Why this note exists

The geometry census yields a small set of design rules in the spirit of a pattern language, but with a property Alexander’s patterns lack: each is stated over a measured scope and carries an explicit falsifier: the observation that, had it held, would have refuted the rule.¹ The rules are descriptive regularities over a complete enumeration, not validated hypotheses about an unobserved population; the falsifier is what the census could have shown and did not. The set is deliberately small and honestly bounded: where an apparent regularity proved to be a base-rate coincidence, it is reported as such rather than presented as a pattern. Size-based rules describe the dimensioned subset (the habitable rooms); count-based rules use the complete inventory.

1. The rules

DR-1: Scale by count, not by dimension. A larger Australian project home is the same standard rooms repeated more often, not the same rooms enlarged. Scope: two- to five-plus-bedroom dwellings (bedroom count, independent of dimensioning). Evidence: the median space count rises about 69 per cent (13 → 22 spaces). Median room area moves only 12 per cent on the median, 27 per cent on the mean; living area is flat near 22 m². Falsifier: had per-room area scaled with the count, the rule would fail. Caveat: the pooled bedroom median falls as bedroom count rises, but this is a composition effect: a rising share of smaller secondary bedrooms, not a shrinking of any one room. The main bedroom in fact grows, 12.3 → 16.8 m².

DR-2: Rooms lengthen faster than they widen. As rooms enlarge they grow in both dimensions, but the long side grows faster than the short, so the aspect ratio rises. A strong modal short side sits at 3,000 mm. Scope: dimensioned rooms across all categories. Evidence: across long-side quintiles the median long side rises from 3.0 to 6.7 m (×2.2) while the median short side rises only from 2.6 to 4.6 m (×1.8). The median aspect ratio climbs from 1.11 to 1.55, and the single most common exact dimension is 3,000 × 3,000 mm. Falsifier: had the short side grown as fast as the long side, the rule would fail.

DR-3: Containment makes a space small and tight; openness makes it large and variable. A space’s size and variability are governed more by its containment than by its nominal type. Scope: all spaces, read through the componential primitives (enclosure, location, edge). Evidence: enclosed spaces sit at a median 12.2 m² (QCD 0.32), open spaces at 16.7 m² (0.48). Internal sit at 12.3 m² (0.32), external at 16.4 m² (0.51). Walled sit at 12.2 m² (0.32), unbounded at 17.7 m². Falsifier: had the enclosure and location primitives not separated size and spread, the rule would fail.

DR-4: Obligation predicts the opening. The opening between two spaces encodes the strength of their coupling: the doorless open-threshold share rises monotonically with how obligatory the adjacency is. Scope: realised interior openings, classified by coupling class. Evidence: the open-threshold share is 22.2 per cent on required (HARD) adjacencies, 8.6 per cent on preference (SOFT), and 4.0 per cent on insufficient; a plain door dominates throughout. Falsifier: had the open-threshold share been flat or higher on weak couplings, the rule would fail. Caveat: this characterises the opening type over the geometry graph (which realises only about 272 of roughly 680 category pairs); the canonical 49-HARD / 50-SOFT coupling split rests on the topology graph (the 15,957-zone access basis), not on the geometry read.

DR-5. A single genuine higher-order bundle: the premium tier. Beyond the obligatory core, only one room co-occurrence rises materially above its base rate: where a dedicated media room is drawn, an alfresco is present 86 per cent of the time against a 61 per cent base rate (co-occurrence ratio about 1.4): a discretionary premium-tier marker. Scope: the discretionary feature set across all 745 plans. Evidence: by contrast the candidate “master suite” (walk-in robe → ensuite, ratio 1.06) and the open kitchen-living-dining co-presence (ratio 1.01) sit at their base rates: coincidences, not patterns. The 745 plans realise about 723 distinct category-presence patterns. Falsifier: had media → alfresco sat at its base rate, there would be no premium-tier rule. The rule deliberately does not claim a rich bundle grammar. Australian plans are near-uniquely composed from a shared obligatory core (secondary bedroom, kitchen, bathroom, living, laundry, each in ≥ 90 per cent of plans), not assembled from recurring higher-order modules.

DR-6: Form follows fixed content. The rooms sized to a fixed physical object are the most dimensionally standardised; the rooms that absorb residual area are the most variable. Scope: all dimensioned categories, ranked by area QCD. Evidence: most standardised: garage (QCD 0.087), main bedroom (0.145), media (0.154); most variable: store (0.637), porch (0.568), alfresco (0.408). Falsifier: had fixed-content rooms shown spread comparable to leftover rooms, the rule would fail. Caveat: it is fixed content, not fixture count, that drives standardisation.

2. Positioning

This rule set extends Alexander’s pattern-language method (qualitative, author-asserted) by reading each rule’s context and parameters off a complete enumeration and attaching a numerical falsifier; it relates to the shape-grammar tradition by offering a measured rather than author-specified generative vocabulary;² and it reads the plan graph through a HARD/SOFT coupling contract rather than space- syntax integration measures.³ All descriptive over a census; CANDIDATE until operator MR-13.