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Mainly, we study the scaling 1-hook property of the coloured Alexander polynomial: $\\mathcal{A}^\\mathcal{K}_R(q)=\\mathcal{A}^\\mathcal{K}_{[1]}(q^{\\vert R\\vert})$ for all 1-hook Young diagrams $R$. Via the Kontsevich construction, it is reformulated as a system of linear equations. It appears that the solutions of this system induce the KP equations in the Hirota form. The Alexander polynomial is a specialization of the HOMFLY polynomial, and it is a kind of a dual to the double scaling limit, which gives the special polynom"},"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":"1805.02761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-05-07T21:49:11Z","cross_cats_sorted":["math-ph","math.GT","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"fd130f1f9e65f51b87596e7e619b956166229f907bc7a11231317fc36bc4c989","abstract_canon_sha256":"beec4f5e16f15f58d2372cacc65a01df205e71023d97e166d85a55b562b63ee8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:21.749989Z","signature_b64":"so4UBbWQ+IyqoK//O6MGoF9FEch4xqBrCyBzSfvDaUYq5jcvcjBetZFL65+3pCqoi0dA/i3iN2nAh4lI8ZWtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc765cc76474bbdc3f896ecbae0ecc41b6e42cb224fc7bfd468421b8a6f6aa4f","last_reissued_at":"2026-05-18T00:10:21.749283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:21.749283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Colored Alexander polynomials and KP hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP","math.QA","nlin.SI"],"primary_cat":"hep-th","authors_text":"A. 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