{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UYYUPKNT3CMEBAFVWPN7MADEJN","short_pith_number":"pith:UYYUPKNT","schema_version":"1.0","canonical_sha256":"a63147a9b3d8984080b5b3dbf600644b6237affe15af226db8bd71e975ebcb6f","source":{"kind":"arxiv","id":"1502.01961","version":1},"attestation_state":"computed","paper":{"title":"Hausdorff measure of hairs without endpoints in the exponential family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Jun Wang, Walter Bergweiler","submitted_at":"2015-02-06T17:27:56Z","abstract_excerpt":"Devaney and Krych showed that for $0<\\lambda<1/e$ the Julia set of $\\lambda e^z$ consists of pairwise disjoint curves, called hairs, which connect finite points, called the endpoints of the hairs, with $\\infty$. McMullen showed that the Julia set has Hausdorff dimension $2$ and Karpi\\'nska showed that the set of hairs without endpoints has Hausdorff dimension $1$. We study for which gauge functions the Hausdorff measure of the set of hairs without endpoints is finite."},"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":"1502.01961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-06T17:27:56Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"04403c3c8d59888ea84df7acfec98a4672b7667a2ab3e514aee8aa40a6f7e688","abstract_canon_sha256":"22a05bf51e05d85be9b3aa5402881a42c0a55856074fb576da5805efcf8607f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:07.909462Z","signature_b64":"ZsZTD2473WJVrFreWDs/8Vx8nLej8P+oHeFn/ywVDW1AC/5Q+dCHZ595g3GhiTugdBT5zPB2L8J2nt9PDqmcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a63147a9b3d8984080b5b3dbf600644b6237affe15af226db8bd71e975ebcb6f","last_reissued_at":"2026-05-18T01:27:07.908774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:07.908774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hausdorff measure of hairs without endpoints in the exponential family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Jun Wang, Walter Bergweiler","submitted_at":"2015-02-06T17:27:56Z","abstract_excerpt":"Devaney and Krych showed that for $0<\\lambda<1/e$ the Julia set of $\\lambda e^z$ consists of pairwise disjoint curves, called hairs, which connect finite points, called the endpoints of the hairs, with $\\infty$. McMullen showed that the Julia set has Hausdorff dimension $2$ and Karpi\\'nska showed that the set of hairs without endpoints has Hausdorff dimension $1$. We study for which gauge functions the Hausdorff measure of the set of hairs without endpoints is finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01961","kind":"arxiv","version":1},"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":"1502.01961","created_at":"2026-05-18T01:27:07.908864+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.01961v1","created_at":"2026-05-18T01:27:07.908864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01961","created_at":"2026-05-18T01:27:07.908864+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYYUPKNT3CME","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYYUPKNT3CMEBAFV","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYYUPKNT","created_at":"2026-05-18T12:29:44.643036+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/UYYUPKNT3CMEBAFVWPN7MADEJN","json":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN.json","graph_json":"https://pith.science/api/pith-number/UYYUPKNT3CMEBAFVWPN7MADEJN/graph.json","events_json":"https://pith.science/api/pith-number/UYYUPKNT3CMEBAFVWPN7MADEJN/events.json","paper":"https://pith.science/paper/UYYUPKNT"},"agent_actions":{"view_html":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN","download_json":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN.json","view_paper":"https://pith.science/paper/UYYUPKNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.01961&json=true","fetch_graph":"https://pith.science/api/pith-number/UYYUPKNT3CMEBAFVWPN7MADEJN/graph.json","fetch_events":"https://pith.science/api/pith-number/UYYUPKNT3CMEBAFVWPN7MADEJN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN/action/storage_attestation","attest_author":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN/action/author_attestation","sign_citation":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN/action/citation_signature","submit_replication":"https://pith.science/pith/UYYUPKNT3CMEBAFVWPN7MADEJN/action/replication_record"}},"created_at":"2026-05-18T01:27:07.908864+00:00","updated_at":"2026-05-18T01:27:07.908864+00:00"}