{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:SHVL4MY4YZ53PZR6JDH5VZ3KMF","short_pith_number":"pith:SHVL4MY4","canonical_record":{"source":{"id":"math/0601741","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2006-01-30T19:17:50Z","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"title_canon_sha256":"1a3d692d9173887bdfbb7ed682b19b97437976302fddfa36c6437118389148fe","abstract_canon_sha256":"43aa0055f8b2fd62b4265c0915fb836b8c9aca65e66378eeefb9b35f3ec1cddc"},"schema_version":"1.0"},"canonical_sha256":"91eabe331cc67bb7e63e48cfdae76a6164a7f7b178e2eb168ca6451bc8c22f6e","source":{"kind":"arxiv","id":"math/0601741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601741","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601741v1","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601741","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"SHVL4MY4YZ53","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"SHVL4MY4YZ53PZR6","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"SHVL4MY4","created_at":"2026-07-04T15:06:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:SHVL4MY4YZ53PZR6JDH5VZ3KMF","target":"record","payload":{"canonical_record":{"source":{"id":"math/0601741","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2006-01-30T19:17:50Z","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"title_canon_sha256":"1a3d692d9173887bdfbb7ed682b19b97437976302fddfa36c6437118389148fe","abstract_canon_sha256":"43aa0055f8b2fd62b4265c0915fb836b8c9aca65e66378eeefb9b35f3ec1cddc"},"schema_version":"1.0"},"canonical_sha256":"91eabe331cc67bb7e63e48cfdae76a6164a7f7b178e2eb168ca6451bc8c22f6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:06:27.108716Z","signature_b64":"jXmN0XqusihEV6FH1SdR49NguVnn55ReMoQUtxt+59lE61yXz4aiBSyiqnEyYiO+WWggyS8w/vnlQwJJZP3eBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91eabe331cc67bb7e63e48cfdae76a6164a7f7b178e2eb168ca6451bc8c22f6e","last_reissued_at":"2026-07-04T15:06:27.108258Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:06:27.108258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0601741","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":"2026-07-04T15:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLQ2hqbFW/kDvxA6HumpPloC6pSiKUdiWvBcdrv4LPLMljqbWNh8nOt9IInqYV1aGooF3i2Lg1XZ3YqVrd9DAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:12:33.649795Z"},"content_sha256":"b18678f8a00f5bcda606cd03ecb9669ac7af7ada151e2805f31e2face354350f","schema_version":"1.0","event_id":"sha256:b18678f8a00f5bcda606cd03ecb9669ac7af7ada151e2805f31e2face354350f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:SHVL4MY4YZ53PZR6JDH5VZ3KMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An introduction to quantum filtering","license":"","headline":"","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"primary_cat":"math.OC","authors_text":"Luc Bouten, Matthew James, Ramon van Handel","submitted_at":"2006-01-30T19:17:50Z","abstract_excerpt":"This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum It\\^o calculus and its use in the modelling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601741","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/math/0601741/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":"2026-07-04T15:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qH4qgo/h0IJBoWvQ75O/wwff/lmRYODtkNQBiJ5P4F70+XnJXs6/2NPHGQIBrhi+EAyi+cU/kVU/yGs4o9z0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:12:33.650172Z"},"content_sha256":"fced9d1eeebc7a567cde0202b429cf7c692511440f634155397b21cb147e4aa1","schema_version":"1.0","event_id":"sha256:fced9d1eeebc7a567cde0202b429cf7c692511440f634155397b21cb147e4aa1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF/bundle.json","state_url":"https://pith.science/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF/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":"2026-08-03T20:12:33Z","links":{"resolver":"https://pith.science/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF","bundle":"https://pith.science/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF/bundle.json","state":"https://pith.science/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHVL4MY4YZ53PZR6JDH5VZ3KMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:SHVL4MY4YZ53PZR6JDH5VZ3KMF","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":"43aa0055f8b2fd62b4265c0915fb836b8c9aca65e66378eeefb9b35f3ec1cddc","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"license":"","primary_cat":"math.OC","submitted_at":"2006-01-30T19:17:50Z","title_canon_sha256":"1a3d692d9173887bdfbb7ed682b19b97437976302fddfa36c6437118389148fe"},"schema_version":"1.0","source":{"id":"math/0601741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601741","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601741v1","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601741","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"SHVL4MY4YZ53","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"SHVL4MY4YZ53PZR6","created_at":"2026-07-04T15:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"SHVL4MY4","created_at":"2026-07-04T15:06:27Z"}],"graph_snapshots":[{"event_id":"sha256:fced9d1eeebc7a567cde0202b429cf7c692511440f634155397b21cb147e4aa1","target":"graph","created_at":"2026-07-04T15:06:27Z","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/math/0601741/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum It\\^o calculus and its use in the modelling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.","authors_text":"Luc Bouten, Matthew James, Ramon van Handel","cross_cats":["math-ph","math.MP","math.PR","quant-ph"],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2006-01-30T19:17:50Z","title":"An introduction to quantum filtering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601741","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:b18678f8a00f5bcda606cd03ecb9669ac7af7ada151e2805f31e2face354350f","target":"record","created_at":"2026-07-04T15:06:27Z","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":"43aa0055f8b2fd62b4265c0915fb836b8c9aca65e66378eeefb9b35f3ec1cddc","cross_cats_sorted":["math-ph","math.MP","math.PR","quant-ph"],"license":"","primary_cat":"math.OC","submitted_at":"2006-01-30T19:17:50Z","title_canon_sha256":"1a3d692d9173887bdfbb7ed682b19b97437976302fddfa36c6437118389148fe"},"schema_version":"1.0","source":{"id":"math/0601741","kind":"arxiv","version":1}},"canonical_sha256":"91eabe331cc67bb7e63e48cfdae76a6164a7f7b178e2eb168ca6451bc8c22f6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91eabe331cc67bb7e63e48cfdae76a6164a7f7b178e2eb168ca6451bc8c22f6e","first_computed_at":"2026-07-04T15:06:27.108258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:06:27.108258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXmN0XqusihEV6FH1SdR49NguVnn55ReMoQUtxt+59lE61yXz4aiBSyiqnEyYiO+WWggyS8w/vnlQwJJZP3eBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:06:27.108716Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b18678f8a00f5bcda606cd03ecb9669ac7af7ada151e2805f31e2face354350f","sha256:fced9d1eeebc7a567cde0202b429cf7c692511440f634155397b21cb147e4aa1"],"state_sha256":"6ceecb45e70bd04f927bcb67695aa562e401c2134ffe20846b99389390ceb58d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLQ/XzajDCjIlxUmuPfOx3gMOAAbgjPlLztEhprDwvDLqNz9VoasFstLA1jVL8lJwS0xHQKpFx5HwAgE3UWsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:12:33.653093Z","bundle_sha256":"044b2f580d4a7b4540a577b976f01339b63a48c2147823be21130c4114e5bfaa"}}