{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:47LKLV23XEXNZ53VONLCNRLO2W","short_pith_number":"pith:47LKLV23","schema_version":"1.0","canonical_sha256":"e7d6a5d75bb92edcf775735626c56ed592e4590fe69dbd51db80f65c09b66740","source":{"kind":"arxiv","id":"1112.2783","version":2},"attestation_state":"computed","paper":{"title":"On regularity for measures in multiplicative free convolution semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ping Zhong","submitted_at":"2011-12-13T03:25:58Z","abstract_excerpt":"Given a probability measure $\\mu$ on the real line, there exists a semigroup $\\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $\\mu_n$ obtained by iterating its free convolution. It was shown in \\cite{[BB2004]} that it is impossible that $\\mu_t$ has no mass in an interval whose endpoints are atoms. We extend this result to semigroups related to multiplicative free convolution. The proofs use subordination results."},"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":"1112.2783","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-13T03:25:58Z","cross_cats_sorted":[],"title_canon_sha256":"35d3f75dd8e6c2faf495789caed18c20097ee19092e9a8d7afad0bb102c63fab","abstract_canon_sha256":"038eb7990d888843d534732618c668c69b9c4d3236d88524a8cf5f280086856a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:27.274348Z","signature_b64":"jBZ/f1iWQquz3bNFkcOtBaU2rMpHw4uis1PHxSj5VjlMxP2jhzfrylyaHeXmrtBV9b5EyRVl4orbupoptsyeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7d6a5d75bb92edcf775735626c56ed592e4590fe69dbd51db80f65c09b66740","last_reissued_at":"2026-05-18T02:21:27.273784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:27.273784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On regularity for measures in multiplicative free convolution semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ping Zhong","submitted_at":"2011-12-13T03:25:58Z","abstract_excerpt":"Given a probability measure $\\mu$ on the real line, there exists a semigroup $\\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $\\mu_n$ obtained by iterating its free convolution. It was shown in \\cite{[BB2004]} that it is impossible that $\\mu_t$ has no mass in an interval whose endpoints are atoms. We extend this result to semigroups related to multiplicative free convolution. The proofs use subordination results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2783","kind":"arxiv","version":2},"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":"1112.2783","created_at":"2026-05-18T02:21:27.273877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2783v2","created_at":"2026-05-18T02:21:27.273877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2783","created_at":"2026-05-18T02:21:27.273877+00:00"},{"alias_kind":"pith_short_12","alias_value":"47LKLV23XEXN","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"47LKLV23XEXNZ53V","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"47LKLV23","created_at":"2026-05-18T12:26:20.644004+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/47LKLV23XEXNZ53VONLCNRLO2W","json":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W.json","graph_json":"https://pith.science/api/pith-number/47LKLV23XEXNZ53VONLCNRLO2W/graph.json","events_json":"https://pith.science/api/pith-number/47LKLV23XEXNZ53VONLCNRLO2W/events.json","paper":"https://pith.science/paper/47LKLV23"},"agent_actions":{"view_html":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W","download_json":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W.json","view_paper":"https://pith.science/paper/47LKLV23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2783&json=true","fetch_graph":"https://pith.science/api/pith-number/47LKLV23XEXNZ53VONLCNRLO2W/graph.json","fetch_events":"https://pith.science/api/pith-number/47LKLV23XEXNZ53VONLCNRLO2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W/action/storage_attestation","attest_author":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W/action/author_attestation","sign_citation":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W/action/citation_signature","submit_replication":"https://pith.science/pith/47LKLV23XEXNZ53VONLCNRLO2W/action/replication_record"}},"created_at":"2026-05-18T02:21:27.273877+00:00","updated_at":"2026-05-18T02:21:27.273877+00:00"}