{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IJLLODKLO2HRT5MPJZHNKLKKAC","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":"aa5dff24fdcddd5c8672c2ccaf6bebe9d59e2ef65a6bd86dd2cbaba174c22eac","cross_cats_sorted":["hep-th","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-12T21:01:48Z","title_canon_sha256":"b2906507f77dc0579770e993f2d0e711f688d891c28cff97f54cfa0a1b757229"},"schema_version":"1.0","source":{"id":"1702.03574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03574","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03574v1","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03574","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"IJLLODKLO2HR","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IJLLODKLO2HRT5MP","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IJLLODKL","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:6aa00f01c92f90b1bed35f6b2226bcb656421c8bc429b714e070970bf23d3f9d","target":"graph","created_at":"2026-05-18T00:50:53Z","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":"The uniformly hyperbolic Anosov C-systems defined on a torus have exponential instability of their trajectories, and as such C-systems have mixing of all orders and nonzero Kolmogorov entropy. The mixing property of all orders means that all its correlation functions tend to zero and the question of a fundamental interest is a speed at which they tend to zero. It was proven that the speed of decay in the C-systems is exponential, that is, the observables on the phase space become independent and uncorrelated exponentially fast. It is important to specify the properties of the C-system which qu","authors_text":"George Savvidy, Konstantin Savvidy","cross_cats":["hep-th","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-12T21:01:48Z","title":"Hyperbolic Anosov C-systems. Exponential Decay of Correlation Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03574","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":"sha256:6376d84ac100e2a133c67a17a4feccd23d28ff3ac514ae467ad799cc1a829032","target":"record","created_at":"2026-05-18T00:50:53Z","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":"aa5dff24fdcddd5c8672c2ccaf6bebe9d59e2ef65a6bd86dd2cbaba174c22eac","cross_cats_sorted":["hep-th","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-12T21:01:48Z","title_canon_sha256":"b2906507f77dc0579770e993f2d0e711f688d891c28cff97f54cfa0a1b757229"},"schema_version":"1.0","source":{"id":"1702.03574","kind":"arxiv","version":1}},"canonical_sha256":"4256b70d4b768f19f58f4e4ed52d4a008e7e82ef23251dca40dffa23b4860516","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4256b70d4b768f19f58f4e4ed52d4a008e7e82ef23251dca40dffa23b4860516","first_computed_at":"2026-05-18T00:50:53.487994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:53.487994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"olfwGCnDGrEf9van5/W6cWuNFEpPTjONmIBoj7va0Z2DCLLxCCaeZFq2D5la/r7BVP5FWTRYMrzna9tgq1PmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:53.488508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6376d84ac100e2a133c67a17a4feccd23d28ff3ac514ae467ad799cc1a829032","sha256:6aa00f01c92f90b1bed35f6b2226bcb656421c8bc429b714e070970bf23d3f9d"],"state_sha256":"91ebcf6bb6bcecf05d5d1bd677dd0c969d6000a94be34136b76e1d14c4bc24f9"}