38813ecb626881c4f5bf149c72163cc621616ea1dd41b93bdedd205bc91e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b41c38813ecb626881c4f5bf149c72163cc621616ea1dd41b93bdedd205bc91e","first_computed_at":"2026-05-17T23:42:37.434383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:37.434383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yRdxfme5H3/ZyFVSbGticDWO0i3kcCEPOGMRMjDof9qdF+vhCtSFsjNBi6fgDK2MLBDoAdXQLVvfALrNrGAFAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:37.435089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d305268fefff849d16214cdf5d460f9871dd8c6232b0e8eba6336a0b51103331","sha256:f2e3bd451001cde0654ca0e22305f0b7457b7dbf0c7ed3abfde2f3d63ea43af5"],"state_sha256":"86e5e81939e7ceafed140a99fbbfbc829a74b8396689bc953d6f6d2e096e8f1f"}