{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4T6R3OPJN26J3APUWNMOKM7XDZ","short_pith_number":"pith:4T6R3OPJ","schema_version":"1.0","canonical_sha256":"e4fd1db9e96ebc9d81f4b358e533f71e5c9f53af8e6ba676ef141ec822492400","source":{"kind":"arxiv","id":"2502.02186","version":3},"attestation_state":"computed","paper":{"title":"Operator $\\ell_p\\to\\ell_q$ norms of Gaussian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Marta Strzelecka, Rafa{\\l} Lata{\\l}a","submitted_at":"2025-02-04T10:01:59Z","abstract_excerpt":"We confirm the conjecture posed by Gu\\'edon, Hinrichs, Litvak, and Prochno in 2017 that $\\mathbb{E}\\|(a_{ij}g_{ij})_{i\\le m, j\\le n}\\colon \\ell_p^n \\to \\ell_q^m\\|$ is comparable, up to constants depending only on $p$ and $q$, to \\[ \\max_i \\|(a_{ij})_j\\|_{p^*} +\\max_j \\|(a_{ij})_i\\|_{q} +\\mathbb{E} \\max_{i,j} |a_{ij}g_{ij}| \\] provided that $1\\le p \\le 2\\le q \\le \\infty$. This was known before only in the case $p=1$ or $q=\\infty$, and in the spectral case $p=2=q$. We also reprove the conjecture in the case $p=2=q$ without using spectral theory (which was employed in the previously known proof)."},"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":"2502.02186","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-04T10:01:59Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b826b6d9400bd7ba329de7a5b610213b15cc6a0bb74b61016b666d7d42be4487","abstract_canon_sha256":"aa2b7b0c6fbf78f746aa072f5890e6992e17818ef446ba8db7e5ed1d5a03ccd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:09:15.051522Z","signature_b64":"OoWblsjItFlDFskUBBasfYgdGx8P41amVvhBbYnimPDUidk8IcrETZGVZ9P/DsbghdH0aGDNJ7XlKjmaAN7dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4fd1db9e96ebc9d81f4b358e533f71e5c9f53af8e6ba676ef141ec822492400","last_reissued_at":"2026-06-10T01:09:15.050518Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:09:15.050518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator $\\ell_p\\to\\ell_q$ norms of Gaussian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Marta Strzelecka, Rafa{\\l} Lata{\\l}a","submitted_at":"2025-02-04T10:01:59Z","abstract_excerpt":"We confirm the conjecture posed by Gu\\'edon, Hinrichs, Litvak, and Prochno in 2017 that $\\mathbb{E}\\|(a_{ij}g_{ij})_{i\\le m, j\\le n}\\colon \\ell_p^n \\to \\ell_q^m\\|$ is comparable, up to constants depending only on $p$ and $q$, to \\[ \\max_i \\|(a_{ij})_j\\|_{p^*} +\\max_j \\|(a_{ij})_i\\|_{q} +\\mathbb{E} \\max_{i,j} |a_{ij}g_{ij}| \\] provided that $1\\le p \\le 2\\le q \\le \\infty$. This was known before only in the case $p=1$ or $q=\\infty$, and in the spectral case $p=2=q$. We also reprove the conjecture in the case $p=2=q$ without using spectral theory (which was employed in the previously known proof)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02186","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02186/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.02186","created_at":"2026-06-10T01:09:15.050690+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.02186v3","created_at":"2026-06-10T01:09:15.050690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02186","created_at":"2026-06-10T01:09:15.050690+00:00"},{"alias_kind":"pith_short_12","alias_value":"4T6R3OPJN26J","created_at":"2026-06-10T01:09:15.050690+00:00"},{"alias_kind":"pith_short_16","alias_value":"4T6R3OPJN26J3APU","created_at":"2026-06-10T01:09:15.050690+00:00"},{"alias_kind":"pith_short_8","alias_value":"4T6R3OPJ","created_at":"2026-06-10T01:09:15.050690+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/4T6R3OPJN26J3APUWNMOKM7XDZ","json":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ.json","graph_json":"https://pith.science/api/pith-number/4T6R3OPJN26J3APUWNMOKM7XDZ/graph.json","events_json":"https://pith.science/api/pith-number/4T6R3OPJN26J3APUWNMOKM7XDZ/events.json","paper":"https://pith.science/paper/4T6R3OPJ"},"agent_actions":{"view_html":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ","download_json":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ.json","view_paper":"https://pith.science/paper/4T6R3OPJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.02186&json=true","fetch_graph":"https://pith.science/api/pith-number/4T6R3OPJN26J3APUWNMOKM7XDZ/graph.json","fetch_events":"https://pith.science/api/pith-number/4T6R3OPJN26J3APUWNMOKM7XDZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ/action/storage_attestation","attest_author":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ/action/author_attestation","sign_citation":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ/action/citation_signature","submit_replication":"https://pith.science/pith/4T6R3OPJN26J3APUWNMOKM7XDZ/action/replication_record"}},"created_at":"2026-06-10T01:09:15.050690+00:00","updated_at":"2026-06-10T01:09:15.050690+00:00"}