{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HFWDFCMDHVOTIMOOYKFLGFNNU7","short_pith_number":"pith:HFWDFCMD","schema_version":"1.0","canonical_sha256":"396c3289833d5d3431cec28ab315ada7da29e6b557808de880495bb278764313","source":{"kind":"arxiv","id":"1501.04400","version":2},"attestation_state":"computed","paper":{"title":"A counterexample shows that not every locally $L^0$--convex topology is necessarily induced by a family of $L^0$--seminorms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mingzhi Wu, Tiexin Guo","submitted_at":"2015-01-19T06:17:27Z","abstract_excerpt":"This paper constructs a counterexample showing that not every locally $L^0$--convex topology is necessarily induced by a family of $L^0$--seminorms. Random convex analysis is the analytic foundation for $L^0$--convex conditional risk measures, this counterexample, however, shows that a locally $L^0$--convex module is not a proper framework for random convex analysis. Further, this paper also gives a necessary and sufficient condition for a locally $L^0$--convex topology to be induced by a family of $L^0$--seminorms. Finally, we give some comments showing that based on random locally convex mod"},"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":"1501.04400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-19T06:17:27Z","cross_cats_sorted":[],"title_canon_sha256":"1e62fb8b1e608e5aa337c7aad14dac03373bc005598ed942b72a51888364b900","abstract_canon_sha256":"fee759cd59b08fa8501a3a272ad6dee6486fee8ee321a63b6d5f04d7e85dc9e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:54.269157Z","signature_b64":"mFlX4wWYFBpFZnx/nlPlQvRqfzxeP2PHYMpwMT0w5t8jTpR/jAlRCdkPBwqyc3mA9zeg8AFp8x2JV5OKthWLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"396c3289833d5d3431cec28ab315ada7da29e6b557808de880495bb278764313","last_reissued_at":"2026-05-18T02:09:54.268416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:54.268416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A counterexample shows that not every locally $L^0$--convex topology is necessarily induced by a family of $L^0$--seminorms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mingzhi Wu, Tiexin Guo","submitted_at":"2015-01-19T06:17:27Z","abstract_excerpt":"This paper constructs a counterexample showing that not every locally $L^0$--convex topology is necessarily induced by a family of $L^0$--seminorms. Random convex analysis is the analytic foundation for $L^0$--convex conditional risk measures, this counterexample, however, shows that a locally $L^0$--convex module is not a proper framework for random convex analysis. Further, this paper also gives a necessary and sufficient condition for a locally $L^0$--convex topology to be induced by a family of $L^0$--seminorms. Finally, we give some comments showing that based on random locally convex mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04400","kind":"arxiv","version":2},"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":"1501.04400","created_at":"2026-05-18T02:09:54.268529+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04400v2","created_at":"2026-05-18T02:09:54.268529+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04400","created_at":"2026-05-18T02:09:54.268529+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFWDFCMDHVOT","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFWDFCMDHVOTIMOO","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFWDFCMD","created_at":"2026-05-18T12:29:25.134429+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.21049","citing_title":"A Bochner-type integration theory for random normed modules","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7","json":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7.json","graph_json":"https://pith.science/api/pith-number/HFWDFCMDHVOTIMOOYKFLGFNNU7/graph.json","events_json":"https://pith.science/api/pith-number/HFWDFCMDHVOTIMOOYKFLGFNNU7/events.json","paper":"https://pith.science/paper/HFWDFCMD"},"agent_actions":{"view_html":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7","download_json":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7.json","view_paper":"https://pith.science/paper/HFWDFCMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04400&json=true","fetch_graph":"https://pith.science/api/pith-number/HFWDFCMDHVOTIMOOYKFLGFNNU7/graph.json","fetch_events":"https://pith.science/api/pith-number/HFWDFCMDHVOTIMOOYKFLGFNNU7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7/action/storage_attestation","attest_author":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7/action/author_attestation","sign_citation":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7/action/citation_signature","submit_replication":"https://pith.science/pith/HFWDFCMDHVOTIMOOYKFLGFNNU7/action/replication_record"}},"created_at":"2026-05-18T02:09:54.268529+00:00","updated_at":"2026-05-18T02:09:54.268529+00:00"}