{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KSIPAJBW7RJKMRHLTN5ZF753E5","short_pith_number":"pith:KSIPAJBW","schema_version":"1.0","canonical_sha256":"5490f02436fc52a644eb9b7b92ffbb275dfb1ec66bb1d509d521e9e85370886b","source":{"kind":"arxiv","id":"1101.3762","version":4},"attestation_state":"computed","paper":{"title":"Categorical Geometry and Integration Without Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ales Pultr, Igor Kriz","submitted_at":"2011-01-19T19:58:05Z","abstract_excerpt":"The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article \\cite{segal}. In our paper we follow his ideas from a different perspective, slightly more categorical, and strongly inspired by the point-free topology.\n  First, we develop a general (point-free) concept of measurability (extending the standard Lebesgue integration when applying to the classical $\\sigma$-algebra). Second (and here we have a major "},"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":"1101.3762","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-19T19:58:05Z","cross_cats_sorted":[],"title_canon_sha256":"d7656d06818f28a9bc8f2b6f73dbaab7262e2d635089ba40057f1b2681217e6d","abstract_canon_sha256":"49b6965e11a01e7503876ff0f5a4d4bde1055f44c4e027d41a667e4660f0bc26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:11.270513Z","signature_b64":"TmhoStdv3mse0ThTJ2yXgd2qonROVLD96nJpsACIIMUtTDuBPp7pjxhQrk5JZ/Qfzpo0IrcIZSD7hE7rJE4/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5490f02436fc52a644eb9b7b92ffbb275dfb1ec66bb1d509d521e9e85370886b","last_reissued_at":"2026-05-18T03:41:11.270002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:11.270002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categorical Geometry and Integration Without Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ales Pultr, Igor Kriz","submitted_at":"2011-01-19T19:58:05Z","abstract_excerpt":"The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article \\cite{segal}. In our paper we follow his ideas from a different perspective, slightly more categorical, and strongly inspired by the point-free topology.\n  First, we develop a general (point-free) concept of measurability (extending the standard Lebesgue integration when applying to the classical $\\sigma$-algebra). Second (and here we have a major "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3762","kind":"arxiv","version":4},"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":"1101.3762","created_at":"2026-05-18T03:41:11.270085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3762v4","created_at":"2026-05-18T03:41:11.270085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3762","created_at":"2026-05-18T03:41:11.270085+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSIPAJBW7RJK","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSIPAJBW7RJKMRHL","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSIPAJBW","created_at":"2026-05-18T12:26:34.985390+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/KSIPAJBW7RJKMRHLTN5ZF753E5","json":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5.json","graph_json":"https://pith.science/api/pith-number/KSIPAJBW7RJKMRHLTN5ZF753E5/graph.json","events_json":"https://pith.science/api/pith-number/KSIPAJBW7RJKMRHLTN5ZF753E5/events.json","paper":"https://pith.science/paper/KSIPAJBW"},"agent_actions":{"view_html":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5","download_json":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5.json","view_paper":"https://pith.science/paper/KSIPAJBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3762&json=true","fetch_graph":"https://pith.science/api/pith-number/KSIPAJBW7RJKMRHLTN5ZF753E5/graph.json","fetch_events":"https://pith.science/api/pith-number/KSIPAJBW7RJKMRHLTN5ZF753E5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5/action/storage_attestation","attest_author":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5/action/author_attestation","sign_citation":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5/action/citation_signature","submit_replication":"https://pith.science/pith/KSIPAJBW7RJKMRHLTN5ZF753E5/action/replication_record"}},"created_at":"2026-05-18T03:41:11.270085+00:00","updated_at":"2026-05-18T03:41:11.270085+00:00"}