We compute a multi-test census of small-height pseudoprimality liars, recording foreach odd composite n the interval-local Miller--Rabin and Euler--Jacobi spectra (n;A), (n;A), the strong-Lucas grid spectrum (n;A) overP1, A, Q\1\, and Baillie--PSW, Frobenius and extra-strong Lucasindicators. A CUDA backend (RTX~5090), verified bit-for-bit against a CPUreference, reaches N=10^11 at A=1000 in 68. 8 hours; it reproduces the priorrecord-holder 3215031751, the OEIS base-2 strong-pseudoprime counts (8607 below10^11), and the empty Baillie--PSW survivor set below 10^11. The strong-Lucas-extremal composites are essentially disjoint from the MR-extremalones (all carry =0; at 10^11 the top-100 sets share one composite), and are dominated by the semiprime family n=p (2p+3). We prove a local CRTcriterion for strong-Lucas pseudoprimality in terms of the rank of apparition (theLucas analogue of the corrected Miller--Rabin local-order criterion, independentlyverified computationally). It identifies q=2p+3 as the coefficient-2 affinefamily aligning the nonsplit p+1 rank with the split q-1 rank, sharpens in themixed character regime to an exact criterion (strong-Lucas v₂ (ₚ) =v₂ (q) ), and exhibits (n;A) as a small-height sum offixed-discriminant slices of Arnault's strong-Lucas parameter counts. The residue clustering n77100 among the strong-Lucas extremes is aselection effect of via the character (5n) and thep4 structure, not a prime-pair density artifact. We give the unconditionalmechanism and a conditional average-order dominance theorem, and isolate the exactanalytic obstruction, a Bateman--Horn and 2-adic rank-equidistributioninput, to a ranked-tail asymptotic; asymptotic claims beyond the enumerated rangeare explicitly avoided.
John Janik (Sat,) studied this question.