{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IEJ34U22FW2WE6VEGY2AL3GDTP","short_pith_number":"pith:IEJ34U22","canonical_record":{"source":{"id":"1903.06086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-14T15:45:13Z","cross_cats_sorted":["math.FA","math.MP","math.OA","quant-ph"],"title_canon_sha256":"6ba676cf70e69a883b54255353e50328bf620ec30e4a2a9886fb607b377917a8","abstract_canon_sha256":"301965be55425e1749a0f4bb3b5106dc839ce4da91f4e7debed65e7d5d56bba1"},"schema_version":"1.0"},"canonical_sha256":"4113be535a2db5627aa4363405ecc39bd1c8e230f8ce4bdb847d5f9dac3b620e","source":{"kind":"arxiv","id":"1903.06086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06086","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06086v1","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06086","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"pith_short_12","alias_value":"IEJ34U22FW2W","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"pith_short_16","alias_value":"IEJ34U22FW2WE6VE","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"pith_short_8","alias_value":"IEJ34U22","created_at":"2026-07-05T01:51:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IEJ34U22FW2WE6VEGY2AL3GDTP","target":"record","payload":{"canonical_record":{"source":{"id":"1903.06086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-14T15:45:13Z","cross_cats_sorted":["math.FA","math.MP","math.OA","quant-ph"],"title_canon_sha256":"6ba676cf70e69a883b54255353e50328bf620ec30e4a2a9886fb607b377917a8","abstract_canon_sha256":"301965be55425e1749a0f4bb3b5106dc839ce4da91f4e7debed65e7d5d56bba1"},"schema_version":"1.0"},"canonical_sha256":"4113be535a2db5627aa4363405ecc39bd1c8e230f8ce4bdb847d5f9dac3b620e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:51:17.222159Z","signature_b64":"k/Ke6G36CMbe48YUCZCjA92sZZoOZOOck3e9NTJ+a6K4HnJGgyBdwJMbGDSE5wENavyEvFJomiNl9pEGairUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4113be535a2db5627aa4363405ecc39bd1c8e230f8ce4bdb847d5f9dac3b620e","last_reissued_at":"2026-07-05T01:51:17.221704Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:51:17.221704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.06086","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":"2026-07-05T01:51:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/W1tjapYFO84Y4DLQhivrwQaO8+2L0db7Afx+31EBTf42aWJpolreW98QUg1TSLOcWYlQpQXsUelOnziSVg9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:30:37.412941Z"},"content_sha256":"e63b4d3102fa8e313d72413dcc4473817faf363c64cc2cd655b5a0b022cb4e31","schema_version":"1.0","event_id":"sha256:e63b4d3102fa8e313d72413dcc4473817faf363c64cc2cd655b5a0b022cb4e31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IEJ34U22FW2WE6VEGY2AL3GDTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On extension of quantum channels and operations to the space of relatively bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"M.E.Shirokov","submitted_at":"2019-03-14T15:45:13Z","abstract_excerpt":"We analyse possibility to extend a quantum operation (sub-unital normal CP linear map on the algebra $B(H)$ of bounded operators on a separable Hilbert space $H$) to the space of all operators on $H$ relatively bounded w.r.t. a given positive unbounded operator.\n  We show that a quantum operation $\\,\\Phi\\,$ can be uniquely extended to a bounded linear operator on the Banach space of all $\\sqrt{G}$-bounded operators on $H$ provided that the operation $\\Phi$ is $G$-limited: the predual operation $\\Phi_*$ maps the set of positive trace class operators $\\rho$ with finite $\\mathrm{Tr}\\rho G$ into i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06086","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.06086/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:51:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQfFMsllqt1R3S/YLklBPf8AUENAh2wGMhP/FfYU2dxbKrzRyn8dKcBSiqbTBbTfkN6jtNAgKgg/AGYv/TrKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:30:37.413921Z"},"content_sha256":"7995d03d9546c00421ed3460f4ae35e4ae840edb4856337624d23bdf4d89ed95","schema_version":"1.0","event_id":"sha256:7995d03d9546c00421ed3460f4ae35e4ae840edb4856337624d23bdf4d89ed95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEJ34U22FW2WE6VEGY2AL3GDTP/bundle.json","state_url":"https://pith.science/pith/IEJ34U22FW2WE6VEGY2AL3GDTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEJ34U22FW2WE6VEGY2AL3GDTP/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":"2026-08-16T13:30:37Z","links":{"resolver":"https://pith.science/pith/IEJ34U22FW2WE6VEGY2AL3GDTP","bundle":"https://pith.science/pith/IEJ34U22FW2WE6VEGY2AL3GDTP/bundle.json","state":"https://pith.science/pith/IEJ34U22FW2WE6VEGY2AL3GDTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEJ34U22FW2WE6VEGY2AL3GDTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IEJ34U22FW2WE6VEGY2AL3GDTP","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":"301965be55425e1749a0f4bb3b5106dc839ce4da91f4e7debed65e7d5d56bba1","cross_cats_sorted":["math.FA","math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-14T15:45:13Z","title_canon_sha256":"6ba676cf70e69a883b54255353e50328bf620ec30e4a2a9886fb607b377917a8"},"schema_version":"1.0","source":{"id":"1903.06086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06086","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06086v1","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06086","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"pith_short_12","alias_value":"IEJ34U22FW2W","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"pith_short_16","alias_value":"IEJ34U22FW2WE6VE","created_at":"2026-07-05T01:51:17Z"},{"alias_kind":"pith_short_8","alias_value":"IEJ34U22","created_at":"2026-07-05T01:51:17Z"}],"graph_snapshots":[{"event_id":"sha256:7995d03d9546c00421ed3460f4ae35e4ae840edb4856337624d23bdf4d89ed95","target":"graph","created_at":"2026-07-05T01:51:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.06086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyse possibility to extend a quantum operation (sub-unital normal CP linear map on the algebra $B(H)$ of bounded operators on a separable Hilbert space $H$) to the space of all operators on $H$ relatively bounded w.r.t. a given positive unbounded operator.\n  We show that a quantum operation $\\,\\Phi\\,$ can be uniquely extended to a bounded linear operator on the Banach space of all $\\sqrt{G}$-bounded operators on $H$ provided that the operation $\\Phi$ is $G$-limited: the predual operation $\\Phi_*$ maps the set of positive trace class operators $\\rho$ with finite $\\mathrm{Tr}\\rho G$ into i","authors_text":"M.E.Shirokov","cross_cats":["math.FA","math.MP","math.OA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-14T15:45:13Z","title":"On extension of quantum channels and operations to the space of relatively bounded operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06086","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:e63b4d3102fa8e313d72413dcc4473817faf363c64cc2cd655b5a0b022cb4e31","target":"record","created_at":"2026-07-05T01:51:17Z","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":"301965be55425e1749a0f4bb3b5106dc839ce4da91f4e7debed65e7d5d56bba1","cross_cats_sorted":["math.FA","math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-14T15:45:13Z","title_canon_sha256":"6ba676cf70e69a883b54255353e50328bf620ec30e4a2a9886fb607b377917a8"},"schema_version":"1.0","source":{"id":"1903.06086","kind":"arxiv","version":1}},"canonical_sha256":"4113be535a2db5627aa4363405ecc39bd1c8e230f8ce4bdb847d5f9dac3b620e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4113be535a2db5627aa4363405ecc39bd1c8e230f8ce4bdb847d5f9dac3b620e","first_computed_at":"2026-07-05T01:51:17.221704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:17.221704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/Ke6G36CMbe48YUCZCjA92sZZoOZOOck3e9NTJ+a6K4HnJGgyBdwJMbGDSE5wENavyEvFJomiNl9pEGairUAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:17.222159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e63b4d3102fa8e313d72413dcc4473817faf363c64cc2cd655b5a0b022cb4e31","sha256:7995d03d9546c00421ed3460f4ae35e4ae840edb4856337624d23bdf4d89ed95"],"state_sha256":"53e5472bfa7c334fc6f0941296a90e4cd42f1cb9ab7f510063a53507d178559f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDBjlwzMu8iHDImdGfoE02PaWE9WlLSyimX/8hYSwThBK/uOLwuohrIeo8jq9PIMXQaS+3cf4BCkv/sU/I/hCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:30:37.418561Z","bundle_sha256":"e3beb61457a39616606f57c01cc96d7a8d4c575723e406dd323df915fc94840b"}}