{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:Y6VMR4J2MMFGXBIKD3BSS4UWHO","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":"fa8084ac077e1a59a43d19f046d2add5a486beaa5b475eada6c213d6ffd97654","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-31T14:55:09Z","title_canon_sha256":"3f751a28eb5126bb1ed40f66cfc5656e83e8e4a348c16be82a59983c2d1e6703"},"schema_version":"1.0","source":{"id":"2407.21653","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.21653","created_at":"2026-07-05T10:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"2407.21653v2","created_at":"2026-07-05T10:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.21653","created_at":"2026-07-05T10:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"Y6VMR4J2MMFG","created_at":"2026-07-05T10:49:45Z"},{"alias_kind":"pith_short_16","alias_value":"Y6VMR4J2MMFGXBIK","created_at":"2026-07-05T10:49:45Z"},{"alias_kind":"pith_short_8","alias_value":"Y6VMR4J2","created_at":"2026-07-05T10:49:45Z"}],"graph_snapshots":[{"event_id":"sha256:cd9a2006272a5aa9c5e5cea6a0e2fc0f03f92f19b22b3afcf095d207dc8750af","target":"graph","created_at":"2026-07-05T10:49:45Z","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/2407.21653/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter $\\beta=1$ arising in K-theory of the flag variety. The probability weight of a permutation is proportional to the principal specialization (setting all variables to 1) of the corresponding Grothendieck polynomial. By mapping this random permutation to a version of TASEP (Totally Asymmetric Simple Exclusion Process), we describe the limiting permuton and fluctuations around it as the order $n$ of the permutation grows to infinity. The fluctuations are of order $n","authors_text":"Alejandro H. Morales, Damir Yeliussizov, Greta Panova, Leonid Petrov","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-31T14:55:09Z","title":"Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.21653","kind":"arxiv","version":2},"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:cf53de511038b35fceb31a34a78948f74f6fc834638ccf7ffb351c8a995d43ce","target":"record","created_at":"2026-07-05T10:49:45Z","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":"fa8084ac077e1a59a43d19f046d2add5a486beaa5b475eada6c213d6ffd97654","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-31T14:55:09Z","title_canon_sha256":"3f751a28eb5126bb1ed40f66cfc5656e83e8e4a348c16be82a59983c2d1e6703"},"schema_version":"1.0","source":{"id":"2407.21653","kind":"arxiv","version":2}},"canonical_sha256":"c7aac8f13a630a6b850a1ec32972963baf7c693766f76106d7ded58a8eeaba5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7aac8f13a630a6b850a1ec32972963baf7c693766f76106d7ded58a8eeaba5d","first_computed_at":"2026-07-05T10:49:45.868161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:49:45.868161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3Sb6deq3OF2aCps9Ra09LN64+lq8dI1namcU3wsdqcL6DSnZz7Fsqpi48Ee109m0fpca6MZwcYEEyjfTnriBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:49:45.868609Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.21653","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf53de511038b35fceb31a34a78948f74f6fc834638ccf7ffb351c8a995d43ce","sha256:cd9a2006272a5aa9c5e5cea6a0e2fc0f03f92f19b22b3afcf095d207dc8750af"],"state_sha256":"cb77e5ac36eb8d3956ab0e806537d6a87c1633cbb5fef828d97da53b785620e0"}