The Rectifier Is the Reader: Identifiability of One-Sided Neural Codes and the Two-Sided Ledger

For a linear code the codebook is a gauge choice: the observation law is preserved by transformations that reshuffle the atoms, so there is no fact of the matter about which dictionary a data stream uses. This paper proves that the rectifier — priced in the first paper of this program as the source of one-sided interference — is exactly the structure that destroys this gauge. The conic identifiability margin mu_i = dist(d_i, cone(D_-i)) is computable by one nonnegative least-squares solve per atom and, for pointed dictionaries, obeys a rectified-Gram sandwich sqrt(1-(g_i/tau)^2) <= mu_i <= sqrt(1-g_i^2) (for g_i <= tau), hence mu^2 >= 1 - P+/tau^2: the rectified frame potential prices interference and certifies readability jointly with pointedness. The certificate is sharp exactly on its own obstruction — a three-atom aimed antipodal conspiracy zeroes the margin at vanishing acute mass while lowering P+ — and no functional of the rectified pairwise data decides identifiability: the obtuse information that decides compresses to the single scalar tau. The level structure of one-sidedness is established (support-cone channel at lambda=0, discontinuous death for lambda>0, odd-cumulant channel decaying at leading order as 1-lambda^3 with the exact in-family cumulant and a positivity theorem), the weight-1 threshold meter is proved angle-blind at every derivative order while read-weighted sweeps reconstruct, the zero-point constants close in the half-normal median (alpha = (4/sqrt pi) PhiInv(3/4) = 1.522160..., beta = 1.909873...), moment evasion is proved at second order and refuted in generality (the degree-(d+2) syzygy channel reads gauge invariants blind to the input density; discovery is enumeration, certification one quadratic functional per relation), and a sealed nine-bar planted referendum battery passed on two seed sets. AI-collaboration disclosure included in the paper.