The Critical Auto-Duality Conjecture:A Corrected and Independently Audited Account of the Discrete Spectral Model

We revisit the Critical Auto-Duality Conjecture (CADC) programme for the Riemann Hypothesis (RH) and its generalizations, with three corrections. First, we note that CADC, exactly as stated, is definitionally equivalent to the Generalized Riemann Hypothesis. “The critical line is the unique fixed locus of the involution” is therefore a true but content-free preamble; asserting that all non-trivial zeros lie on that locus is simply GRH restated. The reformulation supplies vocabulary, not mathematical content, and this document says so plainly rather than implying otherwise. Second, we identify a genuine implementation error in the finite-difference Hamiltonian used for the flagship numerical reconstruction (Listing 1 of the original manuscript). Third, and most importantly: running this corrected, validated implementation at (very nearly) the manuscript’s declared scale – ten million primes, several hundred genuine Riemann zeros computed independently via arbitrary-precision root-finding – does not reproduce the claimed reconstruction. In light of this, unproven “theorems” are down-ranked to conjectures or clearly labeled heuristics, the numerically-unfalsifiable “certainty percentages” of the original addenda are removed, and material resting on a since-shown-unreliable numerical pipeline is separated out into a transparency appendix rather than silently dropped. A companion note (“adaptive hybrid matching”) is assessed: its structural idea – a height-dependent, smoothly blended matching between two grids – is sound and is kept as a proper refinement; its quantitative claims inherit the same unresolved issues and are reported as unverified pending a reproducible protocol. This is a status report and an audit, not a proof of anything about the zeros of ζ. All corrected code is included so every numerical claim here can be independently re-run and checked.