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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"},"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":"1504.05303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-21T04:47:34Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3979523a3beac1a320360bb7c5216bc9da9e45ce6f4cf9916c4f12f508091605","abstract_canon_sha256":"5f9b3804b714677afa55ee5c5718a5db82377416b31e49e09eef9eeb70516f15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:54.018397Z","signature_b64":"aOyRlECSHZBX4CL/pxIhP3fttK5cfPSj9UJhO/AR5YnId6ex0ikHYle1qF0why3m/ruqhyGvvmKdaamuV3jYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"211944f5598ec76a91bdaa8793e690de3bb47ef2270cd94384c96e7b7d269e19","last_reissued_at":"2026-05-18T02:17:54.017650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:54.017650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $A^3$. 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