V31·Act VI · Spacetime

The frozen sky and its angular spectrum

The frozen record map as a full-sphere temperature field beside its angular power spectrum, with the shuffled control drawn faintly underneath.

The relation on screen

C_{ℓ} = \frac{1}{2 ℓ + 1} m \sum ∣ a_{ℓ m} ∣^{2}

The frozen record pattern has an angular power spectrum, computed the way a CMB spectrum is computed.

Symbols

$a_{ℓ m}$: spherical-harmonic coefficients of the frozen field
$C_{ℓ}$: angular power at multipole ℓ

loading angular spectrum

what to look for · Structure above the shuffled control at low ℓ. The control curve is the null hypothesis.

Consensus to physics

01freezeout leaves a fixed record pattern on the observer's two-sphere
02expand that pattern in spherical harmonics
03the coefficients give an angular power spectrum
04compare the spectrum's shape against controls and a reference

In standard physics

The CMB and its C_l curve

A frozen pattern on a sphere, expanded in harmonics, compared to a reference shape. Structurally the same pair of pictures as the Planck all-sky map and its spectrum.

boundary · Not a CMB prediction. The claim level is proxy, the reference is shape comparison only, and no cosmological parameters are derived.

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