The Surviving Count, Audited: Counting Conventions, the Repaired-Density Re-Grade, and the Present Size of the Gap

The vacuum-energy problem in the torsion frame has two halves with separate grades. The dissolution is established: the traditional 10^122 figure is the output of a counting procedure, not a measurement, and in the frame it collapses to one finite number, the surviving count. The count has not been produced: the assembly at DOI 10.5281/zenodo.24082360 proved at inventory tier, over fourteen denominated roads, that no construction from the frame's owned statements returns it. This paper tests the remaining hypothesis about that failure: that the gap is an artifact of the counting itself, a mismatch of counting conventions between the required side and the constructed side. A line-by-line audit reconstructs every convention entering the required count N* and prints its sensitivity; rebuilds the nearest constructed counts (the seam statement's 287, the premise pair's 282) term by term; and applies seven candidate single counting rules, each graded. The ledger is re-graded at the density the frame now derives, rho_A = 2.92 x 10^55 g/cm^3 (the coefficient repair, DOI 10.5281/zenodo.24113586), which supersedes the published value the November 9 grading used. Findings: no counting convention enters N* at all - it is a logarithm of a ratio of two densities, and its fractional part is a property of the measured ratio, not of the notation. The density repair moves the production target from 281 to 283, an integer no construction on record returns; the premise pair's exclusion stands at the governing density with its miss reversed in sign (282 against the required 282.6928, miss -0.6928), and the closest owned count, 287, misses by +4.3072. Of the seven candidate rules, two land arithmetically only at the superseded density, one lands at the governing density and is refuted by the register's own arithmetic (the split 200 + 211 = 411 is exhaustive; there is no 412th cell), and the rest are insufficient, re-denominations, or redefinitions of the quantity graded. The verdict: the remainder is not in the counting. The statement whose addition would produce the count is re-denominated at the governing density (landing windows for the gated total T = 283), and the programme's falsifier re-arms there. Every quantity the paper derives is computed by the deposited script counting_audit.py from the stated inputs. AI-use disclosure: this paper was prepared with the assistance of Dave, an AI system; the author of record is William Alexander Aldred.