{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7PZWZ4UEPF6H33PLMZM33LMKEB","short_pith_number":"pith:7PZWZ4UE","schema_version":"1.0","canonical_sha256":"fbf36cf284797c7dedeb6659bdad8a206d849e46ff57ae4e433bb68315199faf","source":{"kind":"arxiv","id":"1711.09785","version":1},"attestation_state":"computed","paper":{"title":"On compactness in $L^0$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asgar Jamneshan, Jose Miguel Zapata","submitted_at":"2017-11-27T15:51:22Z","abstract_excerpt":"Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\\colon \\Omega\\to \\mathbb{R}$. The focus is on results involving compactness. To this end, a notion of stable compactness is introduced, and it is argued that the conventional notion of compactness does not allow to establish a functional analytic discourse in $L^0$-modules. Several characterizations of stable compactness are discussed, and its importance in applications is highlighted."},"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":"1711.09785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-27T15:51:22Z","cross_cats_sorted":[],"title_canon_sha256":"c3dbf530921605e612090f6f6e7226185a3880235b1369d3835010d849f13bc3","abstract_canon_sha256":"cc5dc9bbe0dd61eb1c6f0542e3f696a932fd1daac7b1e2bf2691fe89ae5a791c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:34.466847Z","signature_b64":"2AeAyGbwdM1ykcIG821bUiyPjZc+yKK2pPFDf4VidrXW5yRfMl1eRetEN5ZYqow8cWOceO0foPUBmqWy7+DnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbf36cf284797c7dedeb6659bdad8a206d849e46ff57ae4e433bb68315199faf","last_reissued_at":"2026-05-18T00:29:34.466237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:34.466237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On compactness in $L^0$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asgar Jamneshan, Jose Miguel Zapata","submitted_at":"2017-11-27T15:51:22Z","abstract_excerpt":"Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\\colon \\Omega\\to \\mathbb{R}$. The focus is on results involving compactness. To this end, a notion of stable compactness is introduced, and it is argued that the conventional notion of compactness does not allow to establish a functional analytic discourse in $L^0$-modules. Several characterizations of stable compactness are discussed, and its importance in applications is highlighted."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09785","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":"1711.09785","created_at":"2026-05-18T00:29:34.466339+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.09785v1","created_at":"2026-05-18T00:29:34.466339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09785","created_at":"2026-05-18T00:29:34.466339+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PZWZ4UEPF6H","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PZWZ4UEPF6H33PL","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PZWZ4UE","created_at":"2026-05-18T12:31:05.417338+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/7PZWZ4UEPF6H33PLMZM33LMKEB","json":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB.json","graph_json":"https://pith.science/api/pith-number/7PZWZ4UEPF6H33PLMZM33LMKEB/graph.json","events_json":"https://pith.science/api/pith-number/7PZWZ4UEPF6H33PLMZM33LMKEB/events.json","paper":"https://pith.science/paper/7PZWZ4UE"},"agent_actions":{"view_html":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB","download_json":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB.json","view_paper":"https://pith.science/paper/7PZWZ4UE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.09785&json=true","fetch_graph":"https://pith.science/api/pith-number/7PZWZ4UEPF6H33PLMZM33LMKEB/graph.json","fetch_events":"https://pith.science/api/pith-number/7PZWZ4UEPF6H33PLMZM33LMKEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB/action/storage_attestation","attest_author":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB/action/author_attestation","sign_citation":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB/action/citation_signature","submit_replication":"https://pith.science/pith/7PZWZ4UEPF6H33PLMZM33LMKEB/action/replication_record"}},"created_at":"2026-05-18T00:29:34.466339+00:00","updated_at":"2026-05-18T00:29:34.466339+00:00"}