Audit of Neo.K's Old "Lattice Rank Convergence" Route

Dismantles the logic chain of the old draft item by item: lattice-ifying the elliptic curve, calculating the lattice L-function, defining the lattice rank and order of vanishing, taking a→0, and claiming "continuity guarantees the equality holds". The audit points out at least two layers of circularity risk: if the proof of the lattice BSD inequality (rank_a(E)≤ord_{s=1}L_a(E,s)) itself already uses classical BSD-type connections, it is circular. The second layer is technical—rank is an integer-valued global arithmetic invariant; "approximate point counts" and "matrix rank" on a numerical lattice will not automatically converge to the Mordell-Weil rank as a→0; one must first establish the equivalence "lattice certificate ⟺ rational point independence/Selmer bounds"; even if L_a(E,s)→L(E,s) converges in some region, it does not automatically imply convergence of the order of vanishing, because the order of vanishing is discontinuous with respect to small perturbations; "both sides converge" does not imply "limits are equal" unless every a has a valid relation A_a=B_a—but if this is exactly lattice BSD, the hard problem is merely moved to the lattice level and not truly solved. Salvaging this requires four independent theorems: GR-1 (faithful discretization, lattice objects must preserve rational points/group law/torsion/height/local reduction), GR-2 (rank certificate equivalence, not visual/numerical rank), GR-3 (analytic order stability, the lattice L-function order of vanishing must be preserved by a rigorous analytic certificate), and GR-4 (non-circular bridging, the equality between GR-2 and GR-3 cannot presuppose BSD). Currently, all four remain uncompleted.