Exact NRF-1 channel factors depend on observable ordering. The source audit preserves ALO-1 as a candidate and leaves coefficient selection open. Refinement exposes an observable-ordering choice Research update · 14 September 2026 · Physical promotion 0 The two quadratic anisotropy channels now have an exact NRF-1 refinement calculation. Its result depends on when the nonlinear observable is formed. This narrows the unresolved coefficient-selection problem to an observable-ordering law; it does not yet select a unique channel ratio. Three orderings, three exact maps For a parent cycle pseudovector zz, aligned child cycle pseudovectors satisfy z‾=14∑i=14zi=12z. \bar z=\frac14\sum_{i=1}^4 z_i=\frac12z. The equal child weights are fixed by normalized S4-invariance. Writing the quadratic family as α𝒬31+β𝒬22\alpha\mathcal Q_{31}+\beta\mathcal Q_{22}, the supplied calculation gives: Operation order Channel map Effect on a nonzero mixed ratio Form each child tensor, then average diag(5/16,3/16)\operatorname{diag}(5/16,3/16) α/β\alpha/\beta is multiplied by 5/35/3. Average pseudovectors, then form the tensor (1/4)I2(1/4)I_2 The ratio is unchanged. Apply exact chain retraction, then form the tensor I2I_2 Both channels are unchanged because R1I1=IR_1I_1=I. For synchronous self-similar NRF-1 with the first ordering, αnβn=(53)nα0β0. \frac{\alpha_n}{\beta_n}=\left(\frac53\right)^n\frac{\alpha_0}{\beta_0}. Only the two pure channels are fixed rays. This is a finite, ordering-dependent refinement calculation, not a physical renormalization-group law. Covariance across alternative refinement branches remains open. Read the NRF-1 theorem and supplied verification. What differs is retained child covariance For the canonical traceless dyad 𝒬\mathcal Q, 14∑i𝒬(zi)−𝒬(z‾)=TF[14∑i(zi−z‾)(zi−z‾)𝖳]. \frac14\sum_i\mathcal Q(z_i)-\mathcal Q(\bar z) =\operatorname{TF}\!\left[\frac14\sum_i(z_i-\bar z)(z_i-\bar z)^{\mathsf T}\right]. The local-first prescription retains the trace-free part of child-scale covariance. Averaging the pseudovector first removes that information before the nonlinear observable is evaluated. In the NRF-1 calculation, the difference is exactly (𝒬31−𝒬22)/16(\mathcal Q_{31}-\mathcal Q_{22})/16. This gives the ordering question concrete mathematical content. Identifying that retained covariance with a physical anisotropy observable still requires a constitutive or measurement bridge. What the source audit establishes The supplied audit finds no existing governed law that forces local anisotropy formation before coarse averaging. Exact support-stock ownership additivity concerns a different object. A historical coarse burden-anisotropy tensor is a candidate construction whose weights and physical interpretation remain downstream; it cannot supply the missing axiom by implication. ALO-1 remains a candidate: anisotropy is a cell-local additive observable formed before normalized top-cell averaging. Under that additional rule, the 5/165/16 and 3/163/16 channel factors apply. Selecting the pure three-dimensional channel would also require the additional nonzero cut–cycle coupling condition described in the theorem; that interaction law has not been derived. Read the observable-ordering source audit and governance record. The next dependencies Derive or independently justify the observable/source/action law that decides local-first versus coarse-carrier-first observation. Test covariance across admissible alternative refinement branches. Supply any required cut–cycle interaction law and overall normalization separately. Keep physical/continuum interpretation gated; neither the ordering nor its coefficients may be chosen to recover a desired gravitational target. The earlier two-channel classification remains exact. This update refines its open coefficient question without closing it. The harmonic-context occupancy problem and the pending real E2 laboratory inputs remain separate, unchanged dependencies. Preserved publication record The two original archives contain 14 members. All 12 manifest-listed payloads match their supplied hashes; both manifest files are also retained. Reported mathematical checks and source-audit conclusions are preserved as supplied, rather than independently rerun or re-audited during this site intake. Packaged manuscript variants v2.40D and v2.40E remain named branch snapshots alongside the main v2.40 manuscript. Their source locks, freezes, candidate status, and open conditions remain intact. The release collection now contains 84 packages and 1,097 package members; the base ledger retains 738 objects. Download the intake receipt · Browse releases