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Cosmic Microwave Background Mu and Y Spectral Distortions: Injection Windows, Templates, and a Lower-Bound Floor
V33-33.6 · F 证据节 / 显影节 ·
33.6 turns Cosmic Microwave Background spectral distortions into a three-template audit: μ_CMB, y_CMB, and a fixed transition residual R(ν) must be jointly required, leave one stable node ν0, and converge to nonzero sky-averaged floors; under V09-compatible translation, these templates stay as ledger-style injection-window readouts rather than a single-origin ontology verdict.
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Keywords: Cosmic Microwave Background spectral distortions, μ_CMB, y_CMB, R(ν), ν0, three-template fit, transition window, mask tightening, monopole floor, template permutation, absolute calibration, V09 ledger translation
Section knowledge units
thesis
33.6 refuses to treat Cosmic Microwave Background spectral distortions as a simple yes-or-no excess. The question is which frozen injection-window templates are actually required once a blackbody reference and preregistered standard terms are removed. The chapter says that a real residual must not warp itself arbitrarily. It must decompose into three fixed parts: a mu-type term, a y-type term, and a transition-window residual R(ν) that neither pure mu nor pure y can absorb. That is why the section is not just about amplitude. It is about shape necessity. If a mu-plus-y description already closes the spectrum, or if the transition term appears only after post-hoc redesign, the claim fails. In V33 terms this is an adjudication of template necessity at protocol-layer, not a single-origin ontology verdict.
mechanism
The measurement ledger is deliberately explicit. The observed spectrum I_obs(ν) is compared with one blackbody reference I_bb(ν, T0) to produce the residual ΔI(ν) together with a full-frequency covariance matrix. The fit then solves for μ_CMB, y_CMB, and the transition amplitude A_r rather than only quoting a visual mismatch. The transition template is not accepted on amplitude alone: the post-fit residual must show one stable zero crossing at ν0, with opposite signs on the two sides. Beyond that, the section builds convergence curves for μ_CMB, y_CMB, and A_r as masks tighten and foreground subtraction deepens, and it repeats the fit after subtracting preregistered standard injection-history components such as Silk damping, reionization, and standard astrophysical y-type terms. A real three-template case has to survive all of this bookkeeping together.
mechanism
The protocol locks the shapes before looking at the outcome. Template normalizations, observing bands, and weighting rules for the mu-type, y-type, and transition-window residual are frozen in advance, and R(ν) is explicitly defined before data analysis begins. Foreground subtraction is likewise preregistered rather than rewritten after seeing the fit. The y-type lane is split into anisotropic contributions and the sky-average component so that cluster-correlated or large-scale-structure-correlated anisotropy cannot masquerade as a monopole floor. Band groupings, mask tiers, and model-standard labels are blinded, then only the node, floor, and replication checks are run after unblinding. Finally, both frequency bands and sky regions are held out for adjudication. This is the chapter’s way of proving that a three-template fit was demanded by the residual itself rather than manufactured by analyst freedom.
evidence
The controls are aimed directly at shape fraud. If band labels are permuted or template combinations are swapped, the transition amplitude should lose significance and ν0 should stop being stable. If an apparent floor is really foreground leakage, tighter masks should drive the fitted amplitudes around rather than letting them converge. If changing bandwidth or band splitting shifts ν0 in step, bandpass structure or foreground-fitting degeneracy is still in charge. Injection tests then ask whether synthetic mu-type, y-type, and single-node transition residuals can all be recovered with the correct amplitudes and node. Finally, the subtraction of standard components is perturbed only within preregistered limits; if the transition term appears only at extreme perturbations, it does not count. These tests are what keep the chapter from confusing flexible fitting with a real injection-window fingerprint.
boundary
The pass line requires three simultaneous results: the transition template materially whitens the residuals and remains significantly nonzero in holdouts, the single node ν0 stays stable across masks and independent pipelines, and μ_CMB, y_CMB, and A_r converge to nonzero floor values under independent absolute-calibration chains. Failure is declared when a mu-plus-y fit already reaches noise-like residuals, when ν0 drifts with mask or bandwidth choices, or when the amplitudes collapse toward zero or cannot align across instrument chains without ad hoc renormalization. The named risks are absolute calibration and bandpass non-idealities, spatial variation in Galactic spectral indices, and residual astrophysical y-type structure or point sources leaking into the monopole estimate. The chapter therefore treats template necessity, node stability, and floor convergence as one inseparable adjudication package.
interface
So 33.6 allows a narrow but real success: the residual spectrum may require μ_CMB, y_CMB, and a single-node R(ν), and all three amplitudes may converge to nonzero sky-averaged floors. Yet the compat bridge keeps the meaning of that result under translation. These templates stay as an injection-window ledger and a readout-layer residual account. They do not automatically certify one unique source script, and they do not let later chapters inherit a finished ontology block. If ν0 is unstable or the floors collapse as masks tighten, the case is rejected and the ledger must be reopened before moving to near-ring or later distortion-window chapters. That is why 33.6 hands off carefully to 33.7 and 33.29 instead of claiming that template success has already settled the whole story.