{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QWADGLNIVLQVIMXJXCVQCE5QDO","short_pith_number":"pith:QWADGLNI","schema_version":"1.0","canonical_sha256":"8580332da8aae15432e9b8ab0113b01b95ddd511e16db3706f48f125a7f9f760","source":{"kind":"arxiv","id":"1801.07103","version":1},"attestation_state":"computed","paper":{"title":"Majoration of the dimension of the space of concatenated solutions of a specific pantograph equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Fran\\c{c}ois Bertazzon","submitted_at":"2018-01-22T13:59:23Z","abstract_excerpt":"For each $\\lambda \\in \\mathbb N^*$, we consider the integral equation: \\[ \\int_{\\lambda y} ^{\\lambda x} f(t)\\, d t = f(x) - f(y) \\mbox{ for every $(x,y)\\in {\\mathbb R}_+^2$,} \\] where $f$ is the concatenation of two continuous functions $f_a,f_b:[0,\\lambda] \\rightarrow {\\mathbb R}$ along a word $u= u_0u_1\\cdots\\in\\{a,b\\}^{\\mathbb N}$ such that $u=\\sigma(u)$, where $\\sigma$ is a $\\lambda$-uniform substitution satisfying some combinatorial conditions.\n  There exists some non-trivial solutions. We show in this work that the dimension of the set of solutions is at most two."},"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":"1801.07103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-22T13:59:23Z","cross_cats_sorted":[],"title_canon_sha256":"b9ae3d371fe45f9d4af09e3e918b02e22230b07d78fd4c8e77f683d464274287","abstract_canon_sha256":"8b0ff99da268eb0953bb6cc76227fd14995c5566c2994ae5f5e975170b2bc2a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:22.246141Z","signature_b64":"mfDSU2gbJunMhbEVbSsTOTd04cDAidPhqcwSUpc1sp53kckKMgkdjabT36vm1NXfNOa3gwVs95s3A/HXmbhKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8580332da8aae15432e9b8ab0113b01b95ddd511e16db3706f48f125a7f9f760","last_reissued_at":"2026-05-18T00:25:22.245529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:22.245529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Majoration of the dimension of the space of concatenated solutions of a specific pantograph equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Fran\\c{c}ois Bertazzon","submitted_at":"2018-01-22T13:59:23Z","abstract_excerpt":"For each $\\lambda \\in \\mathbb N^*$, we consider the integral equation: \\[ \\int_{\\lambda y} ^{\\lambda x} f(t)\\, d t = f(x) - f(y) \\mbox{ for every $(x,y)\\in {\\mathbb R}_+^2$,} \\] where $f$ is the concatenation of two continuous functions $f_a,f_b:[0,\\lambda] \\rightarrow {\\mathbb R}$ along a word $u= u_0u_1\\cdots\\in\\{a,b\\}^{\\mathbb N}$ such that $u=\\sigma(u)$, where $\\sigma$ is a $\\lambda$-uniform substitution satisfying some combinatorial conditions.\n  There exists some non-trivial solutions. We show in this work that the dimension of the set of solutions is at most two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07103","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":"1801.07103","created_at":"2026-05-18T00:25:22.245600+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.07103v1","created_at":"2026-05-18T00:25:22.245600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07103","created_at":"2026-05-18T00:25:22.245600+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWADGLNIVLQV","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWADGLNIVLQVIMXJ","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWADGLNI","created_at":"2026-05-18T12:32:46.962924+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/QWADGLNIVLQVIMXJXCVQCE5QDO","json":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO.json","graph_json":"https://pith.science/api/pith-number/QWADGLNIVLQVIMXJXCVQCE5QDO/graph.json","events_json":"https://pith.science/api/pith-number/QWADGLNIVLQVIMXJXCVQCE5QDO/events.json","paper":"https://pith.science/paper/QWADGLNI"},"agent_actions":{"view_html":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO","download_json":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO.json","view_paper":"https://pith.science/paper/QWADGLNI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.07103&json=true","fetch_graph":"https://pith.science/api/pith-number/QWADGLNIVLQVIMXJXCVQCE5QDO/graph.json","fetch_events":"https://pith.science/api/pith-number/QWADGLNIVLQVIMXJXCVQCE5QDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO/action/storage_attestation","attest_author":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO/action/author_attestation","sign_citation":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO/action/citation_signature","submit_replication":"https://pith.science/pith/QWADGLNIVLQVIMXJXCVQCE5QDO/action/replication_record"}},"created_at":"2026-05-18T00:25:22.245600+00:00","updated_at":"2026-05-18T00:25:22.245600+00:00"}