RIEMANN PROJECT · 23 SEPTEMBER 2026 · v1.61

Local review of the geometry and controls

Review scope: NS-72–74 proofs, their finite evidence, manuscript integration and reported conclusions. This was a self-review in the current task, not an independent audit.

Boundary terms and complete domains

The local-energy argument now explicitly sums the positive derivative functional over all pieces before identifying it with the whole-line operator norm. The initial wording called each finite piece an operator energy; that could hide an endpoint term and was corrected. The compact extension is continuously differentiable, includes both tails and belongs to the required Sobolev space.

The causal factor, actual Green-function matching conditions and interpolation normalization were checked symbolically. The model curvature bounds do not compare the model Gram with the arithmetic Gram.

Coefficient and arithmetic scope

The Möbius templates are specified in physical atom coordinates and then converted exactly to adjacent differences. The old boundary term is displayed and removed only by complete old-space projection. The three-template comparison keeps all cross terms and permits the best fitted combination; individual template coefficients were prescribed in advance.

The curvature rule requires the actual optimized correlations. Its operation count excludes obtaining them and excludes a claim about bit complexity.

The altered-family obstruction

The deformation is unitary on the whole Hilbert space, so complete Gram entries are unchanged. Its transformed target has an explicitly retained exterior tail. Projecting that tail gives the positive floor; an independent dual-evaluation calculation gives the same formula. No density assumption or RH hypothesis enters this lower bound.

The finite-indistinguishability statement concerns a fixed finite list followed by a small deformation. It does not interchange the infinite-size limit and the small-parameter limit. The inserted zero and positive floor belong only to the altered family.

Numerical and integration checks

All solves retain Arb enclosures. Source and inherited-dependency hashes are checked, as are precision, cutoff and published-result overlaps. The cutoff changes the sharpness of a full-tail enclosure, not the mathematical problem. A pilot endpoint-power ambiguity was fixed before the official template runs; those runs use an exact zero endpoint and explicit integer products.

Python diagnostics, Maxima PASS counts, the full manuscript build, rendered new pages, local links and the incremental manifest are recorded in validation.json. No unresolved issue was identified in this self-review pass. The cofinal arithmetic estimate remains open.

Exact identities, proved implications and certified finite computations are distinguished from the still-open arithmetic input. Local self-review only; no independent review or publication-readiness claim.