The Factor and the Floor: The Factor Census of the Residue 1.027500 and the Coherent Noise Floor at the Seam

The vacuum catastrophe, in the form this program has carried it, asks for a derivation of the residue 3ΩΛ = 2.055 from inside the Einstein–Cartan frame supplemented by the Aldred Limit, without reading the value off the observed Lambda. One door in the program's search produced a number at the toll's own address: the shear-friction seam, whose named mechanics — membrane-paradigm shear viscosity, a shear rate set by the frame's own crossing scale across the seam's own thickness, friction supplying a two-surface film's tension, and the Young–Laplace relation — produce p/ρ_A = 2.000000, dial-free. The toll thereby factors at the seam as 2.055 = 2 x 1.027500: the 2 is produced, and the factor f 1.027500 is produced by nothing on record. This paper reports the two waves that closed around that factor. The first is a census. Against a candidate set closed in advance — 51 frame quantities in seven groups, plus one flagged control — the factor was tested singly and in every product and ratio of exactly two: 3,927 raw tests, 2,743 deduplicated. There are no exact matches at the pre-registered bar of relative distance 10⁻⁶. The best test, 1.027190 at relative distance 3.020×10⁻⁴, is not taken, on three independent grounds stated in advance: its distance is 300 times outside the bar; it is built from two rounding artifacts of one rounded headline number; and it fails the look-elsewhere correction — a frame-free rational, 37/36, lands closer, at 2.703×10⁻⁴, and a Monte-Carlo null gives P = 0.01725 against a pre-registered survival bar of P < 0.01. The factor is not a recombination of anything on the record. The second wave tests the factor as a fluctuation. Every granular noise scale the frame can name misses the draw δ = 0.027500 by orders of magnitude: cell-count (Poisson) widths at the seam's own counts miss by 16.40 to 17.35 dex, and the frame-statable everpresent width misses by 35.76 dex; the genuine everpresent construction was excluded before computation because its input is Lambda-derived and banned. One class of scale remains. A coherent, single-draw fluctuation of the seam at the seam's own scale — coherence domains of the seam's own thickness on the seam's own surface — gives a width σ = 1/4π = 0.282095, computed from geometry named a wave earlier, and places the draw at z = +0.097485. The draw is unremarkable under that width, and that unremarkableness is priced, not hidden: the probability of a draw at least this close is P = 0.0777, the model's density at the observed factor is 1.4075 per unit f against ~ 10⁶ for an exact derivation at the campaign's standard, and the evidence the portrait carries is the scale-match — the residue's size is the size of the one noise floor the seam geometry supports — not a prediction of the value. The verdict is stated at full size, here and in the conclusion: the catastrophe is not solved. The sealed bar — derive 2.055 from inside the frame — is unmet. A successor bar in noise form — a mechanism derives the mean 2.000000, the width 1/4π, and the draw inside a pre-stated |z| <= 2 band — is presented in this paper as a proposal, unadopted, with its four costs printed beside its terms: the value leaves the theory; the evidence is one draw; the coherence premise becomes load-bearing; and nothing in the proposal transfers to the program's other lock, whose count is still owed.