{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:A6WI4SVUUEYVBRMXCE6SXRXEQF","short_pith_number":"pith:A6WI4SVU","schema_version":"1.0","canonical_sha256":"07ac8e4ab4a13150c597113d2bc6e4817ece3ba61540ec0622fc8fbfdeb6a2c4","source":{"kind":"arxiv","id":"2606.17525","version":1},"attestation_state":"computed","paper":{"title":"Skew column RSK dynamics and the box-ball system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Matteo Mucciconi, Takashi Imamura, Tomohiro Sasamoto, Travis Scrimshaw","submitted_at":"2026-06-16T05:05:23Z","abstract_excerpt":"The Fomin local rules for Schensted column insertion can be seen as a two-lane box-ball system, in which a carrier moves particles forward or laterally. Running such two-lane dynamics in parallel on a periodic lattice gives rise to a two-dimensional generalization of the box-ball system, which we call the \\emph{skew column RSK dynamics}. Equivalently, this is a deterministic dynamics on pairs of skew semistandard Young tableaux $(P_t,Q_t)_{t \\in \\mathbb{Z}}$. We prove that this dynamics exhibits solitonic behavior and construct an explicit bijection $(P,Q) \\leftrightarrow (H_1,H_2,\\kappa,\\nu)$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.17525","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T05:05:23Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"c73d8f7ccf50964bdf32ac3f6b44cf03da3f4dfb616b740440385dd3371ecfb1","abstract_canon_sha256":"2789fbb018f6085bd2b1355c217ad9a2c99a25fc97d103af4a8e0dce33874b8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:15.126947Z","signature_b64":"JuNsMGoNC0oYVst4SaMY03ya3tmTRDmDGORhTwtwhKbrl8CspvBUhstVUB6kNoU+RgQJMi5QK6yGcO5+8gv1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07ac8e4ab4a13150c597113d2bc6e4817ece3ba61540ec0622fc8fbfdeb6a2c4","last_reissued_at":"2026-06-19T16:10:15.126596Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:15.126596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew column RSK dynamics and the box-ball system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Matteo Mucciconi, Takashi Imamura, Tomohiro Sasamoto, Travis Scrimshaw","submitted_at":"2026-06-16T05:05:23Z","abstract_excerpt":"The Fomin local rules for Schensted column insertion can be seen as a two-lane box-ball system, in which a carrier moves particles forward or laterally. Running such two-lane dynamics in parallel on a periodic lattice gives rise to a two-dimensional generalization of the box-ball system, which we call the \\emph{skew column RSK dynamics}. Equivalently, this is a deterministic dynamics on pairs of skew semistandard Young tableaux $(P_t,Q_t)_{t \\in \\mathbb{Z}}$. We prove that this dynamics exhibits solitonic behavior and construct an explicit bijection $(P,Q) \\leftrightarrow (H_1,H_2,\\kappa,\\nu)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17525","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17525/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.17525","created_at":"2026-06-19T16:10:15.126657+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.17525v1","created_at":"2026-06-19T16:10:15.126657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17525","created_at":"2026-06-19T16:10:15.126657+00:00"},{"alias_kind":"pith_short_12","alias_value":"A6WI4SVUUEYV","created_at":"2026-06-19T16:10:15.126657+00:00"},{"alias_kind":"pith_short_16","alias_value":"A6WI4SVUUEYVBRMX","created_at":"2026-06-19T16:10:15.126657+00:00"},{"alias_kind":"pith_short_8","alias_value":"A6WI4SVU","created_at":"2026-06-19T16:10:15.126657+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF","json":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF.json","graph_json":"https://pith.science/api/pith-number/A6WI4SVUUEYVBRMXCE6SXRXEQF/graph.json","events_json":"https://pith.science/api/pith-number/A6WI4SVUUEYVBRMXCE6SXRXEQF/events.json","paper":"https://pith.science/paper/A6WI4SVU"},"agent_actions":{"view_html":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF","download_json":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF.json","view_paper":"https://pith.science/paper/A6WI4SVU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.17525&json=true","fetch_graph":"https://pith.science/api/pith-number/A6WI4SVUUEYVBRMXCE6SXRXEQF/graph.json","fetch_events":"https://pith.science/api/pith-number/A6WI4SVUUEYVBRMXCE6SXRXEQF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF/action/storage_attestation","attest_author":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF/action/author_attestation","sign_citation":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF/action/citation_signature","submit_replication":"https://pith.science/pith/A6WI4SVUUEYVBRMXCE6SXRXEQF/action/replication_record"}},"created_at":"2026-06-19T16:10:15.126657+00:00","updated_at":"2026-06-19T16:10:15.126657+00:00"}