{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XZLJBV6ZBDTSF3XCJYY5APBHHH","short_pith_number":"pith:XZLJBV6Z","canonical_record":{"source":{"id":"1302.4849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-20T09:39:45Z","cross_cats_sorted":[],"title_canon_sha256":"78a55d20f016e294aa21f1e61b8c6b8b02692349ebf2fbec45b8c09fc0846010","abstract_canon_sha256":"3eddbdc70e54089d437a98df03c90124ce805fb32199f004ab9e8d22d7c73fe4"},"schema_version":"1.0"},"canonical_sha256":"be5690d7d908e722eee24e31d03c2739e4f56a8d9625126f9a71b94fe6a201b2","source":{"kind":"arxiv","id":"1302.4849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4849","created_at":"2026-05-18T02:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4849v2","created_at":"2026-05-18T02:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4849","created_at":"2026-05-18T02:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"XZLJBV6ZBDTS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XZLJBV6ZBDTSF3XC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XZLJBV6Z","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XZLJBV6ZBDTSF3XCJYY5APBHHH","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-20T09:39:45Z","cross_cats_sorted":[],"title_canon_sha256":"78a55d20f016e294aa21f1e61b8c6b8b02692349ebf2fbec45b8c09fc0846010","abstract_canon_sha256":"3eddbdc70e54089d437a98df03c90124ce805fb32199f004ab9e8d22d7c73fe4"},"schema_version":"1.0"},"canonical_sha256":"be5690d7d908e722eee24e31d03c2739e4f56a8d9625126f9a71b94fe6a201b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:47.230086Z","signature_b64":"zhvSICWcm2T2zGQHwWEkhmTxk4bc18a9qEkuA6BWrv00xe8Dt1mhR3AxS8bogJoDIPEauC8UWyW9Drjj/MfiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be5690d7d908e722eee24e31d03c2739e4f56a8d9625126f9a71b94fe6a201b2","last_reissued_at":"2026-05-18T02:49:47.229602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:47.229602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4849","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKnl4RrKNM461CL6XU8dzP4VUR2dHHVSi05dQFzssurmBTgQzW6QEnOFPAp61GkKNgs+M8KcqsrvfvyIvf3dDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:53:20.951195Z"},"content_sha256":"dab7c3aee95abf44a60967f421252261b79934afe6e1516ac5fc88ee7e773d24","schema_version":"1.0","event_id":"sha256:dab7c3aee95abf44a60967f421252261b79934afe6e1516ac5fc88ee7e773d24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XZLJBV6ZBDTSF3XCJYY5APBHHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norms of idempotent Schur multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rupert H. Levene","submitted_at":"2013-02-20T09:39:45Z","abstract_excerpt":"Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers \\eta_0 < \\eta_1 < \\eta_2 < ... < \\eta_6 so that for every bounded, normal D-bimodule map {\\Phi} on B(H) either ||\\Phi|| > \\eta_6, or ||\\Phi|| = \\eta_k for some k <= 6. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm \\eta_k for 0 <= k <= 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a rando"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4849","kind":"arxiv","version":2},"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":"2026-05-18T02:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8QWoyizOkr/4hQ+Asp+HNUBGTcIMEEfkTf+rnbwNYMXoTfWhYy+/Pg8xoGvhhKbt2CEzxuN8NkJjOIio6E1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:53:20.951935Z"},"content_sha256":"b57ba4dd9f92709eaafe1130a382f2f11e0ff8b12dc292336ed41f2be84d60a8","schema_version":"1.0","event_id":"sha256:b57ba4dd9f92709eaafe1130a382f2f11e0ff8b12dc292336ed41f2be84d60a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/bundle.json","state_url":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/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":"2026-06-11T15:53:20Z","links":{"resolver":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH","bundle":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/bundle.json","state":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XZLJBV6ZBDTSF3XCJYY5APBHHH","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":"3eddbdc70e54089d437a98df03c90124ce805fb32199f004ab9e8d22d7c73fe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-20T09:39:45Z","title_canon_sha256":"78a55d20f016e294aa21f1e61b8c6b8b02692349ebf2fbec45b8c09fc0846010"},"schema_version":"1.0","source":{"id":"1302.4849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4849","created_at":"2026-05-18T02:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4849v2","created_at":"2026-05-18T02:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4849","created_at":"2026-05-18T02:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"XZLJBV6ZBDTS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XZLJBV6ZBDTSF3XC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XZLJBV6Z","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:b57ba4dd9f92709eaafe1130a382f2f11e0ff8b12dc292336ed41f2be84d60a8","target":"graph","created_at":"2026-05-18T02:49:47Z","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":"Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers \\eta_0 < \\eta_1 < \\eta_2 < ... < \\eta_6 so that for every bounded, normal D-bimodule map {\\Phi} on B(H) either ||\\Phi|| > \\eta_6, or ||\\Phi|| = \\eta_k for some k <= 6. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm \\eta_k for 0 <= k <= 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a rando","authors_text":"Rupert H. Levene","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-20T09:39:45Z","title":"Norms of idempotent Schur multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4849","kind":"arxiv","version":2},"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:dab7c3aee95abf44a60967f421252261b79934afe6e1516ac5fc88ee7e773d24","target":"record","created_at":"2026-05-18T02:49:47Z","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":"3eddbdc70e54089d437a98df03c90124ce805fb32199f004ab9e8d22d7c73fe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-20T09:39:45Z","title_canon_sha256":"78a55d20f016e294aa21f1e61b8c6b8b02692349ebf2fbec45b8c09fc0846010"},"schema_version":"1.0","source":{"id":"1302.4849","kind":"arxiv","version":2}},"canonical_sha256":"be5690d7d908e722eee24e31d03c2739e4f56a8d9625126f9a71b94fe6a201b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be5690d7d908e722eee24e31d03c2739e4f56a8d9625126f9a71b94fe6a201b2","first_computed_at":"2026-05-18T02:49:47.229602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:47.229602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhvSICWcm2T2zGQHwWEkhmTxk4bc18a9qEkuA6BWrv00xe8Dt1mhR3AxS8bogJoDIPEauC8UWyW9Drjj/MfiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:47.230086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dab7c3aee95abf44a60967f421252261b79934afe6e1516ac5fc88ee7e773d24","sha256:b57ba4dd9f92709eaafe1130a382f2f11e0ff8b12dc292336ed41f2be84d60a8"],"state_sha256":"65425d8746eb1510e9ccefbc4596c6d6638d19e2cc38d16554554c1a89d1699f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5tt/JJbhVA14F7aQEjd29ogZNRUDgujQ7NITBD9jiJHM1itsXlFwppxpE0M6tFo6hjDOEer4VvGUO3fWS5hAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:53:20.956357Z","bundle_sha256":"befe32d17ab6165fd895cb034c0d243b861b4b3d1c98a782f997940d1214680c"}}