{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:22A6AK2RNKQGOGRJ7PNU3FJOZT","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":"8052a2b553bb11fc8f90f1e415a6aee4ed232ebf4a1f0ddb27ebd77a316ee340","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-31T23:50:13Z","title_canon_sha256":"21d311bea57b4a3f1872ff2194db15275db5607c85cfc6e7dc029aed907a79fb"},"schema_version":"1.0","source":{"id":"2606.01501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01501","created_at":"2026-06-02T02:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01501v1","created_at":"2026-06-02T02:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01501","created_at":"2026-06-02T02:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"22A6AK2RNKQG","created_at":"2026-06-02T02:04:34Z"},{"alias_kind":"pith_short_16","alias_value":"22A6AK2RNKQGOGRJ","created_at":"2026-06-02T02:04:34Z"},{"alias_kind":"pith_short_8","alias_value":"22A6AK2R","created_at":"2026-06-02T02:04:34Z"}],"graph_snapshots":[{"event_id":"sha256:f61aaf237c18dddbbd96c99f4af0d4892b7d6b10023bc49cda1ffe742cad3f8f","target":"graph","created_at":"2026-06-02T02:04:34Z","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/2606.01501/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Longest Increasing Subsequence problem - a classic combinatorial challenge with deep connections to statistical mechanics- exhibits a rich thermodynamic landscape. Introducing a temperature we identify two distinct energy scales: A Schottky-like crossover at T_cross and a condensation transition at T_cond, below which the number of maximum-length configurations becomes sub-exponential in system size. We also show that despite the existence of polynomial-time dynamic programming algorithms for the ground state, local Monte Carlo dynamics, after sudden quenches at low temperatures, become tr","authors_text":"Roberto Mulet, Silvio Franz","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-31T23:50:13Z","title":"The Longest Increasing Subsequence Problem revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01501","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:b1bf0fef9bdc86c4518ebcaafcd5da652d6736cfd2752270f03f639d8cef0eb9","target":"record","created_at":"2026-06-02T02:04:34Z","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":"8052a2b553bb11fc8f90f1e415a6aee4ed232ebf4a1f0ddb27ebd77a316ee340","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-31T23:50:13Z","title_canon_sha256":"21d311bea57b4a3f1872ff2194db15275db5607c85cfc6e7dc029aed907a79fb"},"schema_version":"1.0","source":{"id":"2606.01501","kind":"arxiv","version":1}},"canonical_sha256":"d681e02b516aa0671a29fbdb4d952ecce253f6446ad89c50e41f191eb81fb88b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d681e02b516aa0671a29fbdb4d952ecce253f6446ad89c50e41f191eb81fb88b","first_computed_at":"2026-06-02T02:04:34.899641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:34.899641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X05sl1wABQD40oLRD40xArX/fxy3o/jyqNTO7TcZK2A19gqCNghPJcVLM+AMejiHZj5PU/5wJw0Bo4x6HhF4Cg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:34.900078Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1bf0fef9bdc86c4518ebcaafcd5da652d6736cfd2752270f03f639d8cef0eb9","sha256:f61aaf237c18dddbbd96c99f4af0d4892b7d6b10023bc49cda1ffe742cad3f8f"],"state_sha256":"a094d4720ccbf1754ac9d62ecb4651bd7bcc6942bf57f608a407f733859eb29c"}