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The solitons of length $l$ are identified with elements of the $A_1^{(1)}$-crystal $\\tilde{\\mathcal{B}}_{3l}$. The scattering rule for our soliton cellular automaton is identified with the combinatorial $R$ matrix for $A_1^{(1)}$-crystals."},"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":"1109.2836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-09-13T16:08:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"eeda6293f146eeba01373d9a4df7723d85727249f67cc8e8c257a2bf3bdcaa9e","abstract_canon_sha256":"6cf6acc1758fd892afeb21a567d350af77c3b08aaafe565673bc769ddb9800cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:33.546661Z","signature_b64":"WZ2OEaPgylP1Gsj69qJqt8zO0jAxIT0DfDJAGwyZFOUVIvjo5F0taadpy9gafqDA6CS7I9AsmKylnOnaa3ALDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53d15f23064091b1ffe5962dd21dda2b390d249c9010d50bbb26167b6b5005b8","last_reissued_at":"2026-05-18T02:00:33.545990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:33.545990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Soliton cellular automaton associated with $G_2^{(1)}$ crystal base","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Evan A. 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