Bounded-box reduction of the Subbarao–Warren conjecture to a semigroup-friable shifted-prime problem

A unitary perfect number is a positive integer n satisfying σ*(n) = 2n, where σ* denotes the sum of unitary divisors. Only five are known (6, 60, 90, 87360, 146361946186458562560000); Subbarao and Warren (1966) conjectured this list is complete. We work inside a bounded enumeration of the odd dependency graph induced by the fixed-point equation ∏(p_i^{e_i}+1) = 2 ∏ p_i^{e_i}, isolate five candidate "impostor" source strongly-connected component (SCC) kernels, and prove that for every a in their respective seed congruence classes with 1 ≤ a ≤ 10000, at least one of three rigorous filters (Zsigmondy/Higgs exponent, seed-divisor non-3-Higgs witness, or deterministic 2-adic budget overshoot) eliminates the candidate. Across 2119 candidates the split is 495/1611/13/0 (Zsigmondy / non-Higgs / overshoot / unresolved). We further derive a structural reduction: a proven lemma forces the index k of any m = 2k in H_even to be Higgs-cubefree (every prime factor of k is 3-Higgs with exponent at most 3, and every odd divisor of k also gives an element of H_even). The multiplicative closure gives a sharp reduction: |H_even| < ∞ iff |H_even ∩ {2p : p prime}| < ∞, with explicit bound |H_even| ≤ 4^N. Rigorous verification gives |H_even ∩ [2, 35000]| ≤ 166: 10 confirmed elements (all ≤ 122), and 156 NFS-blocked candidates of the form m = 2p for p in [1213, 17467]. Six initial candidates (m ∈ {10294, 10958, 17398, 19066, 20282, 30882}) were closed via deep Pratt-tree descent on large probable-prime divisors found in the Cunningham/FactorDB tables. Ford's theorem on downward-closed prime sets applied to the 3-Higgs primes (smallest omitted prime 17) yields the unconditional asymptotic #{m ≤ X : m ∈ H} ≪ X^{1-η} with Σ 1/m < ∞. We emphasize this thinness is not a finiteness step: it controls reciprocal mass O(1/p), whereas the cyclotomic identity log Φ_{4p}(2) ~ 2p log 2 requires a log-mass bound. The gap is exponential (~2^{2p}/p), identifying the precise missing analytic theorem as the log-mass conjecture: Σ log r ≤ (2 log 2 − δ)p over admissible primes r ≡ 1 mod 4p with (r-1)/(4p) in the 3-Higgs semigroup. We prove conditional finiteness of H_even under (i) effective Chebotarev (GRH) for the relevant Galois extensions plus (ii) effective ω(Φ_{4p}(2)) ≫ log p lower bounds. Supplementary code, factor cache, and verification scripts are released as additional files.