{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:2PTLM7DML6GHVWX2IIZQM4UGF3","short_pith_number":"pith:2PTLM7DM","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"},"canonical_sha256":"d3e6b67c6c5f8c7adafa42330672862ee02e481e153ed61e27c27d6bebbcd6c6","source":{"kind":"arxiv","id":"math/9601204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9601204","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/9601204v1","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9601204","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"2PTLM7DML6GH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"2PTLM7DML6GHVWX2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"2PTLM7DM","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:2PTLM7DML6GHVWX2IIZQM4UGF3","target":"record","payload":{"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"},"canonical_sha256":"d3e6b67c6c5f8c7adafa42330672862ee02e481e153ed61e27c27d6bebbcd6c6","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"},"source_kind":"arxiv","source_id":"math/9601204","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8mK/FJFc/4kmaLHt4q75/gd5XZaH8g+861WzgavYQgj/9j7C9DuwpSay+INXaC1fEGknrF0Q2hHoL9vlXJZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:30:59.158416Z"},"content_sha256":"2a8ee35136b0b806ab0a4ea471e32f404338fd9d37b17f0d8c6053ffede98ff6","schema_version":"1.0","event_id":"sha256:2a8ee35136b0b806ab0a4ea471e32f404338fd9d37b17f0d8c6053ffede98ff6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:2PTLM7DML6GHVWX2IIZQM4UGF3","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vYYVxlZwHJiKC3dUyqansflnK2Zh7wlblyXMQ1nBxT++ThGwvdArbTveO89wJAH0xNv1qeU6xnMoJmkpVgIwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:30:59.158767Z"},"content_sha256":"ea08512ab14fa0349fd3cd5286f8d314e6b52bca155c6ff5f1113c4b2aa46a38","schema_version":"1.0","event_id":"sha256:ea08512ab14fa0349fd3cd5286f8d314e6b52bca155c6ff5f1113c4b2aa46a38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/bundle.json","state_url":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T04:30:59Z","links":{"resolver":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3","bundle":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/bundle.json","state":"https://pith.science/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2PTLM7DML6GHVWX2IIZQM4UGF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:2PTLM7DML6GHVWX2IIZQM4UGF3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c79bf70b6ccc389f454f586101a5761d13e9ef85de0fbfd1c31ddaaf8367c50d","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1996-01-26T00:00:00Z","title_canon_sha256":"b66011f19d3bd3db2c480d21845bf9580b6a9030c274f41419570f58ed892651"},"schema_version":"1.0","source":{"id":"math/9601204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9601204","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/9601204v1","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9601204","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"2PTLM7DML6GH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"2PTLM7DML6GHVWX2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"2PTLM7DM","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:ea08512ab14fa0349fd3cd5286f8d314e6b52bca155c6ff5f1113c4b2aa46a38","target":"graph","created_at":"2026-05-18T01:05:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Valentin Ferenczi","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1996-01-26T00:00:00Z","title":"Q.H.I. spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601204","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2a8ee35136b0b806ab0a4ea471e32f404338fd9d37b17f0d8c6053ffede98ff6","target":"record","created_at":"2026-05-18T01:05:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c79bf70b6ccc389f454f586101a5761d13e9ef85de0fbfd1c31ddaaf8367c50d","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1996-01-26T00:00:00Z","title_canon_sha256":"b66011f19d3bd3db2c480d21845bf9580b6a9030c274f41419570f58ed892651"},"schema_version":"1.0","source":{"id":"math/9601204","kind":"arxiv","version":1}},"canonical_sha256":"d3e6b67c6c5f8c7adafa42330672862ee02e481e153ed61e27c27d6bebbcd6c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3e6b67c6c5f8c7adafa42330672862ee02e481e153ed61e27c27d6bebbcd6c6","first_computed_at":"2026-05-18T01:05:47.914393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:47.914393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w2Wgt0oiue/DrWfDEbh+qysdNarOM3w3O4qlaJUWSrzY1x3eVcBnvZjVfUbsIslU3sNKG6MLk3b7Cfx1/BQECw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:47.914865Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9601204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8ee35136b0b806ab0a4ea471e32f404338fd9d37b17f0d8c6053ffede98ff6","sha256:ea08512ab14fa0349fd3cd5286f8d314e6b52bca155c6ff5f1113c4b2aa46a38"],"state_sha256":"1c755df6e93305f186cb21b0b82e2c513aeb881b88c13ac13b2a1014d86d1f42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjoTULMqAq1WV2QS15Yxvt9YRBHVLC3jvfQUy933grHyE+rEJbkFjh1RdGBmNjqYPVGeLt7bA+cAdx2WZLXaDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:30:59.160751Z","bundle_sha256":"b2aff19b4b6b5fdd62b450f76c2bf9d246e4b04a2e2a266d70809e0cd98ca0a8"}}