{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SQDIHKS3QD6H6VTSPKOQXOK6AD","short_pith_number":"pith:SQDIHKS3","canonical_record":{"source":{"id":"1112.4884","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:31:36Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"863e7b2cd9b738a0967256eb416e7cee92dea69b4884c40e1dfef70b81585545","abstract_canon_sha256":"06b4022cbbdfa7f1b97a4b74d2990cd64623f1de8fca70249f9489a47e6bbab1"},"schema_version":"1.0"},"canonical_sha256":"940683aa5b80fc7f56727a9d0bb95e00e9eb5ad54497f9d9d0a9aefc841c375c","source":{"kind":"arxiv","id":"1112.4884","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4884","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4884v3","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4884","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"SQDIHKS3QD6H","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SQDIHKS3QD6H6VTS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SQDIHKS3","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SQDIHKS3QD6H6VTSPKOQXOK6AD","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4884","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:31:36Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"863e7b2cd9b738a0967256eb416e7cee92dea69b4884c40e1dfef70b81585545","abstract_canon_sha256":"06b4022cbbdfa7f1b97a4b74d2990cd64623f1de8fca70249f9489a47e6bbab1"},"schema_version":"1.0"},"canonical_sha256":"940683aa5b80fc7f56727a9d0bb95e00e9eb5ad54497f9d9d0a9aefc841c375c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:23.540651Z","signature_b64":"Y3xQe1UiRoEebsVnH0yuFGPYWKTUTaVhsJiXurNG6tArA3BKNTdjH++INEK6eU8QfPUqAp9Bu2ZrA91m7xvCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"940683aa5b80fc7f56727a9d0bb95e00e9eb5ad54497f9d9d0a9aefc841c375c","last_reissued_at":"2026-05-18T03:51:23.539840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:23.539840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4884","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sv+WMvCfZA1LPYgqhb3T3jRXVXBr9d5tSlVa32WHZHgzO4y+103rki9Dy8NGfkgGasPjbYNFcs7BUOpQrwDPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:17:44.068551Z"},"content_sha256":"cdc71a25dd29b3e566e64b8606c863f67ae1e856d03fd6739dd5fb4a6cda03b7","schema_version":"1.0","event_id":"sha256:cdc71a25dd29b3e566e64b8606c863f67ae1e856d03fd6739dd5fb4a6cda03b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SQDIHKS3QD6H6VTSPKOQXOK6AD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal and maximal $p$-operator space structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Nico Spronk, Serap Oztop","submitted_at":"2011-12-20T23:31:36Z","abstract_excerpt":"We show that $L^\\infty(\\mu)$, in its capacity as multiplication operators on $L^p(\\mu)$, is minimal as a $p$-operator space for a decomposable measure $\\mu$. We conclude that $L^1(\\mu)$ has a certain maximal type $p$-operator space structure which facilitates computations with $L^1(\\mu)$ and the projective tensor product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4884","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":""},"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":"2026-05-18T03:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3G7ao8xC3DMQs/9A8fVt2aJsWIhDueTeqyba0NNWr6wJhO0Mh3mL9pbqMRHYGUr4DBTuFFGfSdgSL1oAEuPXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:17:44.069100Z"},"content_sha256":"f5cb88b2d715b9581c11ff90562dee65402d669c9f31f27c3dfa84808ba71b2e","schema_version":"1.0","event_id":"sha256:f5cb88b2d715b9581c11ff90562dee65402d669c9f31f27c3dfa84808ba71b2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD/bundle.json","state_url":"https://pith.science/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD/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":"2026-05-27T11:17:44Z","links":{"resolver":"https://pith.science/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD","bundle":"https://pith.science/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD/bundle.json","state":"https://pith.science/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQDIHKS3QD6H6VTSPKOQXOK6AD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SQDIHKS3QD6H6VTSPKOQXOK6AD","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":"06b4022cbbdfa7f1b97a4b74d2990cd64623f1de8fca70249f9489a47e6bbab1","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:31:36Z","title_canon_sha256":"863e7b2cd9b738a0967256eb416e7cee92dea69b4884c40e1dfef70b81585545"},"schema_version":"1.0","source":{"id":"1112.4884","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4884","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4884v3","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4884","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"SQDIHKS3QD6H","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SQDIHKS3QD6H6VTS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SQDIHKS3","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:f5cb88b2d715b9581c11ff90562dee65402d669c9f31f27c3dfa84808ba71b2e","target":"graph","created_at":"2026-05-18T03:51:23Z","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":"We show that $L^\\infty(\\mu)$, in its capacity as multiplication operators on $L^p(\\mu)$, is minimal as a $p$-operator space for a decomposable measure $\\mu$. We conclude that $L^1(\\mu)$ has a certain maximal type $p$-operator space structure which facilitates computations with $L^1(\\mu)$ and the projective tensor product.","authors_text":"Nico Spronk, Serap Oztop","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:31:36Z","title":"Minimal and maximal $p$-operator space structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4884","kind":"arxiv","version":3},"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:cdc71a25dd29b3e566e64b8606c863f67ae1e856d03fd6739dd5fb4a6cda03b7","target":"record","created_at":"2026-05-18T03:51:23Z","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":"06b4022cbbdfa7f1b97a4b74d2990cd64623f1de8fca70249f9489a47e6bbab1","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:31:36Z","title_canon_sha256":"863e7b2cd9b738a0967256eb416e7cee92dea69b4884c40e1dfef70b81585545"},"schema_version":"1.0","source":{"id":"1112.4884","kind":"arxiv","version":3}},"canonical_sha256":"940683aa5b80fc7f56727a9d0bb95e00e9eb5ad54497f9d9d0a9aefc841c375c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"940683aa5b80fc7f56727a9d0bb95e00e9eb5ad54497f9d9d0a9aefc841c375c","first_computed_at":"2026-05-18T03:51:23.539840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:23.539840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y3xQe1UiRoEebsVnH0yuFGPYWKTUTaVhsJiXurNG6tArA3BKNTdjH++INEK6eU8QfPUqAp9Bu2ZrA91m7xvCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:23.540651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4884","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdc71a25dd29b3e566e64b8606c863f67ae1e856d03fd6739dd5fb4a6cda03b7","sha256:f5cb88b2d715b9581c11ff90562dee65402d669c9f31f27c3dfa84808ba71b2e"],"state_sha256":"f953ed0f74de8c454cee81fcdc4277b17f416c1fdda5a2e9cea029ad6339d2b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZ8DgWvXXW0zimM9VIfTlkz8HCb7GDUUzHkxEXYEPo8hhE230VhRLryATeGKD1UWjyQt6JsAOrWUFNCuQNOlAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:17:44.072173Z","bundle_sha256":"a4718860e641b32a816b3812edb5c502ea4ec76edeb6ca8ffed1cc8f7be93ae0"}}