Loading /Users/alex/.maxima/maxima-init.mac
batch("audits/prime-scaling-admission-2026-09-29-v1/check_identities.mac")
display2d:false
checks:0
assertzero(label,expression):=block([value:ratsimp(expression)],
           if value # 0 then error(label,value),checks:checks+1,true)
inner(v,w):=sum(v[ii,1]*w[ii,1],ii,1,length(v))
normsq(v):=inner(v,v)
ident:ident(3)
small:matrix([1,0,0],[0,0,0],[0,0,0])
large:matrix([1,0,0],[0,1,0],[0,0,0])
v:matrix([x1],[x2],[x3])
assertzero("energy split",
           normsq((ident-small) . v)-normsq((ident-large) . v)
                                    -normsq((large-small) . v))
assertzero("extra old energy",normsq((large-small) . v)-x2^2)
assertzero("new residual energy",normsq((ident-large) . v)-x3^2)
hsmall:z-x^2/a
hlarge:z-(c*x^2-2*b*x*y+a*y^2)/(a*c-b^2)
assertzero("Schur loss",hsmall-hlarge+(-(a*y-b*x)^2)/(a*(a*c-b^2)))
gram:matrix([1,1-eps],[1-eps,1])
signed:matrix([1],[-1])
masked:matrix([1],[0])
assertzero("full signed cost",inner(signed,gram . signed)-2*eps)
assertzero("masked cost",inner(masked,gram . masked)-1)
assertzero("positive determinant",determinant(gram)-eps*(2-eps))
u:matrix([u1],[u2],[u3])
w:matrix([w1],[w2],[w3])
assertzero("signed channel split",
           normsq(u-w)-normsq(u)-normsq(w)+2*inner(u,w))
mob(n):=block([facts:ifactors(n),has_square:false],
    for pe in facts do if pe[2] > 1 then has_square:true,
    if has_square then 0 else (-1)^length(facts))
coef(nn,kk):=-mob(kk)*log((2*nn)/kk)
for nn thru 16 do
    for pp in [2,3,5] do
        (for kk from pp*nn+1 thru 2*pp*nn do
             block([rhs],
                   rhs:if mod(kk,pp) # 0 then coef(pp*nn,kk)
                           else (if mod(kk/pp,pp) # 0 then -coef(nn,kk/pp)
                                     else 0),
                   assertzero("prime-free/divisible coefficient identity",
                              coef(pp*nn,kk)-rhs)))
print("PASS: exact bookkeeping checks",checks)
PASS: exact bookkeeping checks 1368 
print("No uniform arithmetic bound, numerical NB certificate or RH conclusion.")
No uniform arithmetic bound, numerical NB certificate or RH conclusion. 
quit()