{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:ZZH5IPQXX76P4W44OGXLXVXJKR","short_pith_number":"pith:ZZH5IPQX","schema_version":"1.0","canonical_sha256":"ce4fd43e17bffcfe5b9c71aebbd6e95467ed7c605cb48afb604ca04d6bff9a7b","source":{"kind":"arxiv","id":"math/0505484","version":2},"attestation_state":"computed","paper":{"title":"Translation-invariant generalized topologies induced by probabilistic norms","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GN","authors_text":"Bernardo Lafuerza-Guillen, Jose L. Rodriguez","submitted_at":"2005-05-23T20:49:49Z","abstract_excerpt":"In this paper we consider probabilistic normed spaces as defined by Alsina, Sklar, and Schweizer, but equipped with non necessarily continuous triangle functions. Such spaces endow a generalized topology that is Fr\\'echet-separable, translation-invariant and countably generated by radial and circled 0-neighborhoods. Conversely, we show that such generalized topologies are probabilistically normable."},"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":"math/0505484","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2005-05-23T20:49:49Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c44e74a0fc147a2be0011a4ce8d22e81bdb7faf666bc6fa48a8caebc6c4f3514","abstract_canon_sha256":"082f7e82cef22923bfc99b7de2f038a0acf04de925aecd72bb86b7ee0bcf400d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:33.800451Z","signature_b64":"KC2VMBIoMhCyHMfBPB2oX91ys2H5WJpvdO5NEdKlNFUK/Voxu10C5c2n5fmsz3Y98NtgknO4HDkZuL4X3EOaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce4fd43e17bffcfe5b9c71aebbd6e95467ed7c605cb48afb604ca04d6bff9a7b","last_reissued_at":"2026-05-18T04:42:33.799902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:33.799902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Translation-invariant generalized topologies induced by probabilistic norms","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GN","authors_text":"Bernardo Lafuerza-Guillen, Jose L. Rodriguez","submitted_at":"2005-05-23T20:49:49Z","abstract_excerpt":"In this paper we consider probabilistic normed spaces as defined by Alsina, Sklar, and Schweizer, but equipped with non necessarily continuous triangle functions. Such spaces endow a generalized topology that is Fr\\'echet-separable, translation-invariant and countably generated by radial and circled 0-neighborhoods. Conversely, we show that such generalized topologies are probabilistically normable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505484","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":"math/0505484","created_at":"2026-05-18T04:42:33.799988+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0505484v2","created_at":"2026-05-18T04:42:33.799988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505484","created_at":"2026-05-18T04:42:33.799988+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZZH5IPQXX76P","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZZH5IPQXX76P4W44","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZZH5IPQX","created_at":"2026-05-18T12:25:53.939244+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/ZZH5IPQXX76P4W44OGXLXVXJKR","json":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR.json","graph_json":"https://pith.science/api/pith-number/ZZH5IPQXX76P4W44OGXLXVXJKR/graph.json","events_json":"https://pith.science/api/pith-number/ZZH5IPQXX76P4W44OGXLXVXJKR/events.json","paper":"https://pith.science/paper/ZZH5IPQX"},"agent_actions":{"view_html":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR","download_json":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR.json","view_paper":"https://pith.science/paper/ZZH5IPQX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0505484&json=true","fetch_graph":"https://pith.science/api/pith-number/ZZH5IPQXX76P4W44OGXLXVXJKR/graph.json","fetch_events":"https://pith.science/api/pith-number/ZZH5IPQXX76P4W44OGXLXVXJKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR/action/storage_attestation","attest_author":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR/action/author_attestation","sign_citation":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR/action/citation_signature","submit_replication":"https://pith.science/pith/ZZH5IPQXX76P4W44OGXLXVXJKR/action/replication_record"}},"created_at":"2026-05-18T04:42:33.799988+00:00","updated_at":"2026-05-18T04:42:33.799988+00:00"}