{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HBN3EPBXMP2E6GRUGNINBORNJO","short_pith_number":"pith:HBN3EPBX","schema_version":"1.0","canonical_sha256":"385bb23c3763f44f1a343350d0ba2d4b99b75f3ef0f0e8eb07a3c36bc939b6bc","source":{"kind":"arxiv","id":"2503.10319","version":2},"attestation_state":"computed","paper":{"title":"Free Perpetuities I: Existence, Subordination and Tail Asymptotics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Bartosz Ko{\\l}odziejek, Kamil Szpojankowski, Serban Belinschi","submitted_at":"2025-03-13T12:54:49Z","abstract_excerpt":"We study the free analogue of the classical affine fixed-point (or perpetuity) equation\n  \\[\n  \\mathbb{X} \\stackrel{d}{=} \\mathbb{A}^{1/2}\\mathbb{X}\\,\\mathbb{A}^{1/2} + \\mathbb{B},\n  \\] where $\\mathbb{X}$ is assumed to be $*$-free from the pair $(\\mathbb{A},\\mathbb{B})$, with $\\mathbb{A}\\ge 0$ and $\\mathbb{B}=\\mathbb{B}^*$. Our analysis covers both the subcritical regime, where $\\tau(\\mathbb{A})<1$, and the critical case $\\tau(\\mathbb{A})=1$, in which the solution $\\mathbb{X}$ is necessarily unbounded. When $\\tau(\\mathbb{A})=1$, we prove that the series defining $\\mathbb{X}$ converges bilatera"},"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":"2503.10319","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-03-13T12:54:49Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"40ee770b89386c74921accf268d92c1d141c6fce4eeb1c329aea32c77ce72e24","abstract_canon_sha256":"737c3e6024c27bf250894485a9dd7b090b41bcc13c93ff35804fc099dabafb96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:53.376635Z","signature_b64":"MwYl8bvfNYg/EDs6ozQ+zwD7k9o3r8XxGWDH59Zut/HLga4l6oV6EtZhNFNCKL83kIrPDeZ4LaMnFXAGNGr+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"385bb23c3763f44f1a343350d0ba2d4b99b75f3ef0f0e8eb07a3c36bc939b6bc","last_reissued_at":"2026-07-05T10:41:53.376102Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:53.376102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Free Perpetuities I: Existence, Subordination and Tail Asymptotics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Bartosz Ko{\\l}odziejek, Kamil Szpojankowski, Serban Belinschi","submitted_at":"2025-03-13T12:54:49Z","abstract_excerpt":"We study the free analogue of the classical affine fixed-point (or perpetuity) equation\n  \\[\n  \\mathbb{X} \\stackrel{d}{=} \\mathbb{A}^{1/2}\\mathbb{X}\\,\\mathbb{A}^{1/2} + \\mathbb{B},\n  \\] where $\\mathbb{X}$ is assumed to be $*$-free from the pair $(\\mathbb{A},\\mathbb{B})$, with $\\mathbb{A}\\ge 0$ and $\\mathbb{B}=\\mathbb{B}^*$. Our analysis covers both the subcritical regime, where $\\tau(\\mathbb{A})<1$, and the critical case $\\tau(\\mathbb{A})=1$, in which the solution $\\mathbb{X}$ is necessarily unbounded. When $\\tau(\\mathbb{A})=1$, we prove that the series defining $\\mathbb{X}$ converges bilatera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.10319","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.10319/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2503.10319","created_at":"2026-07-05T10:41:53.376164+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.10319v2","created_at":"2026-07-05T10:41:53.376164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.10319","created_at":"2026-07-05T10:41:53.376164+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBN3EPBXMP2E","created_at":"2026-07-05T10:41:53.376164+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBN3EPBXMP2E6GRU","created_at":"2026-07-05T10:41:53.376164+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBN3EPBX","created_at":"2026-07-05T10:41:53.376164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.19115","citing_title":"Finite free perpetuities","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31054","citing_title":"On the empirical spectral distribution of matrix perpetuities","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO","json":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO.json","graph_json":"https://pith.science/api/pith-number/HBN3EPBXMP2E6GRUGNINBORNJO/graph.json","events_json":"https://pith.science/api/pith-number/HBN3EPBXMP2E6GRUGNINBORNJO/events.json","paper":"https://pith.science/paper/HBN3EPBX"},"agent_actions":{"view_html":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO","download_json":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO.json","view_paper":"https://pith.science/paper/HBN3EPBX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.10319&json=true","fetch_graph":"https://pith.science/api/pith-number/HBN3EPBXMP2E6GRUGNINBORNJO/graph.json","fetch_events":"https://pith.science/api/pith-number/HBN3EPBXMP2E6GRUGNINBORNJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO/action/storage_attestation","attest_author":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO/action/author_attestation","sign_citation":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO/action/citation_signature","submit_replication":"https://pith.science/pith/HBN3EPBXMP2E6GRUGNINBORNJO/action/replication_record"}},"created_at":"2026-07-05T10:41:53.376164+00:00","updated_at":"2026-07-05T10:41:53.376164+00:00"}