Two firms file the same numbers

Timeliness and durability are not separately identified from a reported series

Jason C. Braatz · preprint, posted 2026-08-29 · 60 pages · not peer reviewed, not submitted

A balance sheet reports a thing that is wearing out whether or not anyone writes it down. This paper shows that a prompt reporter of a durable asset and a slow reporter of a perishable one produce numerically identical filings, to fourteen decimal places, while the physical stocks behind them differ by a factor of 250,000. That collapses a large family of accounting comparisons, and the paper is equally clear about the prediction of its own that failed.

Abstract

Model the reporting layer of a balance sheet as a low-pass filter on a physical layer that degrades whether or not anyone records it: a share φ of each true change passes through at once, the remainder released at rate α from an unrecognised gap, against a physical decay rate δ.

The triples (α, δ, φ) and (δ, α, φδ/α) generate the identical reported series. The filter's two roots exchange and the exchange preserves φδ exactly, so a reported series contains the product of timeliness and decay and nothing further about either. A prompt reporter of a durable asset and a slow reporter of a perishable one file the same numbers to fourteen decimal places while their physical stocks differ by a factor of 250,000. Where the asset's physical scale is unobserved, which is every firm-level series, the ambiguity is not two-valued but a continuum: a factor of 1.67 in that unobserved scale sweeps φ across the entire unit interval.

The corollary is cross-sectional and it is sharp. Classes are ordered by (1 − φ) ⊙ δ, divided elementwise by (α − δ): not by φ. On the four GAAP asset classes, with the decay rates the standards themselves imply, the composite does not blur the intended ranking; it inverts it, Kendall τ = −1. Drawing δ independently across classes, the intended ordering survives in 11.5% of 4,000 ladders. The boundary between the region where such a design works and the region where it does not is exact, is drawn in quantities the design already declares, and sits at a δ-leverage-to-budget ratio of 0.61; the GAAP ladder sits at 2.58. This constrains every cross-sectional conditional-conservatism comparison, because the burden it moves is the burden of showing that asset life is constant across the compared groups.

The repair follows from the theorem rather than from any empirical finding: anything supplying δ from outside the series restores φ. Returns do it, at a price that is a rate rather than a proof and that runs backwards for the slowest assets. Disclosed useful lives do it for free, for the two classes the standards put on a schedule, and license a within-life-band design that needs no new data. At δ = 0 there is no parameter to recover, because φ has left the dynamics.

The framework's sharpest prediction, recognition lag ordered by GAAP asset class, was pre-registered, tested on 688 EDGAR-derived events across two sectors declared in advance, powered at 0.95–1.00, and failed (Jonckheere–Terpstra z = −0.290, −0.095). §9 reports the failure at full length and §10 states exactly what it retracts. The identification result does not excuse it: the one statistic the composite spares is the timing statistic the registration used, and what defeated that registration was a second identification gap upstream of the first.

Keywords: identification · conditional conservatism · reporting lag · impairment · observational equivalence · asset life · pre-registration
JEL: M41, D80, C18, G14, E01

The other preprint: A levy cannot tax what its base cannot see