{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FCBNXD7ZHARHNR6TFEUUJBHG7O","short_pith_number":"pith:FCBNXD7Z","canonical_record":{"source":{"id":"1201.1272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-01-05T19:47:17Z","cross_cats_sorted":["math.CT","quant-ph"],"title_canon_sha256":"d264c79a68bcc85f6b15391d40b3c6aa398aec04f2565f625999fc62d248300f","abstract_canon_sha256":"ea84e21d2b52a5efe34aeea14edde4cb1297647283a7cbd03728811fa7e1c953"},"schema_version":"1.0"},"canonical_sha256":"2882db8ff9382276c7d329294484e6fba5b18f6ab5c627662e47fe32a4491e3a","source":{"kind":"arxiv","id":"1201.1272","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1272","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1272v2","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1272","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"FCBNXD7ZHARH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FCBNXD7ZHARHNR6T","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FCBNXD7Z","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FCBNXD7ZHARHNR6TFEUUJBHG7O","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-01-05T19:47:17Z","cross_cats_sorted":["math.CT","quant-ph"],"title_canon_sha256":"d264c79a68bcc85f6b15391d40b3c6aa398aec04f2565f625999fc62d248300f","abstract_canon_sha256":"ea84e21d2b52a5efe34aeea14edde4cb1297647283a7cbd03728811fa7e1c953"},"schema_version":"1.0"},"canonical_sha256":"2882db8ff9382276c7d329294484e6fba5b18f6ab5c627662e47fe32a4491e3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:50.334396Z","signature_b64":"GigkRtgETP52IYQpKyiBbG6tIzjxeGv6BqIjORgFQ67ejtQEnlCLN4ck61F3bkUvD0yvdjIAfMqCVhwZfGcBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2882db8ff9382276c7d329294484e6fba5b18f6ab5c627662e47fe32a4491e3a","last_reissued_at":"2026-05-18T03:50:50.333655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:50.333655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1272","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":"2026-05-18T03:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCPYutECF6qj1pvBU41TPMZ4I+P/1v7EpVfhnqlz5CHS74fqN7hazf2cYSvqLwVqaXBm8Dx+ZOpp5o13tT0xCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:05:03.386546Z"},"content_sha256":"c0b460fa397f1f95369fed9ea7ee75f48a77aafeef7e3e2c1562517b8f0840ea","schema_version":"1.0","event_id":"sha256:c0b460fa397f1f95369fed9ea7ee75f48a77aafeef7e3e2c1562517b8f0840ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FCBNXD7ZHARHNR6TFEUUJBHG7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relating Operator Spaces via Adjunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","quant-ph"],"primary_cat":"cs.LO","authors_text":"Bart Jacobs, Jorik Mandemaker","submitted_at":"2012-01-05T19:47:17Z","abstract_excerpt":"This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various Hilbert-Schmidt isomorphisms of the form tr(A-), are expressed in terms of dual adjunctions, and maps between them. Of particular interest is the connection with quantum structures, via a dual adjunction between convex sets and effect modules. The approach systematically uses categories of modules, via their description as Eilenberg-Moore algebras of a monad."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1272","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":"2026-05-18T03:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tl5R7R5OqwnDOedvmSa5n/XXCW8GJ2oUKIRLk+/wa2XUtKvzAD/jU3G/suvD3h3j7sWTyaepB9/ybd2MJlKVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:05:03.386899Z"},"content_sha256":"b6d129b2d19fa3b75768803b75bee46138fc4c74c0defd0cc8e158e3aa1ceda6","schema_version":"1.0","event_id":"sha256:b6d129b2d19fa3b75768803b75bee46138fc4c74c0defd0cc8e158e3aa1ceda6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O/bundle.json","state_url":"https://pith.science/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O/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":"2026-05-27T15:05:03Z","links":{"resolver":"https://pith.science/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O","bundle":"https://pith.science/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O/bundle.json","state":"https://pith.science/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCBNXD7ZHARHNR6TFEUUJBHG7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FCBNXD7ZHARHNR6TFEUUJBHG7O","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":"ea84e21d2b52a5efe34aeea14edde4cb1297647283a7cbd03728811fa7e1c953","cross_cats_sorted":["math.CT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-01-05T19:47:17Z","title_canon_sha256":"d264c79a68bcc85f6b15391d40b3c6aa398aec04f2565f625999fc62d248300f"},"schema_version":"1.0","source":{"id":"1201.1272","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1272","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1272v2","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1272","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"FCBNXD7ZHARH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FCBNXD7ZHARHNR6T","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FCBNXD7Z","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:b6d129b2d19fa3b75768803b75bee46138fc4c74c0defd0cc8e158e3aa1ceda6","target":"graph","created_at":"2026-05-18T03:50:50Z","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":"This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various Hilbert-Schmidt isomorphisms of the form tr(A-), are expressed in terms of dual adjunctions, and maps between them. Of particular interest is the connection with quantum structures, via a dual adjunction between convex sets and effect modules. The approach systematically uses categories of modules, via their description as Eilenberg-Moore algebras of a monad.","authors_text":"Bart Jacobs, Jorik Mandemaker","cross_cats":["math.CT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-01-05T19:47:17Z","title":"Relating Operator Spaces via Adjunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1272","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:c0b460fa397f1f95369fed9ea7ee75f48a77aafeef7e3e2c1562517b8f0840ea","target":"record","created_at":"2026-05-18T03:50:50Z","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":"ea84e21d2b52a5efe34aeea14edde4cb1297647283a7cbd03728811fa7e1c953","cross_cats_sorted":["math.CT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-01-05T19:47:17Z","title_canon_sha256":"d264c79a68bcc85f6b15391d40b3c6aa398aec04f2565f625999fc62d248300f"},"schema_version":"1.0","source":{"id":"1201.1272","kind":"arxiv","version":2}},"canonical_sha256":"2882db8ff9382276c7d329294484e6fba5b18f6ab5c627662e47fe32a4491e3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2882db8ff9382276c7d329294484e6fba5b18f6ab5c627662e47fe32a4491e3a","first_computed_at":"2026-05-18T03:50:50.333655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:50.333655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GigkRtgETP52IYQpKyiBbG6tIzjxeGv6BqIjORgFQ67ejtQEnlCLN4ck61F3bkUvD0yvdjIAfMqCVhwZfGcBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:50.334396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1272","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0b460fa397f1f95369fed9ea7ee75f48a77aafeef7e3e2c1562517b8f0840ea","sha256:b6d129b2d19fa3b75768803b75bee46138fc4c74c0defd0cc8e158e3aa1ceda6"],"state_sha256":"eb35680ed13153e94c952cc700780bcacd3a3b41b3e20723f4b025cea37390bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SWLEA6twqytCSLMrlUU0FELzr24Qqu2yM+eeqkJDXXGNxIX81d1laPpvdzbouj4XpNMmokmjKQVIOgu/GozBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:05:03.389827Z","bundle_sha256":"ea7226069dee69c143f0943403de59f0f25e89d032f7805ecedcec8322f09c2c"}}