Everyone proves uniqueness under Lasry–Lions monotonicity. Almost nobody exhibits the dimension of the equilibrium set when monotonicity fails — and this tree already computed one exactly, over the rationals, and filed it as a validation detail.
Nothing on this page is claimed, certified, enclosed or proved. No kernel, no certificate, no falsifier, no ledger record, and no literature gate has run on it. It names a direction and what would have to be true. A prospectus that reads like a result is the defect, so this one says so at the top and is not published.
S1's equilibrium face is exactly 6-dimensional over the rationals, with ker(J)
exactly equal to that face — nullity 6, no gauge. Alongside it, a measured non-uniqueness that
was demonstrated rather than hidden: S1 totals unique across reseeds to 6.8e-14 while the SPLIT
moves by ~5.9, because c = j¹+j² is monotone but not strictly. That pair
— a certified invariant and a certified degree of freedom in the same equilibrium — is
the shape of the result.
Uniqueness proofs are a sufficient condition applied where it holds. The interesting regime is where it does not, and there the literature mostly reports “multiple equilibria may exist”. Exact rational face computation turns that sentence into an integer. Not “we found two solutions” — the solution set is a face of dimension d, and here is the proof.
S1 is AFFINE. It never needed interval arithmetic to close, so it cannot exercise the bound C1 is meant to state (named, not started). A method demonstrated only on the case that does not need it is a method without a subject.
Candidate instance, opened the same day:
edge-of-chaos.html. The mean-field neural-network fixed point q* = V(q*) is
genuinely nonlinear, and at χ₁ = 1 the correlation map's fixed point is exactly
non-hyperbolic — derivative equal to one. That is a geometric degeneracy in a nonlinear
system, which is precisely what C1 has been waiting for. It carries its own blocker; see that page.
N: HIGHEST of the five — nearest to genuinely new territory. A: HIGH. Both unverified.
Highest occupancy risk of the five. Degenerate-equilibrium structure is studied in variational analysis, bifurcation theory and algebraic geometry under other names. Run the literature gate before investing, and expect it to bite.