{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6MPGTIUDSA5OH55U47NWU4S7O5","short_pith_number":"pith:6MPGTIUD","schema_version":"1.0","canonical_sha256":"f31e69a283903ae3f7b4e7db6a725f777130cf74c430444ac13bf1833c0b854f","source":{"kind":"arxiv","id":"1511.03770","version":1},"attestation_state":"computed","paper":{"title":"The Hadamard product and the free convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arijit Chakrabarty","submitted_at":"2015-11-12T04:28:46Z","abstract_excerpt":"It is shown that if a probability measure $\\nu$ is supported on a closed subset of $(0,\\infty)$, that is, its support is bounded away from zero, then the free multiplicative convolution of $\\nu$ and the semicircle law is absolutely continuous with respect to the Lebesgue measure. For the proof, a result concerning the Hadamard product of a deterministic matrix and a scaled Wigner matrix is proved and subsequently used. As a byproduct, a result, showing that the limiting spectral distribution of the Hadamard product is same as that of a symmetric random matrix with entries from a mean zero stat"},"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":"1511.03770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-12T04:28:46Z","cross_cats_sorted":[],"title_canon_sha256":"e8a1d39090198049cb1a107465ed3a6153cba34bd0b96635c1717e9d8ee686c2","abstract_canon_sha256":"7a1a4e64b04b667ad7694a48da0fdfa77221ee4b49c79c11ed8355e521da1605"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:06.826871Z","signature_b64":"NGp6Pcbd10bq/fJ+TwHc3IMGqlAJGdpu4eqkMhDP7WUfaExF29vwzQjHbsWmDExWbkTvUsNMIr+XE+j/z9doDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f31e69a283903ae3f7b4e7db6a725f777130cf74c430444ac13bf1833c0b854f","last_reissued_at":"2026-05-18T01:27:06.826348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:06.826348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hadamard product and the free convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arijit Chakrabarty","submitted_at":"2015-11-12T04:28:46Z","abstract_excerpt":"It is shown that if a probability measure $\\nu$ is supported on a closed subset of $(0,\\infty)$, that is, its support is bounded away from zero, then the free multiplicative convolution of $\\nu$ and the semicircle law is absolutely continuous with respect to the Lebesgue measure. For the proof, a result concerning the Hadamard product of a deterministic matrix and a scaled Wigner matrix is proved and subsequently used. As a byproduct, a result, showing that the limiting spectral distribution of the Hadamard product is same as that of a symmetric random matrix with entries from a mean zero stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03770","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":"1511.03770","created_at":"2026-05-18T01:27:06.826440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03770v1","created_at":"2026-05-18T01:27:06.826440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03770","created_at":"2026-05-18T01:27:06.826440+00:00"},{"alias_kind":"pith_short_12","alias_value":"6MPGTIUDSA5O","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6MPGTIUDSA5OH55U","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6MPGTIUD","created_at":"2026-05-18T12:29:07.941421+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/6MPGTIUDSA5OH55U47NWU4S7O5","json":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5.json","graph_json":"https://pith.science/api/pith-number/6MPGTIUDSA5OH55U47NWU4S7O5/graph.json","events_json":"https://pith.science/api/pith-number/6MPGTIUDSA5OH55U47NWU4S7O5/events.json","paper":"https://pith.science/paper/6MPGTIUD"},"agent_actions":{"view_html":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5","download_json":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5.json","view_paper":"https://pith.science/paper/6MPGTIUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03770&json=true","fetch_graph":"https://pith.science/api/pith-number/6MPGTIUDSA5OH55U47NWU4S7O5/graph.json","fetch_events":"https://pith.science/api/pith-number/6MPGTIUDSA5OH55U47NWU4S7O5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5/action/storage_attestation","attest_author":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5/action/author_attestation","sign_citation":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5/action/citation_signature","submit_replication":"https://pith.science/pith/6MPGTIUDSA5OH55U47NWU4S7O5/action/replication_record"}},"created_at":"2026-05-18T01:27:06.826440+00:00","updated_at":"2026-05-18T01:27:06.826440+00:00"}