Prime Blocks and Additive Divisor Obstructions in Cyclotomic Littlewood Polynomials

These working papers study the Borwein–Choi conjecture on recursive prime-block factorizations of cyclotomic Littlewood polynomials. Main results An analytical proof for every length 2ᵗpq, with t ≥ 0 and distinct odd primes p and q. An arbitrary-formal-series two-correction lemma, giving a coefficient failure by j + (⌊j/i⌋ + 1)i. Factors supported on the first block can be absorbed into the baseline. Analytical factorization for every length 2ᵗpᵃq when p > 2ᵗ, and for every 2pᵃq and 4pᵃq without size restrictions, with a ≥ 1. The proof includes the interacting obstructions at 4·3ᵃ·5 and 4·3ᵃ·7. An isolated-obstruction criterion for further prime configurations, including every 2ᵗ35r outside O(log X) possible exceptional primes r ≤ X. A separate prime-power insertion theorem relative to an arbitrary cofactor, plus exact multiplicity tests, trace-propagation identities, and polynomial norm reductions. Companion paper The independent companion determines the complete cyclotomic divisor, including multiplicities, of the three-run word +ᵃ−ᵇ+ᵃ and gives classifications through three sign changes. Its proof includes the required six-term vanishing-sum argument. Included material The deposit includes both papers, editable LaTeX sources, exact-arithmetic programs and certificates, a dependency map, and a separate scope and corrections report. Repeated cyclotomic factors are allowed. The principal factorization proofs are analytical; finite computations provide supplementary checks. Scope The unrestricted Borwein–Choi conjecture remains unresolved here. The stated families do not cover general repeated powers on both odd primes or arbitrary additional prime supports. The papers are working manuscripts; external validation and priority for the further deductions are not asserted.