{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ASBBIL6QC2L4WXVFCSVVWB7BPB","short_pith_number":"pith:ASBBIL6Q","schema_version":"1.0","canonical_sha256":"0482142fd01697cb5ea514ab5b07e1787839a94998b448c1232970cfc52d12de","source":{"kind":"arxiv","id":"1007.4509","version":2},"attestation_state":"computed","paper":{"title":"Fixed points of inhomogeneous smoothing transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerold Alsmeyer, Matthias Meiners","submitted_at":"2010-07-26T17:19:12Z","abstract_excerpt":"We consider the inhomogeneous version of the fixed-point equation of the smoothing transformation, that is, the equation $X \\stackrel{d}{=} C + \\sum_{i \\geq 1} T_i X_i$, where $\\stackrel{d}{=}$ means equality in distribution, $(C,T_1,T_2,...)$ is a given sequence of non-negative random variables and $X_1,X_2,...$ is a sequence of i.i.d.\\ copies of the non-negative random variable $X$ independent of $(C,T_1,T_2,...)$. In this situation, $X$ (or, more precisely, the distribution of $X$) is said to be a fixed point of the (inhomogeneous) smoothing transform. In the present paper, we give a necess"},"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":"1007.4509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-26T17:19:12Z","cross_cats_sorted":[],"title_canon_sha256":"9c5848ed687be165d408004265b8a6543b59e2ca8d16d24f8c14dcb7c5dde739","abstract_canon_sha256":"bab80c326a6eda0d0071b8ec9a570d02fddfe552ec9fd48e3c81287a1a706e83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:45.147113Z","signature_b64":"JoMauTMDn/KF28E1kigwVQM/tOr2fhhnQxZa7yO4Vfd8/f22cS37X1nzplqgbITZQn61fmtH/cRWa0tzFF8SBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0482142fd01697cb5ea514ab5b07e1787839a94998b448c1232970cfc52d12de","last_reissued_at":"2026-05-18T04:06:45.146487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:45.146487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed points of inhomogeneous smoothing transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerold Alsmeyer, Matthias Meiners","submitted_at":"2010-07-26T17:19:12Z","abstract_excerpt":"We consider the inhomogeneous version of the fixed-point equation of the smoothing transformation, that is, the equation $X \\stackrel{d}{=} C + \\sum_{i \\geq 1} T_i X_i$, where $\\stackrel{d}{=}$ means equality in distribution, $(C,T_1,T_2,...)$ is a given sequence of non-negative random variables and $X_1,X_2,...$ is a sequence of i.i.d.\\ copies of the non-negative random variable $X$ independent of $(C,T_1,T_2,...)$. In this situation, $X$ (or, more precisely, the distribution of $X$) is said to be a fixed point of the (inhomogeneous) smoothing transform. In the present paper, we give a necess"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4509","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":"1007.4509","created_at":"2026-05-18T04:06:45.146582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.4509v2","created_at":"2026-05-18T04:06:45.146582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4509","created_at":"2026-05-18T04:06:45.146582+00:00"},{"alias_kind":"pith_short_12","alias_value":"ASBBIL6QC2L4","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"ASBBIL6QC2L4WXVF","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"ASBBIL6Q","created_at":"2026-05-18T12:26:05.355336+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/ASBBIL6QC2L4WXVFCSVVWB7BPB","json":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB.json","graph_json":"https://pith.science/api/pith-number/ASBBIL6QC2L4WXVFCSVVWB7BPB/graph.json","events_json":"https://pith.science/api/pith-number/ASBBIL6QC2L4WXVFCSVVWB7BPB/events.json","paper":"https://pith.science/paper/ASBBIL6Q"},"agent_actions":{"view_html":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB","download_json":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB.json","view_paper":"https://pith.science/paper/ASBBIL6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.4509&json=true","fetch_graph":"https://pith.science/api/pith-number/ASBBIL6QC2L4WXVFCSVVWB7BPB/graph.json","fetch_events":"https://pith.science/api/pith-number/ASBBIL6QC2L4WXVFCSVVWB7BPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB/action/storage_attestation","attest_author":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB/action/author_attestation","sign_citation":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB/action/citation_signature","submit_replication":"https://pith.science/pith/ASBBIL6QC2L4WXVFCSVVWB7BPB/action/replication_record"}},"created_at":"2026-05-18T04:06:45.146582+00:00","updated_at":"2026-05-18T04:06:45.146582+00:00"}