{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NC6W7YDHJ2IHYT6OONQFXLQ4G3","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":"1aacf6ad52e6fec947f71e2e067cbb9d47d9eb08edd3e5b2f469768f8c417430","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-17T13:12:28Z","title_canon_sha256":"9fdb66007a5770cc00bf1cffe3fa1d7fd5919fb5612275df034b8b610ed13fc6"},"schema_version":"1.0","source":{"id":"1502.04882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04882","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04882v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04882","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"NC6W7YDHJ2IH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NC6W7YDHJ2IHYT6O","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NC6W7YDH","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d91fff3a9da915d3c52ff5d9932f8fbc180ee8b60f880c3eb28c230b4d4cb366","target":"graph","created_at":"2026-05-18T02:26:53Z","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":"An important result on submajorization, which goes back to Hardy, Littlewood and P\\'olya, states that $b\\preceq a$ if and only if there is a doubly stochastic matrix $A$ such that $b=Aa$. We prove that under monotonicity assumptions on vectors $a$ and $b$ respective matrix $A$ may be chosen monotone. This result is then applied to show that $(\\widetilde{L^p},L^{\\infty})$ is a Calder\\'on couple for $1\\leq p<\\infty $, where $\\widetilde{L^{p}}$ is the K\\\"othe dual of the Ces\\`aro space $Ces_{p'}$ (or equivalently the down space $L^{p'}_{\\downarrow}$). In particular, $(\\widetilde{L^1},L^{\\infty})$","authors_text":"Karol Lesnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-17T13:12:28Z","title":"Monotone substochastic operators and a new Calderon couple"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04882","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":"sha256:0b32af9de3c832dbfcb2d24bdec6140a8849e9a1b4fe0ecc20d64d439ef95d73","target":"record","created_at":"2026-05-18T02:26:53Z","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":"1aacf6ad52e6fec947f71e2e067cbb9d47d9eb08edd3e5b2f469768f8c417430","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-17T13:12:28Z","title_canon_sha256":"9fdb66007a5770cc00bf1cffe3fa1d7fd5919fb5612275df034b8b610ed13fc6"},"schema_version":"1.0","source":{"id":"1502.04882","kind":"arxiv","version":1}},"canonical_sha256":"68bd6fe0674e907c4fce73605bae1c36c2180f9dd377f6c23a84d1eb30ee69e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68bd6fe0674e907c4fce73605bae1c36c2180f9dd377f6c23a84d1eb30ee69e6","first_computed_at":"2026-05-18T02:26:53.636857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:53.636857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LPmtEO8DWd8cd+4uEFj48zHjf4zWwIvGXlAylZznkQCvex3aWXoT2iIHzbF7cJpXXscXRu/Gwa5GDi3nQ/83Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:53.637416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b32af9de3c832dbfcb2d24bdec6140a8849e9a1b4fe0ecc20d64d439ef95d73","sha256:d91fff3a9da915d3c52ff5d9932f8fbc180ee8b60f880c3eb28c230b4d4cb366"],"state_sha256":"163db01c20c5972a8d110f40e95da08c39f34d06dc324c1d9ac6318d916fe793"}