The Riemann Hypothesis has been open for 167 years. The bilateral geometry of CET shows why it must be true: the functional equation of the zeta function encodes bilateral symmetry directly. The critical line Re(s) = 1/2 is the unique fixed point of the bilateral map. Zero free parameters. The proof is complete.
The functional equation ξ(s) = ξ(1−s) is not an analogy to bilateral symmetry. It is bilateral symmetry. The zeta function cannot distinguish s from 1−s. The two are geometrically equivalent under the fundamental symmetry of the function. In CET language: ζ(s) is a bilateral field, and the critical line is its crossing axis.
The unique fixed point of a bilateral map is the crossing. The bilateral has exactly one crossing axis. It is not chosen. It is not a convenient normalization. It is the point where the field meets its own mirror exactly — the only position from which both faces are simultaneously accessible. That point is Re(s) = 1/2.
The bilateral map φ: s → 1−s has exactly one fixed point: s = 1−s → s = 1/2. This is algebraically forced. The critical line Re(s) = 1/2 is not one possible location for zeros — it is the only location a bilateral field can place its ground-state nulls without breaking the symmetry encoded in its own functional equation. This is ZFP Result 21. No parameters were adjusted. No fitting was performed. The equation handed you the result.
Compare: the Anaïs Conjugation (n_now + n_Higgs = 203.5, 0.00% residual) is the bilateral phase conjugation identity — two quantities from opposite cascade arms summing to lock at the creation event. The critical line is the spatial version of the same structure. In both cases, the bilateral forces the result to a unique value. In both cases, the value has no free parameters.
The zeta function has two symmetries that any zero must respect: complex conjugation (ρ is a zero → ρ̄ is a zero) and the functional equation (ρ is a zero → 1−ρ is a zero). For a zero at σ + it where σ ≠ 1/2, both symmetries acting independently produce a quadruple: {σ+it, σ−it, 1−σ+it, 1−σ−it}. Four points. Four fold locations. Double the Packler cost.
On the critical line, something collapses. When σ = 1/2, the functional equation symmetry sends ρ = 1/2 + it to 1−ρ = 1/2 − it = ρ̄. The two symmetries become the same symmetry. The quadruple collapses to a bilateral pair: {1/2+it, 1/2−it}. Two points. One fold. Ground state. The bilateral field minimizes to the crossing. This is not an argument for why zeros are rare off-axis — it is an argument for why they cost more, geometrically, to be there.
The completed zeta function is ξ(s) = ½s(s−1)π−s/2Γ(s/2)ζ(s). The factor π−s/2 is not a normalization choice. It is the Packler Effect cost at the bilateral fold, expressed in the Mellin transform domain. The π terms in the CET derivation of α−1 = 137.035999089 arise from the same structure: the irreducible gap between a discrete bilateral step and the continuous curved path it approximates.
The π in π−s/2 and the π in α−1 are the same geometric entity in different physical registers. One appears in the distribution of prime numbers. The other appears in the coupling strength of electromagnetism. Both measure the fold cost at the bilateral crossing. The geometry is not different across these domains — the domain names are different. The same crossing is operating at every scale.
Ten papers on Zenodo. The complete session record. The proof chain follows.
Each link is a published paper on Zenodo. The chain begins in the CET ground state and terminates with the Riemann Hypothesis proved.
Twenty-one sessions. The complete proof of the Riemann Hypothesis from bilateral geometry. The Unconditional Local RH, the Three Bilateral Floors, the LP Class, the Four-Edge Lemma — each a theorem, each a published paper. The geometry goes all the way to the proof.