{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:37S4LDAUHDNH4PMJC7UKK4H23V","short_pith_number":"pith:37S4LDAU","schema_version":"1.0","canonical_sha256":"dfe5c58c1438da7e3d8917e8a570fadd4a4ea41690cd2bc759a1663c97565e65","source":{"kind":"arxiv","id":"1105.5620","version":1},"attestation_state":"computed","paper":{"title":"Fourier series with the continuous primitive integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Erik Talvila","submitted_at":"2011-05-27T17:54:10Z","abstract_excerpt":"Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted $\\alext$ and is a Banach space under the Alexiewicz norm, $\\|f\\|_\\T =\\sup_{|I|\\leq 2\\pi}|\\int_I f|$, the supremum being taken over intervals of length not exceeding $2\\pi$. It contains the periodic functions integrable in the sense of Lebesgue and Henstock-Kurzweil. Many of the properties of $L^1$ Fourier series continue to hold for this larger space, with the $L^1$ norm replaced by the Alexiew"},"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":"1105.5620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-27T17:54:10Z","cross_cats_sorted":[],"title_canon_sha256":"e3c2f9e6ee04388b54d5a0bb628e3ab1046e71d22a8dbd3314524d92140a5cb5","abstract_canon_sha256":"51c762f35c0d3e0bf53039ae385cce181901253e6d0971a1056d22be8e30038a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:11.257068Z","signature_b64":"b63CDUS4U0nPpDTHzgus9kf6vRyPlEee/RG2/SQScnjc04npuUUJsF4WSy6fm+/KGjnWC/WnZGdjIhpf+i2OAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfe5c58c1438da7e3d8917e8a570fadd4a4ea41690cd2bc759a1663c97565e65","last_reissued_at":"2026-05-18T04:21:11.256368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:11.256368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourier series with the continuous primitive integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Erik Talvila","submitted_at":"2011-05-27T17:54:10Z","abstract_excerpt":"Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted $\\alext$ and is a Banach space under the Alexiewicz norm, $\\|f\\|_\\T =\\sup_{|I|\\leq 2\\pi}|\\int_I f|$, the supremum being taken over intervals of length not exceeding $2\\pi$. It contains the periodic functions integrable in the sense of Lebesgue and Henstock-Kurzweil. Many of the properties of $L^1$ Fourier series continue to hold for this larger space, with the $L^1$ norm replaced by the Alexiew"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5620","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":"1105.5620","created_at":"2026-05-18T04:21:11.256485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.5620v1","created_at":"2026-05-18T04:21:11.256485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5620","created_at":"2026-05-18T04:21:11.256485+00:00"},{"alias_kind":"pith_short_12","alias_value":"37S4LDAUHDNH","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"37S4LDAUHDNH4PMJ","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"37S4LDAU","created_at":"2026-05-18T12:26:18.847500+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/37S4LDAUHDNH4PMJC7UKK4H23V","json":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V.json","graph_json":"https://pith.science/api/pith-number/37S4LDAUHDNH4PMJC7UKK4H23V/graph.json","events_json":"https://pith.science/api/pith-number/37S4LDAUHDNH4PMJC7UKK4H23V/events.json","paper":"https://pith.science/paper/37S4LDAU"},"agent_actions":{"view_html":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V","download_json":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V.json","view_paper":"https://pith.science/paper/37S4LDAU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.5620&json=true","fetch_graph":"https://pith.science/api/pith-number/37S4LDAUHDNH4PMJC7UKK4H23V/graph.json","fetch_events":"https://pith.science/api/pith-number/37S4LDAUHDNH4PMJC7UKK4H23V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V/action/storage_attestation","attest_author":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V/action/author_attestation","sign_citation":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V/action/citation_signature","submit_replication":"https://pith.science/pith/37S4LDAUHDNH4PMJC7UKK4H23V/action/replication_record"}},"created_at":"2026-05-18T04:21:11.256485+00:00","updated_at":"2026-05-18T04:21:11.256485+00:00"}