{"paper":{"title":"Multiple Landen values and the tribonacci numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"David Broadhurst","submitted_at":"2015-04-21T04:47:34Z","abstract_excerpt":"Multiple Landen values (MLVs) are defined as iterated integrals on the interval $x\\in[0,1]$ of the differential forms $A=d\\log(x)$, $B=-d\\log(1-x)$, $F=-d\\log(1-\\rho^2x)$ and $G=-d\\log(1-\\rho x)$, where $\\rho=(\\sqrt{5}-1)/2$ is the golden section. I conjecture that the dimension of the space of ${\\mathbb Z}$-linearly independent MLVs of weight $w$ is a tribonacci number $T_w$, generated by $1/(1-x-x^2- x^3)=1+\\sum_{w>0}T_w x^w$, and that a basis is provided by all the words in the $\\{A,G\\}$ sub-alphabet that neither end in $A$ nor contain $A^3$. For $w<9$, I construct a much more efficient bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05303","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}