{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N7ILQP5EQWIX46BYQMRQDGPFD2","short_pith_number":"pith:N7ILQP5E","canonical_record":{"source":{"id":"1512.01906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-07T04:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"50df13f6a5b06eab7e29f4f28fd1280a28d8c908d893bd1c841e7dd54f2fd726","abstract_canon_sha256":"3b092aef1731226d9ecc254ab6d9750c38c7aa3593a13842bf5c39439248d1cc"},"schema_version":"1.0"},"canonical_sha256":"6fd0b83fa485917e783883230199e51e8eab8a3ccc9ef804dc6baa44ba184470","source":{"kind":"arxiv","id":"1512.01906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01906","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01906v1","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01906","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"N7ILQP5EQWIX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7ILQP5EQWIX46BY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7ILQP5E","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N7ILQP5EQWIX46BYQMRQDGPFD2","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-07T04:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"50df13f6a5b06eab7e29f4f28fd1280a28d8c908d893bd1c841e7dd54f2fd726","abstract_canon_sha256":"3b092aef1731226d9ecc254ab6d9750c38c7aa3593a13842bf5c39439248d1cc"},"schema_version":"1.0"},"canonical_sha256":"6fd0b83fa485917e783883230199e51e8eab8a3ccc9ef804dc6baa44ba184470","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:14.144376Z","signature_b64":"/rr/6dxDU90WYsqejKJYcecBz4kWku1QS455t3wzQMVORxJnPIthh/ryw3JB64DbLZ9FR1g09W9HtqFcrYWSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd0b83fa485917e783883230199e51e8eab8a3ccc9ef804dc6baa44ba184470","last_reissued_at":"2026-05-18T01:04:14.143792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:14.143792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01906","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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1EFPQys6hM3i+FFz/22BrE4V95TnR+UmK/K+ouX/Bd3Bb0PE6TIu/eBb1dkmdXWjcjW1ZpmtGFw5zAHRO+pVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:21:02.636757Z"},"content_sha256":"e4ea21565418522cbb934de0ff29bbfadc7e5d7fb79264a2b2d4ca34110ebd8d","schema_version":"1.0","event_id":"sha256:e4ea21565418522cbb934de0ff29bbfadc7e5d7fb79264a2b2d4ca34110ebd8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N7ILQP5EQWIX46BYQMRQDGPFD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Markovian correlation functions for open quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Christian Karlewski, Jinshuang Jin, Michael Marthaler","submitted_at":"2015-12-07T04:17:13Z","abstract_excerpt":"Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the conventional time-nonlocal master equation into dispersed time-local equations-of-motion. The validity of our approximations is discussed and we find that the non-Markovian terms have to be included for short times. While calculations of the density matrix at short times suffer from the initial value problem, a correlation function has a well defined initial state."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01906","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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0K+mxY/sbWW6q274z3xrL5zPpbL0dOXUSQ7RJiK1OymHvcHkNgPIrge1ZmNYZL2HeXh45Kv32zM98r2gg8XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:21:02.637483Z"},"content_sha256":"299ce43cb8508da042192af54c58fa73cbfe842c54e2decf6844dd34a63b1999","schema_version":"1.0","event_id":"sha256:299ce43cb8508da042192af54c58fa73cbfe842c54e2decf6844dd34a63b1999"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7ILQP5EQWIX46BYQMRQDGPFD2/bundle.json","state_url":"https://pith.science/pith/N7ILQP5EQWIX46BYQMRQDGPFD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7ILQP5EQWIX46BYQMRQDGPFD2/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":"2026-05-31T09:21:02Z","links":{"resolver":"https://pith.science/pith/N7ILQP5EQWIX46BYQMRQDGPFD2","bundle":"https://pith.science/pith/N7ILQP5EQWIX46BYQMRQDGPFD2/bundle.json","state":"https://pith.science/pith/N7ILQP5EQWIX46BYQMRQDGPFD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7ILQP5EQWIX46BYQMRQDGPFD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N7ILQP5EQWIX46BYQMRQDGPFD2","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":"3b092aef1731226d9ecc254ab6d9750c38c7aa3593a13842bf5c39439248d1cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-07T04:17:13Z","title_canon_sha256":"50df13f6a5b06eab7e29f4f28fd1280a28d8c908d893bd1c841e7dd54f2fd726"},"schema_version":"1.0","source":{"id":"1512.01906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01906","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01906v1","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01906","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"N7ILQP5EQWIX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7ILQP5EQWIX46BY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7ILQP5E","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:299ce43cb8508da042192af54c58fa73cbfe842c54e2decf6844dd34a63b1999","target":"graph","created_at":"2026-05-18T01:04:14Z","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":"Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the conventional time-nonlocal master equation into dispersed time-local equations-of-motion. The validity of our approximations is discussed and we find that the non-Markovian terms have to be included for short times. While calculations of the density matrix at short times suffer from the initial value problem, a correlation function has a well defined initial state.","authors_text":"Christian Karlewski, Jinshuang Jin, Michael Marthaler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-07T04:17:13Z","title":"Non-Markovian correlation functions for open quantum systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01906","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:e4ea21565418522cbb934de0ff29bbfadc7e5d7fb79264a2b2d4ca34110ebd8d","target":"record","created_at":"2026-05-18T01:04:14Z","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":"3b092aef1731226d9ecc254ab6d9750c38c7aa3593a13842bf5c39439248d1cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-07T04:17:13Z","title_canon_sha256":"50df13f6a5b06eab7e29f4f28fd1280a28d8c908d893bd1c841e7dd54f2fd726"},"schema_version":"1.0","source":{"id":"1512.01906","kind":"arxiv","version":1}},"canonical_sha256":"6fd0b83fa485917e783883230199e51e8eab8a3ccc9ef804dc6baa44ba184470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd0b83fa485917e783883230199e51e8eab8a3ccc9ef804dc6baa44ba184470","first_computed_at":"2026-05-18T01:04:14.143792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:14.143792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/rr/6dxDU90WYsqejKJYcecBz4kWku1QS455t3wzQMVORxJnPIthh/ryw3JB64DbLZ9FR1g09W9HtqFcrYWSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:14.144376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4ea21565418522cbb934de0ff29bbfadc7e5d7fb79264a2b2d4ca34110ebd8d","sha256:299ce43cb8508da042192af54c58fa73cbfe842c54e2decf6844dd34a63b1999"],"state_sha256":"00de4bedf3b0c78fab630414d25e87e355df8a72a3e7a081d6ffaf8263bc4edb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWG5DRhGK0cA6rw5TqMoT/iDe5DyEWLLO10+/dLfayPZtwjUzPV5kyyW6onqk/jVd4AV2afilj2F62VvqdSPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:21:02.641306Z","bundle_sha256":"0e0fb9aa9cc3685021d86f5f7cfc9763206ebbe8c954d24ddd38b81b5bbfcff1"}}