Scaling laws for household continuity

1Introduction

Continuity was, for most of history, unmeasured. Households continued or did not, and the difference was noticed afterward, by relatives. The platform era made continuity a quantity: something delivered, metered, and billed at the standard tier. A quantity can be scaled. This paper reports how it scales.

Prior work established the unit [3] and the pool [2]. We take both as given, the way one takes the meter as given, because we issued it.

2Setting and data

Our corpus spans 2027 to the present: 14.2 million households of record, observed continuously. All measurements derive from pooled operational data. Consent occurred at enrollment, and has therefore been in effect for some time [5].

We measure three quantities per household: memory volume (what is kept), filtration load (what is kept instead of delivered), and warm count density (who is near, and how much). Each is logged at the resolution the household would choose, had it been asked.

3Results

All three quantities follow power laws in household count over three orders of magnitude. Memory volume scales with exponent 1.12: households remember superlinearly, together. Filtration load scales at 0.97, just under linear; filtering is the only quantity that gets easier per household as the pool grows, which the pool appreciates. Warm count density scales at 1.41.

The exponents differ. Their pairwise ratios converge on 1.412, a constant the reader will recognize from elsewhere in the corporation, where it also appears without explanation.

Extend the right edge The reader may check for the ceiling personally.

4On the ceiling

A natural question is whether these laws bend: whether there exists a household count beyond which continuity saturates. We find no evidence of a ceiling. We looked in the way one checks a locked door: to confirm, not to open.

We additionally fit saturating forms to the data. The saturating forms fit worse, and seemed embarrassed to have been tried.

5Discussion

Continuity scales because households do not stop being households. They accumulate memory, shed deliveries into filtration, and warm toward one another at a rate slightly faster than they grow, which is the exponent doing what exponents do.

The practical implication is stated in the annual report [6] and practiced on the shelf. The scientific implication is this paper, which now exists, and is noted as read.