{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SWKDWPF5WNHF7SJM2STGKBFSOX","short_pith_number":"pith:SWKDWPF5","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"},"canonical_sha256":"95943b3cbdb34e5fc92cd4a66504b275c5fd58e6032328abcfe12274513bd2cd","source":{"kind":"arxiv","id":"2608.04539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04539","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04539v1","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04539","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"SWKDWPF5WNHF","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"pith_short_16","alias_value":"SWKDWPF5WNHF7SJM","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"pith_short_8","alias_value":"SWKDWPF5","created_at":"2026-08-06T01:35:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SWKDWPF5WNHF7SJM2STGKBFSOX","target":"record","payload":{"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"},"canonical_sha256":"95943b3cbdb34e5fc92cd4a66504b275c5fd58e6032328abcfe12274513bd2cd","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"},"source_kind":"arxiv","source_id":"2608.04539","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":"2026-08-06T01:35:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lo98D9NiuCiGYvvvvB2+E3IkObGkxfx2km6o7SP4N+8/v8IipMD4Ua3oul6/unEBXDsKVi27y4Lir1SmXobrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:58:56.524040Z"},"content_sha256":"f32af9b5d6bdd5f70c105fccce1238bead7421fcf452bfc10502f38fcc6cf039","schema_version":"1.0","event_id":"sha256:f32af9b5d6bdd5f70c105fccce1238bead7421fcf452bfc10502f38fcc6cf039"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SWKDWPF5WNHF7SJM2STGKBFSOX","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-06T01:35:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+Oius+Zug3DZR20T63OAsU/W3RkVPxCf+fq+SN36FTcdbjAgjRW5oLHi8oY/oZjPzAbhK6FHM0YGLe/pwsEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:58:56.524565Z"},"content_sha256":"869660d64e1b44f0bb9822eacf6eaf5bbef4ececde78c2ad6a530418b35238ff","schema_version":"1.0","event_id":"sha256:869660d64e1b44f0bb9822eacf6eaf5bbef4ececde78c2ad6a530418b35238ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/bundle.json","state_url":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/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":"2026-08-13T09:58:56Z","links":{"resolver":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX","bundle":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/bundle.json","state":"https://pith.science/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWKDWPF5WNHF7SJM2STGKBFSOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SWKDWPF5WNHF7SJM2STGKBFSOX","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":"299ee36ede94926b069e8093a436abc448f7e1ad413eab123244c5b2b2835ea1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T07:15:44Z","title_canon_sha256":"05f5a4f4d60ee4bf0b9991399f5a03e477c50add63fccb27b68d780b6057054f"},"schema_version":"1.0","source":{"id":"2608.04539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04539","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04539v1","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04539","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"SWKDWPF5WNHF","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"pith_short_16","alias_value":"SWKDWPF5WNHF7SJM","created_at":"2026-08-06T01:35:48Z"},{"alias_kind":"pith_short_8","alias_value":"SWKDWPF5","created_at":"2026-08-06T01:35:48Z"}],"graph_snapshots":[{"event_id":"sha256:869660d64e1b44f0bb9822eacf6eaf5bbef4ececde78c2ad6a530418b35238ff","target":"graph","created_at":"2026-08-06T01:35:48Z","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/2608.04539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Qing-Ao Xiang, Xin-Yuan Yang, Ya-Ju Song, Yan Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T07:15:44Z","title":"Coupling Does Not Reduce the Auxiliary-Mode Count for $1/|\\omega|$ Spectra in Passive Lindblad Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04539","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:f32af9b5d6bdd5f70c105fccce1238bead7421fcf452bfc10502f38fcc6cf039","target":"record","created_at":"2026-08-06T01:35:48Z","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":"299ee36ede94926b069e8093a436abc448f7e1ad413eab123244c5b2b2835ea1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-05T07:15:44Z","title_canon_sha256":"05f5a4f4d60ee4bf0b9991399f5a03e477c50add63fccb27b68d780b6057054f"},"schema_version":"1.0","source":{"id":"2608.04539","kind":"arxiv","version":1}},"canonical_sha256":"95943b3cbdb34e5fc92cd4a66504b275c5fd58e6032328abcfe12274513bd2cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95943b3cbdb34e5fc92cd4a66504b275c5fd58e6032328abcfe12274513bd2cd","first_computed_at":"2026-08-06T01:35:48.115194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:35:48.115194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b26jzzKOzyJGaAYexZur9PvtdhXx5vlXnHr56KXy0Bqw9mi0TrP/e/mudIpecg9NUkK05sg4FL8Qb7Z284CiAQ==","signature_status":"signed_v1","signed_at":"2026-08-06T01:35:48.116612Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f32af9b5d6bdd5f70c105fccce1238bead7421fcf452bfc10502f38fcc6cf039","sha256:869660d64e1b44f0bb9822eacf6eaf5bbef4ececde78c2ad6a530418b35238ff"],"state_sha256":"9d50f8a40269bec4340bf069845a0c65bf08cb1e885a86346c66d1a44c8a5df5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oA6t3OpAEKeJpZvrwxd0DssyPqD/G5QaGsaNvJvZOFrjK+foV+7KLeBXhHP3ycSrtpBvBY9gmnYiQA1aEnMJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:58:56.530576Z","bundle_sha256":"427bffb4e4c036361d5a1071a279909eb96711a7d8e441c61ba7ba9b8942e664"}}