{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SWKDWPF5WNHF7SJM2STGKBFSOX","short_pith_number":"pith:SWKDWPF5","schema_version":"1.0","canonical_sha256":"95943b3cbdb34e5fc92cd4a66504b275c5fd58e6032328abcfe12274513bd2cd","source":{"kind":"arxiv","id":"2608.04539","version":1},"attestation_state":"computed","paper":{"title":"Coupling Does Not Reduce the Auxiliary-Mode Count for $1/|\\omega|$ Spectra in Passive Lindblad Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Qing-Ao Xiang, Xin-Yuan Yang, Ya-Ju Song, Yan Liu","submitted_at":"2026-08-05T07:15:44Z","abstract_excerpt":"Representing continuous environments by finitely many Markovian auxiliary modes is fundamental in non-Markovian open quantum systems, yet a critical question remains: at a fixed mode budget, can coherent intermode coupling reduce the spectral approximation error? We prove that intermode coupling offers no advantage when passive, number-conserving Gaussian Lindblad auxiliary networks approximate a $1/|\\omega|$ spectrum over a finite two-sided frequency band. For any mode budget $N$, the general coupled class and its uncoupled diagonal subclass share the same optimal error, which is exactly the "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.04539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T07:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"05f5a4f4d60ee4bf0b9991399f5a03e477c50add63fccb27b68d780b6057054f","abstract_canon_sha256":"299ee36ede94926b069e8093a436abc448f7e1ad413eab123244c5b2b2835ea1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:35:48.116612Z","signature_b64":"b26jzzKOzyJGaAYexZur9PvtdhXx5vlXnHr56KXy0Bqw9mi0TrP/e/mudIpecg9NUkK05sg4FL8Qb7Z284CiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95943b3cbdb34e5fc92cd4a66504b275c5fd58e6032328abcfe12274513bd2cd","last_reissued_at":"2026-08-06T01:35:48.115194Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:35:48.115194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupling Does Not Reduce the Auxiliary-Mode Count for $1/|\\omega|$ Spectra in Passive Lindblad Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Qing-Ao Xiang, Xin-Yuan Yang, Ya-Ju Song, Yan Liu","submitted_at":"2026-08-05T07:15:44Z","abstract_excerpt":"Representing continuous environments by finitely many Markovian auxiliary modes is fundamental in non-Markovian open quantum systems, yet a critical question remains: at a fixed mode budget, can coherent intermode coupling reduce the spectral approximation error? We prove that intermode coupling offers no advantage when passive, number-conserving Gaussian Lindblad auxiliary networks approximate a $1/|\\omega|$ spectrum over a finite two-sided frequency band. For any mode budget $N$, the general coupled class and its uncoupled diagonal subclass share the same optimal error, which is exactly the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04539","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/2608.04539/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.04539","created_at":"2026-08-06T01:35:48.116986+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04539v1","created_at":"2026-08-06T01:35:48.116986+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04539","created_at":"2026-08-06T01:35:48.116986+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWKDWPF5WNHF","created_at":"2026-08-06T01:35:48.116986+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWKDWPF5WNHF7SJM","created_at":"2026-08-06T01:35:48.116986+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWKDWPF5","created_at":"2026-08-06T01:35:48.116986+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX","json":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX.json","graph_json":"https://pith.science/api/pith-number/SWKDWPF5WNHF7SJM2STGKBFSOX/graph.json","events_json":"https://pith.science/api/pith-number/SWKDWPF5WNHF7SJM2STGKBFSOX/events.json","paper":"https://pith.science/paper/SWKDWPF5"},"agent_actions":{"view_html":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX","download_json":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX.json","view_paper":"https://pith.science/paper/SWKDWPF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04539&json=true","fetch_graph":"https://pith.science/api/pith-number/SWKDWPF5WNHF7SJM2STGKBFSOX/graph.json","fetch_events":"https://pith.science/api/pith-number/SWKDWPF5WNHF7SJM2STGKBFSOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/action/storage_attestation","attest_author":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/action/author_attestation","sign_citation":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/action/citation_signature","submit_replication":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/action/replication_record"}},"created_at":"2026-08-06T01:35:48.116986+00:00","updated_at":"2026-08-06T01:35:48.116986+00:00"}