{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SCS2SJV7777576BNO4KEL3EK2A","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c3e8427573438dd8a15dc8121c5e6f42284cbc01efb4bafc3c3267094c904132","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-14T00:46:58Z","title_canon_sha256":"5645e91dd9cc7bfbf7378413d0b302ff2f82edf76695bc1e289f430d2d62ce93"},"schema_version":"1.0","source":{"id":"1109.2958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2958","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2958v1","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2958","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"SCS2SJV77775","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SCS2SJV7777576BN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SCS2SJV7","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:7d2fa4ea550d86f86bb5183f1b13bb418bb9c709253219e96118da481d732888","target":"graph","created_at":"2026-05-18T03:07:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with distributional values everywhere or nearly everywhere.\n  Our integral has the property that if $f$ is locally distributionally integrable over the real line and $\\psi\\in\\mathcal{D}(\\mathbb{R}%) $ is a test function, then $f\\psi$ is distributionally integrable, and the formula% [<\\mathsf{f},\\psi> =(\\mathfrak{dist}) \\int_{-\\infty}^{\\infty}f(x) \\psi(x) \\,\\mathrm{d}% x\\,,] d","authors_text":"Jasson Vindas, Ricardo Estrada","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-14T00:46:58Z","title":"A General Integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2958","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6a7fc0a09549782da20d71b5bf6d48bcfd5e4c8493076cb1e047608bd8191a05","target":"record","created_at":"2026-05-18T03:07:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c3e8427573438dd8a15dc8121c5e6f42284cbc01efb4bafc3c3267094c904132","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-14T00:46:58Z","title_canon_sha256":"5645e91dd9cc7bfbf7378413d0b302ff2f82edf76695bc1e289f430d2d62ce93"},"schema_version":"1.0","source":{"id":"1109.2958","kind":"arxiv","version":1}},"canonical_sha256":"90a5a926bfffffdff82d771445ec8ad015a02b0cdda7802d7bf21b7cf5546275","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90a5a926bfffffdff82d771445ec8ad015a02b0cdda7802d7bf21b7cf5546275","first_computed_at":"2026-05-18T03:07:41.466477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:41.466477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mIm6Sj9ktSrNZmkXbbE4h5pS7WO3K2vnE7WnJaCyZK9Nv+E3Np31DpHSP6HExoSoJbqtUE5acz8TP/H9JWbjCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:41.466897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a7fc0a09549782da20d71b5bf6d48bcfd5e4c8493076cb1e047608bd8191a05","sha256:7d2fa4ea550d86f86bb5183f1b13bb418bb9c709253219e96118da481d732888"],"state_sha256":"3b7dbff509b6d7ce414cd3549427c2db14fcb4e1a0b9f566fb49b502918ce520"}