{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3UYWVUML5DG2FYMHXVCGLVEDMI","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":"1eb77734df34b94bc166020d5df59077b8e82e59887ebc5b185d351f62c7cd1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T14:35:42Z","title_canon_sha256":"927640b6bccbce1c3554725771635daa644fd2b1f2fb1a21fed2badb7192f4ed"},"schema_version":"1.0","source":{"id":"1704.02949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02949","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02949v1","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02949","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"3UYWVUML5DG2","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3UYWVUML5DG2FYMH","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3UYWVUML","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:4ec58a45ec7bed17b535ad1cf30da13077b61b433e913db9e87ea59a5e8ff582","target":"graph","created_at":"2026-05-18T00:46:43Z","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":"This paper is a survey of a new family of Banach spaces ${KS}^2$ and $SD^2$ that provide the same structure for the Henstock-Kurzweil (HK) integrable functions as the $L^p$ spaces provide for the Lebesgue integrable functions. These spaces also contain the wide sense Denjoy integrable functions. They were first use to provide the foundations for the Feynman formulation of quantum mechanics. It has recently been observed that these spaces contain the test functions $\\mathcal{D}$ as a continuous dense embedding. Thus, by the Hahn-Banach theorem, $\\mathcal{D}' \\subset \\mathcal{B}'$.  A new family","authors_text":"Tepper L Gill","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T14:35:42Z","title":"Banach spaces for the Schwartz distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02949","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:cdd16f6a160c3c6404ddae78e561dc8cbca61afbc95030b051315e1573891a1d","target":"record","created_at":"2026-05-18T00:46:43Z","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":"1eb77734df34b94bc166020d5df59077b8e82e59887ebc5b185d351f62c7cd1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-29T14:35:42Z","title_canon_sha256":"927640b6bccbce1c3554725771635daa644fd2b1f2fb1a21fed2badb7192f4ed"},"schema_version":"1.0","source":{"id":"1704.02949","kind":"arxiv","version":1}},"canonical_sha256":"dd316ad18be8cda2e187bd4465d4836228f58bdbcd4211193bd0cff8cb77ab3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd316ad18be8cda2e187bd4465d4836228f58bdbcd4211193bd0cff8cb77ab3d","first_computed_at":"2026-05-18T00:46:43.597868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:43.597868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uc+92gDK4HGtCLmvs0kZzRkvwU3MqeQgfucYZ1hS7RI7DcFHVowMF7j1kJOgcKPZPcj/u2riR+DHlHZ5sBNxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:43.598579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd16f6a160c3c6404ddae78e561dc8cbca61afbc95030b051315e1573891a1d","sha256:4ec58a45ec7bed17b535ad1cf30da13077b61b433e913db9e87ea59a5e8ff582"],"state_sha256":"e8b5d89a4a58a7a1d0953231cdce0e57b485386243105f2627b60e30ea3808c4"}