{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:45JNCM4BQOJYYTVFHMBD3PZPMQ","short_pith_number":"pith:45JNCM4B","schema_version":"1.0","canonical_sha256":"e752d1338183938c4ea53b023dbf2f6407ab722c8806ec22f33672f6089a2984","source":{"kind":"arxiv","id":"1405.6265","version":1},"attestation_state":"computed","paper":{"title":"Maximums on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto, Predrag R. Jelenkovic","submitted_at":"2014-05-24T03:56:10Z","abstract_excerpt":"We study the minimal/endogenous solution $R$ to the maximum recursion on weighted branching trees given by $$R\\stackrel{\\mathcal{D}}{=}\\left(\\bigvee_{i=1}^NC_iR_i \\right)\\vee Q,$$ where $(Q,N,C_1,C_2,\\dots)$ is a random vector with $N\\in \\mathbb{N}\\cup\\{\\infty\\}$, $P(|Q|>0)>0$ and nonnegative weights $\\{C_i\\}$, and $\\{R_i\\}_{i\\in\\mathbb{N}}$ is a sequence of i.i.d. copies of $R$ independent of $(Q,N,C_1,C_2,\\dots)$; $\\stackrel{\\mathcal{D}}{=}$ denotes equality in distribution. Furthermore, when $Q>0$ this recursion can be transformed into its additive equivalent, which corresponds to the maxim"},"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":"1405.6265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-24T03:56:10Z","cross_cats_sorted":[],"title_canon_sha256":"1e1394080acf2d8743ea4e64c331846045aed2e0549f783e92b012884b32967f","abstract_canon_sha256":"0828009212a72a42f9201cc3b2c91f7e00de568aa428d08222532961ced850be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:07.660589Z","signature_b64":"2CnHHdQzvwDDh80ALGU8S5c1a1MzlSRwLw4y8dk2XNinTlyuWACNl7pgJ9HBOEwd5qKjg49vRFQutZ1oxEu6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e752d1338183938c4ea53b023dbf2f6407ab722c8806ec22f33672f6089a2984","last_reissued_at":"2026-05-18T02:51:07.660095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:07.660095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximums on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto, Predrag R. Jelenkovic","submitted_at":"2014-05-24T03:56:10Z","abstract_excerpt":"We study the minimal/endogenous solution $R$ to the maximum recursion on weighted branching trees given by $$R\\stackrel{\\mathcal{D}}{=}\\left(\\bigvee_{i=1}^NC_iR_i \\right)\\vee Q,$$ where $(Q,N,C_1,C_2,\\dots)$ is a random vector with $N\\in \\mathbb{N}\\cup\\{\\infty\\}$, $P(|Q|>0)>0$ and nonnegative weights $\\{C_i\\}$, and $\\{R_i\\}_{i\\in\\mathbb{N}}$ is a sequence of i.i.d. copies of $R$ independent of $(Q,N,C_1,C_2,\\dots)$; $\\stackrel{\\mathcal{D}}{=}$ denotes equality in distribution. Furthermore, when $Q>0$ this recursion can be transformed into its additive equivalent, which corresponds to the maxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6265","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":"1405.6265","created_at":"2026-05-18T02:51:07.660162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6265v1","created_at":"2026-05-18T02:51:07.660162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6265","created_at":"2026-05-18T02:51:07.660162+00:00"},{"alias_kind":"pith_short_12","alias_value":"45JNCM4BQOJY","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"45JNCM4BQOJYYTVF","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"45JNCM4B","created_at":"2026-05-18T12:28:14.216126+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/45JNCM4BQOJYYTVFHMBD3PZPMQ","json":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ.json","graph_json":"https://pith.science/api/pith-number/45JNCM4BQOJYYTVFHMBD3PZPMQ/graph.json","events_json":"https://pith.science/api/pith-number/45JNCM4BQOJYYTVFHMBD3PZPMQ/events.json","paper":"https://pith.science/paper/45JNCM4B"},"agent_actions":{"view_html":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ","download_json":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ.json","view_paper":"https://pith.science/paper/45JNCM4B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6265&json=true","fetch_graph":"https://pith.science/api/pith-number/45JNCM4BQOJYYTVFHMBD3PZPMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/45JNCM4BQOJYYTVFHMBD3PZPMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ/action/storage_attestation","attest_author":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ/action/author_attestation","sign_citation":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ/action/citation_signature","submit_replication":"https://pith.science/pith/45JNCM4BQOJYYTVFHMBD3PZPMQ/action/replication_record"}},"created_at":"2026-05-18T02:51:07.660162+00:00","updated_at":"2026-05-18T02:51:07.660162+00:00"}