{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:YGRMDXDLQMWX5FLFVG25FOP2NK","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":"f198057a316ff568dec2cf66e740533b7b1314bb947b3f935c595c9ebfa7460d","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP","nlin.CD","physics.flu-dyn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-10-04T09:14:21Z","title_canon_sha256":"a26db6ab3392e97074d0dee2c746ccd3563b8fc93f54da8cb1e2001ab1481e1c"},"schema_version":"1.0","source":{"id":"0710.0958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0958","created_at":"2026-05-18T04:11:29Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0958v1","created_at":"2026-05-18T04:11:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0958","created_at":"2026-05-18T04:11:29Z"},{"alias_kind":"pith_short_12","alias_value":"YGRMDXDLQMWX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YGRMDXDLQMWX5FLF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YGRMDXDL","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:b29a6ae9e7d1f073ecfc92d74cb7a6c159a6ed8a58ff3e78c624cb9994e16b4a","target":"graph","created_at":"2026-05-18T04:11:29Z","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":"We consider the general response theory proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions allows for writing a set of Kramers-Kronig relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of observable susceptibilities obey Kramers-Kronig relations. Specific results are provided for arbitrary order harmonic response, which allows for a very comprehensive Kramers-Kronig analysis and the es","authors_text":"Valerio Lucarini","cross_cats":["cond-mat.str-el","math-ph","math.MP","nlin.CD","physics.flu-dyn"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-10-04T09:14:21Z","title":"Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0958","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":"sha256:8d018526504c88be16ba3fe76907fd138511c5451d4eaaa929bafe29f9ee54ac","target":"record","created_at":"2026-05-18T04:11:29Z","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":"f198057a316ff568dec2cf66e740533b7b1314bb947b3f935c595c9ebfa7460d","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP","nlin.CD","physics.flu-dyn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-10-04T09:14:21Z","title_canon_sha256":"a26db6ab3392e97074d0dee2c746ccd3563b8fc93f54da8cb1e2001ab1481e1c"},"schema_version":"1.0","source":{"id":"0710.0958","kind":"arxiv","version":1}},"canonical_sha256":"c1a2c1dc6b832d7e9565a9b5d2b9fa6a96d0faa134b36ccb19af15d2bdf383e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1a2c1dc6b832d7e9565a9b5d2b9fa6a96d0faa134b36ccb19af15d2bdf383e6","first_computed_at":"2026-05-18T04:11:29.395753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:29.395753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sQZWru3JxF2wsBqPzJ8P/8Ci5FRjICyZb+ifaYMaFBC0jyqInjk1drGNNQ8YH3XfJYZMDuNZMZdlqlRAZdMOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:29.396388Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.0958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d018526504c88be16ba3fe76907fd138511c5451d4eaaa929bafe29f9ee54ac","sha256:b29a6ae9e7d1f073ecfc92d74cb7a6c159a6ed8a58ff3e78c624cb9994e16b4a"],"state_sha256":"7aff6082d4182cdd1a8c081b08326c82521f2e9da31c3b50ecc2e1da606b3013"}