{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PAMHU7AH4J3VZRMZJVSXWQ7SZ3","short_pith_number":"pith:PAMHU7AH","canonical_record":{"source":{"id":"1310.7352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-28T09:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"232f0d0290605c976e8fb8efa56e09f15fca69458185c5da0b894c6cb58689d8","abstract_canon_sha256":"9c5834e1e3230bca75f0b5e5fbf5541e19f631862f878b822f45c09a0c38eec9"},"schema_version":"1.0"},"canonical_sha256":"78187a7c07e2775cc5994d657b43f2cec8ac5057db5e3d2d05f4bf4920a419d8","source":{"kind":"arxiv","id":"1310.7352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7352","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7352v1","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7352","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"PAMHU7AH4J3V","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PAMHU7AH4J3VZRMZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PAMHU7AH","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PAMHU7AH4J3VZRMZJVSXWQ7SZ3","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-28T09:33:29Z","cross_cats_sorted":[],"title_canon_sha256":"232f0d0290605c976e8fb8efa56e09f15fca69458185c5da0b894c6cb58689d8","abstract_canon_sha256":"9c5834e1e3230bca75f0b5e5fbf5541e19f631862f878b822f45c09a0c38eec9"},"schema_version":"1.0"},"canonical_sha256":"78187a7c07e2775cc5994d657b43f2cec8ac5057db5e3d2d05f4bf4920a419d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:45.604176Z","signature_b64":"fCftETltdzldQu2GQPJ2IziSp0dI8ojTIKmzqLbbAG6vgwaaq56fHRJ9jT2FsiNCqOZ1NGVTBUHmPdI8mES9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78187a7c07e2775cc5994d657b43f2cec8ac5057db5e3d2d05f4bf4920a419d8","last_reissued_at":"2026-05-18T03:08:45.603649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:45.603649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7352","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":"2026-05-18T03:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgPG8WsEDVpalcY9/12puNoT4BGjvVbbLA7BB6oUbm9Xu5K3qp86HHQWk+lxCfw6BLJp5+Ny3DvZkKTCSEGqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:37:19.136309Z"},"content_sha256":"92bfafa87def1e340b3ce8ec0154433b9f0219c0b9dc617b59ba248a24c35f0c","schema_version":"1.0","event_id":"sha256:92bfafa87def1e340b3ce8ec0154433b9f0219c0b9dc617b59ba248a24c35f0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PAMHU7AH4J3VZRMZJVSXWQ7SZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ideals of operators on $(\\oplus \\ell^\\infty(n))_{\\ell^1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denny H. Leung","submitted_at":"2013-10-28T09:33:29Z","abstract_excerpt":"The unique maximal ideal in the Banach algebra $L(E)$, $E = (\\oplus \\ell^\\infty(n))_{\\ell^1}$, is identified. The proof relies on techniques developed by Laustsen, Loy and Read and a dichotomy result for operators mapping into $L^1$ due to Laustsen, Odell, Schlumprecht and Zs\\'{a}k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7352","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":"2026-05-18T03:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZavtimppMxSADgyrjUBVtizpmrEBdh1gO9r9APVSWmCGVswn7WqVeBvoTIeuS+GdTfOFJXG38hf1u4KvodDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:37:19.137056Z"},"content_sha256":"9af3245b795cec40507e6272d97fd376c4250602743a7913936565412d2eb3dd","schema_version":"1.0","event_id":"sha256:9af3245b795cec40507e6272d97fd376c4250602743a7913936565412d2eb3dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3/bundle.json","state_url":"https://pith.science/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3/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":"2026-05-30T22:37:19Z","links":{"resolver":"https://pith.science/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3","bundle":"https://pith.science/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3/bundle.json","state":"https://pith.science/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PAMHU7AH4J3VZRMZJVSXWQ7SZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PAMHU7AH4J3VZRMZJVSXWQ7SZ3","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":"9c5834e1e3230bca75f0b5e5fbf5541e19f631862f878b822f45c09a0c38eec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-28T09:33:29Z","title_canon_sha256":"232f0d0290605c976e8fb8efa56e09f15fca69458185c5da0b894c6cb58689d8"},"schema_version":"1.0","source":{"id":"1310.7352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7352","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7352v1","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7352","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"PAMHU7AH4J3V","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PAMHU7AH4J3VZRMZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PAMHU7AH","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:9af3245b795cec40507e6272d97fd376c4250602743a7913936565412d2eb3dd","target":"graph","created_at":"2026-05-18T03:08:45Z","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":"The unique maximal ideal in the Banach algebra $L(E)$, $E = (\\oplus \\ell^\\infty(n))_{\\ell^1}$, is identified. The proof relies on techniques developed by Laustsen, Loy and Read and a dichotomy result for operators mapping into $L^1$ due to Laustsen, Odell, Schlumprecht and Zs\\'{a}k.","authors_text":"Denny H. Leung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-28T09:33:29Z","title":"Ideals of operators on $(\\oplus \\ell^\\infty(n))_{\\ell^1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7352","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":"sha256:92bfafa87def1e340b3ce8ec0154433b9f0219c0b9dc617b59ba248a24c35f0c","target":"record","created_at":"2026-05-18T03:08:45Z","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":"9c5834e1e3230bca75f0b5e5fbf5541e19f631862f878b822f45c09a0c38eec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-28T09:33:29Z","title_canon_sha256":"232f0d0290605c976e8fb8efa56e09f15fca69458185c5da0b894c6cb58689d8"},"schema_version":"1.0","source":{"id":"1310.7352","kind":"arxiv","version":1}},"canonical_sha256":"78187a7c07e2775cc5994d657b43f2cec8ac5057db5e3d2d05f4bf4920a419d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78187a7c07e2775cc5994d657b43f2cec8ac5057db5e3d2d05f4bf4920a419d8","first_computed_at":"2026-05-18T03:08:45.603649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:45.603649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCftETltdzldQu2GQPJ2IziSp0dI8ojTIKmzqLbbAG6vgwaaq56fHRJ9jT2FsiNCqOZ1NGVTBUHmPdI8mES9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:45.604176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92bfafa87def1e340b3ce8ec0154433b9f0219c0b9dc617b59ba248a24c35f0c","sha256:9af3245b795cec40507e6272d97fd376c4250602743a7913936565412d2eb3dd"],"state_sha256":"21c56192e5efe3da1d4f529348d83aa7b30e24550800420db8960f9fba0ba79b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rk8Xx69DwUGLQLPdeFXnubN/Lp42tXDuCQq1x6CqCN8jAdERdrHVkjxZpUEwcsePEHgaogZE6vpW4Ylb/ek+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:37:19.140365Z","bundle_sha256":"7e8b9871bd37dc86e2679249d0d262bb5c0dc1deefb41f2689db3f7d89f59b41"}}