{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:DYILINCBRD6PUIGEGGVLTAZUUG","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":"5a4204e77b64d5bf986c2a0365792738d7ebe0ba24a1f26fdcad7ea2d75c0052","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1993-12-22T16:45:41Z","title_canon_sha256":"7a487376e4d7e75908145121327273c76c2b88578e3a1d10d855570c0701c7ac"},"schema_version":"1.0","source":{"id":"math/9312207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9312207","created_at":"2026-07-04T15:08:56Z"},{"alias_kind":"arxiv_version","alias_value":"math/9312207v1","created_at":"2026-07-04T15:08:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9312207","created_at":"2026-07-04T15:08:56Z"},{"alias_kind":"pith_short_12","alias_value":"DYILINCBRD6P","created_at":"2026-07-04T15:08:56Z"},{"alias_kind":"pith_short_16","alias_value":"DYILINCBRD6PUIGE","created_at":"2026-07-04T15:08:56Z"},{"alias_kind":"pith_short_8","alias_value":"DYILINCB","created_at":"2026-07-04T15:08:56Z"}],"graph_snapshots":[{"event_id":"sha256:f16500acb646cad61f89643771c1584ff69c3f7dc263669dff08379b8d2337a8","target":"graph","created_at":"2026-07-04T15:08:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9312207/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a positive solution for the hyperplane conjecture of quotient spaces F of $L_p$, where $1<p\\kll\\infty$. \\[ vol(B_F)^{\\frac{n-1}{n}} \\kl c_0 \\pl p' \\pl \\sup_{H \\p hyperplane} vol(B_F\\cap H) \\pl.\\] This result is extended to Banach lattices which does not contain $\\ell_1^n$'s uniformly. Our main tools are tensor products and minimal volume ratio with respect to $L_p$-sections.","authors_text":"Marius Junge","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1993-12-22T16:45:41Z","title":"Hyperplane conjecture for quotient spaces of $L_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9312207","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":"sha256:3728d8b838982e5872f057e3dbb5a8cad4029eac4073ca72e2863c1d658b8a2a","target":"record","created_at":"2026-07-04T15:08:56Z","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":"5a4204e77b64d5bf986c2a0365792738d7ebe0ba24a1f26fdcad7ea2d75c0052","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1993-12-22T16:45:41Z","title_canon_sha256":"7a487376e4d7e75908145121327273c76c2b88578e3a1d10d855570c0701c7ac"},"schema_version":"1.0","source":{"id":"math/9312207","kind":"arxiv","version":1}},"canonical_sha256":"1e10b4344188fcfa20c431aab98334a1bfbe121388529fc9da5b3808261aee33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e10b4344188fcfa20c431aab98334a1bfbe121388529fc9da5b3808261aee33","first_computed_at":"2026-07-04T15:08:56.683665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:56.683665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3sW1MaC9KX+O05E3rBVikv1pHCmIj8nKpy5trr5gqwej3Xc4Pa7kPc5g0HTl2u2mTwHrVWz8IMgY8uN9cDXKBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:56.684120Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9312207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3728d8b838982e5872f057e3dbb5a8cad4029eac4073ca72e2863c1d658b8a2a","sha256:f16500acb646cad61f89643771c1584ff69c3f7dc263669dff08379b8d2337a8"],"state_sha256":"e3497988b26bc89250dcd27b7f04bbfab899dd02a4e55d4ec3effcaa103539f3"}