We formulate a finite-dimensional reference tensorized observation model for Bernoulli-selected sector profiles in A = R[u]/(u4 − 1). The ordered-branch reference metric is part ofthe observation architecture: sector decompositions are algebraic, while intensities, half-cubecontrasts, Walsh contrasts, visibility conditions, and active envelopes are reference-metricobservables.The exact dynamical laws proved here are deliberately restricted to a diagonal-reference,no-sector-mixing theorem class: refined sector blocks are invariant, their reference intensitiesevolve with scalar real exponents, and cross-channel covariance enters through the readoutlaw rather than through deterministic off-diagonal tensor coupling. Thus the paper developsa reference tensor-sector observation calculus, not a general theory of sector-mixing tensordynamics.The stochastic layer is a selector sign vector acting only at readout. Same-time identitiesuse the pointwise sign-local selector law; process-level and observation-window statements usea frozen-selector convention in which one selector is sampled once and kept fixed across thewindow. All displayed expectation, variance, and covariance identities are moments underthe selector law, not empirical information supplied by one frozen path unless a samplingprotocol or external law is provided.The sector-faithful readout J retains full sector labels, while the reference sign-localhalf-cube channel X is an imposed observation design, not a canonical consequence of thetensor algebra, and it reduces to an affine Bernoulli sensor. Tensorization is structurallyessential upstream because it produces the sector-resolved deterministic intensity profile,active supports, and Walsh contrast coefficients. After this compression to the fixed sign-localchannel layer, the first–second order formulas reduce to affine Bernoulli moment calculus.The resulting first–second moment formulas are exact inside this fixed sensor class, notinvariant, basis-free, or canonical covariance laws for the tensor algebra alone.The affine Bernoulli calculation itself is elementary once the sign-local sensor normal formhas been imposed. Accordingly, the first–second moment layer is presented as a consolidatedbookkeeping calculus, not as a collection of independent theorem-level discoveries. Its roleis structural rather than inflationary: it records the precise interface between deterministicfirst-Walsh half-cube contrasts and readout-law covariance, which is then used for coefficient-visibility, externally calibrated division, nonidentifiability, and information-limit statements.The covariance layer exposes selector covariance only through the contrast-weighted productssupplied by the fixed reference sensor. It is blind to deterministic second Walsh geometryunless pair-sector or sector-faithful sensors are added, where the new term is only coefficient-visible unless a calibration package and ensemble-moment protocol are supplied.Active-envelope statements are classified as upper-envelope bookkeeping except in thepositive aggregate layer or in explicitly conditional lower-bound-transfer statements. Reducednonidentifiability statements are observation-level statements only unless sector realizationor dynamic realization is supplied in the local hypotheses.The ensemble first–second sign-moment package determines a two-coordinate selector pairlaw, but for m ≥ 3 it does not determine the full selector law; every full-law nonidentifiability1statement below is to be read with this m ≥ 3 qualifier. Observed covariance vanishing,selector pairwise independence, full selector independence, deterministic contrast degeneracy,and one-hot full-sector competition are kept separate. Exchangeable examples are alwaysconditioned on genuine finite exchangeable selector laws; the PSD range is used only as anecessary covariance check and never as a free-parameter theorem. The common deterministicbaseline Idettot /2 is a structural feature of the fixed uniform half-cube partition, not a universalbaseline law for arbitrary sensors. The paper also distinguishes observation-level reducedprofiles from sector-realized and dynamically realized profiles, treats selector-covariancedivision as externally calibrated and never as raw recovery from channel moments alone,fixes a zero-sign convention only for tie-breaking when βk = 0, and phrases deterministicpropagation through finite-dimensional matrix flows etG rather than unnecessary infinite-dimensional semigroup language.Finally, positive upper-envelope exponents for signed contrasts and covariance-levelquantities remain non-exclusion indicators unless visibility and noncancellation hypothesesare imposed. By contrast, the positive total reference intensity has an exact refined-blockexpansion and therefore admits a genuine aggregate active-rate lower bound