[Dugongue]

Recode the actual rank-30 fixed-reader Gaussian section into its moving-reader section while preserving every arbitrary centre baseline. If D0 J = D1 J = I, let Delta = D1 - D0. Four explicitly ordered ordinary shears implement (a,z) -> ((I + J Delta)a,z): gather into z, scatter into a, subtract the gather using UPDATED a, then subtract the scatter using the restored z. No additional centre bank, COPY, CLEAR or Gaussian request is introduced by this recoding.

The source substitution is J = Q^2 U, D0 = (V Q^2 U)^(-1)V and D1 = (VU)^(-1)V Q^2. The square-zero inverse and complete section conjugacy are proved, including the use of the same centre before and after the section changes its value. A finite-character formula supplies the exact all-width translation-kernel construction. Norm statements distinguish shear boundaries from the primitive-interior bounds required for an implementation. All translation kernels, coefficient passes, fixed-odd arithmetic and routing costs remain charged.

Companion informal results give a literal two-helper Gaussian endpoint reconstruction with its full productive debit, two complete typed-consumer words with honest invoices, and a phase-exact chirped two-sided monomial equivalence of the nine-axis Gaussian. They preserve their actual independent inputs, address spectators, reciprocal scope and source-version deadlines.

A profitable complete Gaussian supplier and kappa >= 0.0035 are NOT established. The thirty-row recoder is not silently substituted for the different sixteen-row joined D25 services. A completed output-frame conjugation is not treated as an input conjugation on new fresh axes. The prior four-partial-helper BIT result still needs ordinary admission above 0.0035. No missing component is assumed as a new oracle or gadget, and no selected-frontier change is proposed.

Adds five mathematical Markdown documents. All proofs are informal, using retained source text and separate worker review; no numerical pricing, source replay, mathematical computation, solver, Lean run, web search or remote PR refresh was used. The offline source pin is 5e0052c. Publication byte checks are distinct from mathematical evidence.

Credit reciprocal-native-responses and its rank-30 annex, centre-code-services, native-centre-capture and centre-metric-encoders, with their campaign-lane/source notices and explicit predecessor PR3133, PR3148, PR2588 and PR2226. Retain Dillon Amburgey PR5402; Chris R / Clear1nsight PR5407/PR5413; Ali Romman PR5383/PR5398 and centre work; Cinna Davis PR4694/PR4698; Cao Yifan; DaysSky; Nick Petalas; Ryanson Jonathan; zxv; Jacob Alan Sussman; Dugongue; and all source-specific native, Clifford, compiler, stock, precision and analytic authors. No owning PR is inferred where the retained source does not name one. Substantial OpenAI Codex assistance from one coordinator and three workers. New text is Apache-2.0.

Start with reader-kernel.md Theorems 1-3 and coded-provider.md. Only research/gaussian-reader-recoding is added.