{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:2PTLM7DML6GHVWX2IIZQM4UGF3","short_pith_number":"pith:2PTLM7DM","schema_version":"1.0","canonical_sha256":"d3e6b67c6c5f8c7adafa42330672862ee02e481e153ed61e27c27d6bebbcd6c6","source":{"kind":"arxiv","id":"math/9601204","version":1},"attestation_state":"computed","paper":{"title":"Q.H.I. spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Valentin Ferenczi","submitted_at":"1996-01-26T00:00:00Z","abstract_excerpt":"A Banach space $X$ is said to be Q.H.I. if eve\\-ry infinite dimensional quo\\-tient spa\\-ce of $X$ is H.I.: that is, a space is Q.H.I. if the H.I. property is not only stable passing to subspaces, but also passing to quotients and to the dual. We show that Gowers-Maurey's space is Q.H.I.; then we provide an example of a reflexive H.I. space ${\\cal X}$ whose dual is not H.I., from which it follows that $\\cal X$ is not Q.H.I."},"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/9601204","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1996-01-26T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"b66011f19d3bd3db2c480d21845bf9580b6a9030c274f41419570f58ed892651","abstract_canon_sha256":"c79bf70b6ccc389f454f586101a5761d13e9ef85de0fbfd1c31ddaaf8367c50d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:47.914865Z","signature_b64":"w2Wgt0oiue/DrWfDEbh+qysdNarOM3w3O4qlaJUWSrzY1x3eVcBnvZjVfUbsIslU3sNKG6MLk3b7Cfx1/BQECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3e6b67c6c5f8c7adafa42330672862ee02e481e153ed61e27c27d6bebbcd6c6","last_reissued_at":"2026-05-18T01:05:47.914393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:47.914393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Q.H.I. spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Valentin Ferenczi","submitted_at":"1996-01-26T00:00:00Z","abstract_excerpt":"A Banach space $X$ is said to be Q.H.I. if eve\\-ry infinite dimensional quo\\-tient spa\\-ce of $X$ is H.I.: that is, a space is Q.H.I. if the H.I. property is not only stable passing to subspaces, but also passing to quotients and to the dual. We show that Gowers-Maurey's space is Q.H.I.; then we provide an example of a reflexive H.I. space ${\\cal X}$ whose dual is not H.I., from which it follows that $\\cal X$ is not Q.H.I."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601204","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":"math/9601204","created_at":"2026-05-18T01:05:47.914476+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9601204v1","created_at":"2026-05-18T01:05:47.914476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9601204","created_at":"2026-05-18T01:05:47.914476+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PTLM7DML6GH","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PTLM7DML6GHVWX2","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PTLM7DM","created_at":"2026-05-18T12:25:47.700082+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/2PTLM7DML6GHVWX2IIZQM4UGF3","json":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3.json","graph_json":"https://pith.science/api/pith-number/2PTLM7DML6GHVWX2IIZQM4UGF3/graph.json","events_json":"https://pith.science/api/pith-number/2PTLM7DML6GHVWX2IIZQM4UGF3/events.json","paper":"https://pith.science/paper/2PTLM7DM"},"agent_actions":{"view_html":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3","download_json":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3.json","view_paper":"https://pith.science/paper/2PTLM7DM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9601204&json=true","fetch_graph":"https://pith.science/api/pith-number/2PTLM7DML6GHVWX2IIZQM4UGF3/graph.json","fetch_events":"https://pith.science/api/pith-number/2PTLM7DML6GHVWX2IIZQM4UGF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/action/storage_attestation","attest_author":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/action/author_attestation","sign_citation":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/action/citation_signature","submit_replication":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/action/replication_record"}},"created_at":"2026-05-18T01:05:47.914476+00:00","updated_at":"2026-05-18T01:05:47.914476+00:00"}