{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CDRJFO7FIMKZQPFSJHZVIEAQJX","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":"872247724f64e226e3ac829768b1991a03a41725ad4800957005c2b1f4d3f5ed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-11T12:07:54Z","title_canon_sha256":"784e9d2650dccfa96f8f6ccccd5610118cb8993bcc6c0e52f705eabb060fbd59"},"schema_version":"1.0","source":{"id":"2606.13251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13251","created_at":"2026-06-12T01:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13251v1","created_at":"2026-06-12T01:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13251","created_at":"2026-06-12T01:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"CDRJFO7FIMKZ","created_at":"2026-06-12T01:09:48Z"},{"alias_kind":"pith_short_16","alias_value":"CDRJFO7FIMKZQPFS","created_at":"2026-06-12T01:09:48Z"},{"alias_kind":"pith_short_8","alias_value":"CDRJFO7F","created_at":"2026-06-12T01:09:48Z"}],"graph_snapshots":[{"event_id":"sha256:c740cf62385f23af65729c51eee751c7f153301f5313bca89ab2978bf662aa70","target":"graph","created_at":"2026-06-12T01:09:48Z","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/2606.13251/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the extension of the Kubo--Martin--Schwinger (KMS) thermal equilibrium condition to non-Hermitian Hamiltonians with real spectra and biorthogonal eigensystems, providing a systematic analysis through three complementary routes. Our central result is a thermodynamic characterisation of quasi-Hermiticity: for $H \\in M_d(\\mathbb{C})$ diagonalisable with real spectrum, the biorthogonal Gibbs functional $\\omega_{\\rm{bi}}(A) = Z_{\\rm{bi}}^{-1} \\sum_n e^{-\\beta E_n}\\langle\\phi_n|A|\\psi_n\\rangle$ satisfies $\\omega_{\\rm{bi}}(A^\\dag A) \\geq 0$ for all $A$ if and only if $H$ is quasi-Hermi","authors_text":"Chen Lan, Hao Yang, Luyao Ma","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-11T12:07:54Z","title":"Kubo-Martin-Schwinger conditions for non-Hermitian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13251","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":"sha256:9417305135a6fda86d86852158332e2e0d40bf570a1d3ea1d674e71f8130ed1f","target":"record","created_at":"2026-06-12T01:09:48Z","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":"872247724f64e226e3ac829768b1991a03a41725ad4800957005c2b1f4d3f5ed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-11T12:07:54Z","title_canon_sha256":"784e9d2650dccfa96f8f6ccccd5610118cb8993bcc6c0e52f705eabb060fbd59"},"schema_version":"1.0","source":{"id":"2606.13251","kind":"arxiv","version":1}},"canonical_sha256":"10e292bbe54315983cb249f35410104dec862f7d8cc979ae498e5b9057d91f31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10e292bbe54315983cb249f35410104dec862f7d8cc979ae498e5b9057d91f31","first_computed_at":"2026-06-12T01:09:48.950745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:48.950745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbhysVSvgo0e4moNLWR6stOUNBZG+Vh4SXwWeip7DxYwCyYZTLudxhJI+1ehCwdewP1Gl7FUMgd/n4vckWHTDQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:48.951233Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9417305135a6fda86d86852158332e2e0d40bf570a1d3ea1d674e71f8130ed1f","sha256:c740cf62385f23af65729c51eee751c7f153301f5313bca89ab2978bf662aa70"],"state_sha256":"0855375a065fa36f602f01c48e20718b943042ec73f1c36f28100ef6631391e4"}