{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:SCB6I5NMFVTHQXH4IJQMX7PZ7T","short_pith_number":"pith:SCB6I5NM","schema_version":"1.0","canonical_sha256":"9083e475ac2d66785cfc4260cbfdf9fcd650031ab79ec586cfad2af132bacc6d","source":{"kind":"arxiv","id":"0911.1513","version":3},"attestation_state":"computed","paper":{"title":"Multi-variable translation equation which arises from homothety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CA","authors_text":"Giedrius Alkauskas","submitted_at":"2009-11-08T10:50:18Z","abstract_excerpt":"In many regular cases, there exists a (properly defined) limit of iterations of a function in several real variables, and this limit satisfies the functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a vector. This is a special case of a well-known translation equation. In this paper we present a complete solution to this functional equation in case f is a continuous function on a single point compactification of a 2-dimensional real vector space. It appears that, up to conjugation by a homogeneous continuous function, there are exactly four solutions. Further, in a 1-dim"},"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":"0911.1513","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-11-08T10:50:18Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a66b262dc6214e0700af53306b6d78568886c55352ce635b0f6e6629bf66553f","abstract_canon_sha256":"a18092cc0532d348825ac345971bd906976d52f0c878bcc93df7165971982af4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:23.687669Z","signature_b64":"Ramaxesh3n1Sd16yksRsJQMzVLJF1ORHcJXda9oaLc17nd9J50DHLiXjjNUKclSMAtGGHQh2KrgRPVGqgBK4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9083e475ac2d66785cfc4260cbfdf9fcd650031ab79ec586cfad2af132bacc6d","last_reissued_at":"2026-05-18T04:18:23.686972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:23.686972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-variable translation equation which arises from homothety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CA","authors_text":"Giedrius Alkauskas","submitted_at":"2009-11-08T10:50:18Z","abstract_excerpt":"In many regular cases, there exists a (properly defined) limit of iterations of a function in several real variables, and this limit satisfies the functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a vector. This is a special case of a well-known translation equation. In this paper we present a complete solution to this functional equation in case f is a continuous function on a single point compactification of a 2-dimensional real vector space. It appears that, up to conjugation by a homogeneous continuous function, there are exactly four solutions. Further, in a 1-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1513","kind":"arxiv","version":3},"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":"0911.1513","created_at":"2026-05-18T04:18:23.687081+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.1513v3","created_at":"2026-05-18T04:18:23.687081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1513","created_at":"2026-05-18T04:18:23.687081+00:00"},{"alias_kind":"pith_short_12","alias_value":"SCB6I5NMFVTH","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"SCB6I5NMFVTHQXH4","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"SCB6I5NM","created_at":"2026-05-18T12:26:01.383474+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/SCB6I5NMFVTHQXH4IJQMX7PZ7T","json":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T.json","graph_json":"https://pith.science/api/pith-number/SCB6I5NMFVTHQXH4IJQMX7PZ7T/graph.json","events_json":"https://pith.science/api/pith-number/SCB6I5NMFVTHQXH4IJQMX7PZ7T/events.json","paper":"https://pith.science/paper/SCB6I5NM"},"agent_actions":{"view_html":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T","download_json":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T.json","view_paper":"https://pith.science/paper/SCB6I5NM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.1513&json=true","fetch_graph":"https://pith.science/api/pith-number/SCB6I5NMFVTHQXH4IJQMX7PZ7T/graph.json","fetch_events":"https://pith.science/api/pith-number/SCB6I5NMFVTHQXH4IJQMX7PZ7T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T/action/storage_attestation","attest_author":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T/action/author_attestation","sign_citation":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T/action/citation_signature","submit_replication":"https://pith.science/pith/SCB6I5NMFVTHQXH4IJQMX7PZ7T/action/replication_record"}},"created_at":"2026-05-18T04:18:23.687081+00:00","updated_at":"2026-05-18T04:18:23.687081+00:00"}