{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V5X2JF2DQF2475ZZHGF7O7EECB","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":"7f0119659c07a2985baf0cc91e3c0756e6fe0ff38bc51b2283c8d27131134325","cross_cats_sorted":["nlin.AO","physics.chem-ph","physics.soc-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-03-18T18:21:42Z","title_canon_sha256":"53bec70495caec2bc2321979b28185fe8fe1b9d516771c9ab6ed55e2544df605"},"schema_version":"1.0","source":{"id":"1103.3681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3681","created_at":"2026-05-18T03:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3681v1","created_at":"2026-05-18T03:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3681","created_at":"2026-05-18T03:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"V5X2JF2DQF24","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V5X2JF2DQF2475ZZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V5X2JF2D","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:82d7de1061adc1a981753a4f4302851830a60b6609671dd08c75912426538076","target":"graph","created_at":"2026-05-18T03:23:35Z","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":"Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game - the archetype of complex dynamics. A variable that provides complete and accurate description of","authors_text":"Sergei V. Krivov","cross_cats":["nlin.AO","physics.chem-ph","physics.soc-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-03-18T18:21:42Z","title":"Optimal Dimensionality Reduction of Complex Dynamics: The Chess Game as Diffusion on a Free Energy Landscape"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3681","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:f009c7adeadafd5b1d4d1973b67eeba04de04e278f4c6482c6628dbfb5706e6b","target":"record","created_at":"2026-05-18T03:23:35Z","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":"7f0119659c07a2985baf0cc91e3c0756e6fe0ff38bc51b2283c8d27131134325","cross_cats_sorted":["nlin.AO","physics.chem-ph","physics.soc-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-03-18T18:21:42Z","title_canon_sha256":"53bec70495caec2bc2321979b28185fe8fe1b9d516771c9ab6ed55e2544df605"},"schema_version":"1.0","source":{"id":"1103.3681","kind":"arxiv","version":1}},"canonical_sha256":"af6fa497438175cff739398bf77c84104310b6b7815058b84784a736f21a4b3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af6fa497438175cff739398bf77c84104310b6b7815058b84784a736f21a4b3a","first_computed_at":"2026-05-18T03:23:35.274759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:35.274759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J5MRoYNiZdsISVExq7LKSFGb9X3MQPOd7DdePjbz0KsWewixrpm0PF5aweQ1WJ0Dlviiy7hra82sA2YToYQ3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:35.275492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f009c7adeadafd5b1d4d1973b67eeba04de04e278f4c6482c6628dbfb5706e6b","sha256:82d7de1061adc1a981753a4f4302851830a60b6609671dd08c75912426538076"],"state_sha256":"eb283627eae1ba40445e9a6319597cf227c3a57fd804aece02e196bc504ab77e"}