PASS complete lattice basis and order 21 mod seven
PASS full length-three eigenchain and nonzero socle-to-top pairing
PASS exact images of three generators
PASS 343 exact arithmetic unit carries
PASS full 343-point orbit decomposition {1: 1, 21: 16, 3: 2}
PASS embedded seven-point socle packet
PASS semisimple order three and nontrivial order-seven shear
PASS lattice-avoidance arithmetic for conductor-three packet
Exact audit passed, with no Gamma algebraicity claim.
NUMERIC distribution n= 2 n^3= 8 log residual 2.66955535804e-39 expected F(nz)
NUMERIC distribution n= 3 n^3= 27 log residual 1.23778995899e-38 expected F(nz)
NUMERIC distribution n= 5 n^3= 125 log residual 5.00933800595e-38 expected 1
NUMERIC distribution n= 7 n^3= 343 log residual 9.99377924873e-38 expected F(nz)
Numerics are not an interval certificate; the proof is geometric-series Fourier filtering.