The Equatorial Witness: The Cold = −Profile Branch of the Founding-Profile Reading of the CMB Cold Spot Fails Falsifier F-CS1 on the Planck PR3 Sky

Result note for Paper 2 of the CMB anomalies series, 'The Cold Spot at 123.4 Degrees' (DOI: 10.5281/zenodo.24039066). Paper 2 showed that the founding profile at multipoles {2, 3} can place a cold ring at the CMB Cold Spot's polar angle, 123.40 degrees from the alignment axis at galactic (-100, 60), on exactly one surviving branch: temperature proportional to the negative of the profile (cold = -profile) at A3/A2 = +2.1406. That branch carries a sharp, amplitude-free prediction: because the octopole vanishes identically at 90 degrees from the axis, the azimuthal average there must be hot, at +0.1592 of the axis cold depth. This note reports the pre-registered measurement of that average on the Planck PR3 SMICA map (77.6% of sky after the common mask, Nside 512). The measured equatorial witness is cold: -6.02 microK, computed identically from the ring table and from the raw pixels (N = 32,400), at W/D_pt = -0.2774 against the predicted +0.1592. Four of six pre-registered clauses fail; two pass (a hot ring at 71.5 degrees, and a cold ring at the Cold Spot's latitude, deeper than predicted). A rotated-axis null (1,000 random axes, seed 20261108) returns p_raw = 0.7280 and p_joint = 0.2110. A verification rerun (geometry assertion 123.399 degrees passed, input-dipole audit +0.3 microK, inpainting-mask variant graded) reproduced the result exactly; the executed notebook is deposited with this note. Verdict: the cold = -profile branch fails falsifier F-CS1, finally, and with it the founding-profile account of the Cold Spot at {2, 3}. Scope, printed exactly: F-CS2 and F-CS3 are not graded by this measurement; the bounce/torsion framework's remaining claims are not executed by this test; Paper 2's constraint on the standard reading (the Eridanus supervoid supplies about -20 microK against the spot's about -150 microK central decrement, a minority contribution at standard amplitude) is untouched.