Bundle review table

02-building-shape

README.md

# Test 02 — Building energy use is set by the envelope-to-volume ratio

**Result.** Not supported, and not really testable as posed. Across 27,403 New York City buildings with a disclosed energy benchmark and a matched tax lot, the envelope-to-volume ratio is almost a restatement of floor area and height: it correlates at −0.90 with log floor area and −0.49 with log floor count. Neither measure orders energy intensity. The rank correlation between site energy use intensity and the shape ratio is +0.04 overall, −0.06 in offices and +0.08 in multifamily; for floor area it is −0.09, +0.08 and −0.12. A model with use type alone explains 4.0% of the variance in log intensity; adding floor area changes it to 4.0%, adding the shape ratio to 4.1%, and the fullest model, with occupancy, decade built and building count, reaches 6.7%. Cross-validated R² is essentially identical for floor area and shape (difference −0.0001, 95% bootstrap CI −0.0004 to 0.0000).

There is one small, weak signal in the claim's direction: at fixed floor-area decile, use type and occupancy, a tenfold increase in floor count is associated with 1.2% lower intensity (coefficient −0.012 on log10 floors, SE 0.0071, p = 0.09), and it is confined to housing — in commercial buildings the same coefficient is strongly positive. The claim that intensity should "collapse onto" the ratio is not what the data show.

## What was tested

The hypothesis is quoted verbatim in `hypothesis.md`: building energy use is set by the ratio of envelope area to volume rather than by floor area, so a compact tall building can use less energy per square metre than a low sprawling one "despite more glazing". Predictions: intensity collapses onto the envelope-to-volume ratio (P1); compact buildings outperform sprawling ones (P2); glazing matters less than shape (P3). Refutation: intensity tracking floor area at controlled shape would restore the benchmark.

## Method

- **Energy.** NYC Local Law 84 disclosure, calendar years 2022–2024. The latest year available per property is kept; site EUI in kBtu/ft² is converted to kWh/m² (×3.154). Records outside 10–600 kWh/m², 200–200,000 m² of floor area, 1–100 floors, built before 1800, or with occupancy outside 5–100% are dropped.
- **Geometry.** PLUTO tax-lot attributes joined on BBL, keeping the largest building area per lot. Footprint = gross floor area ÷ floor count; height = floors × 3.2 m; envelope = perimeter × height + roof, with a square footprint; volume = footprint × height. Shape ratio = envelope ÷ volume (m⁻¹). This is an estimate from a square-footprint assumption, not a survey geometry.
- **Sample.** Eight use types with at least 200 buildings: multifamily (21,096), office (2,436), K-12 school (1,971), hotel (715), warehouse (430), retail (315), mixed use (238), college (202). **27,403 buildings.**
- **Models.** Log site EUI on use-type dummies plus log floor area, log shape ratio, log floors, occupancy, decade built and log building count; OLS. Out-of-sample R² from grouped 5-fold cross-validation by property id.

## Result

**The ratio is not a separate variable.** Because footprint is estimated as floor area ÷ floors, the shape ratio is a deterministic function of the same two quantities: 4/√(area per floor) + 1/height. Its correlation with log floor area is −0.896. Any test that puts both in a regression is asking which algebraic combination fits better, not which physical mechanism governs energy use.

**Neither fits.** Table of in-sample and cross-validated R²:

| Model | In-sample R² | 5-fold CV R² |
|---|---:|---:|
| use type only | 0.0404 | 0.0395 |
| type + log floor area | 0.0404 | 0.0394 |
| type + log shape ratio | 0.0405 | 0.0395 |
| type + floor area + floors | 0.0410 | 0.0400 |
| type + area + shape | 0.0407 | 0.0397 |
| full (area, floors, occupancy, decade, buildings) | 0.0672 | 0.0659 |

The shape coefficient in the area-plus-shape model is −0.097, which is the wrong sign for the claim (higher envelope-to-volume goes with *lower* intensity), and it is an artefact of the near-collinearity. In the office-only model, floor area has a positive coefficient (+0.046, p = 0.001): bigger offices use slightly more per square metre, not less.

**Deciles.** Median intensity rises from 225 kWh m⁻² in the smallest floor-area decile to 206 in the largest — a 9% decline across three orders of magnitude of size. Across shape-ratio deciles it is non-monotonic: 205, 209, 210, 219, 222, 228, 232, 231, 229, 201.

**P2, weakly.** At fixed floor-area decile, type and occupancy, the coefficient on log floors is −0.012 (SE 0.0071, p = 0.09): taller buildings are about 1% less intense per tenfold increase in height. This is consistent with a small compactness or scale benefit in housing, but it does not survive as a significant effect, it reverses in commercial buildings (log-floors coefficient +0.197 when multifamily is excluded), and it does not rescue the claim's stronger form.

**P3 is not testable here.** The disclosure data contain no glazing area, so the prediction that glazing matters less than shape cannot be evaluated. We did not substitute window-to-wall ratio estimates from another source.

## Sensitivity

- **Excluding multifamily** (n = 6,307 commercial, institutional and warehouse buildings) raises the full model's R² to 0.152 and reverses the height result: the coefficient on log floors is +0.197 (about 57% higher intensity per tenfold increase in height), with floor area at +0.037. In non-residential New York, taller buildings at a given floor area are *more* intense, not less. P2 fails in the sector where one would most expect envelope geometry to matter.
- **Single-building lots** (n = 25,702): R² 0.0666, conclusions unchanged.
- **Without the occupancy control**: R² 0.0598, so occupancy is not masking a shape effect.

## What this test cannot see

Footprint is inferred from floor area and floor count, so the shape ratio is not independent data — this is the central limitation, and it is why the claim cannot be cleanly separated from the benchmark it opposes. EUI is measured at the property level and mixes tenant loads, heating fuel choice, and occupancy schedules; occupant density, which the data record only crudely, is likely to dominate. The data are one city, one climate, and buildings that comply with a disclosure law — not a random sample of the stock. Glazing, insulation, HVAC efficiency and envelope age are unobserved. And because the design is cross-sectional, it says nothing about what happens when a building is made more compact.

## Disclosure

Designed and executed with AI assistance (DeepSeek, via its coding agent). Not peer reviewed. This is an analysis of public benchmarking data, not architectural, engineering or energy advice.

---

*Figures: `figures/eui_by_floor_area_type.png`, `figures/eui_by_floor_area_decile.png`, `figures/eui_by_decile.png`. Numbers: `results.json`. Data: `data.csv`. Sources: `SOURCE.md`.*

hypothesis.md

# Hypothesis, quoted verbatim, and pre-specified criteria

**Source.** *Original Theories*, Volume VIII, entry 98 (slug `building-shape-ratio`), Incoprea research notebook (`incoprea.com/research`); corpus export `frontier-theories-8/build/data_v8_5.py`.

## The claim, verbatim

> Building energy use is set by the ratio of envelope area to volume rather than by floor area, so a compact tall building can use less energy per square metre than a low sprawling one despite more glazing.

**Predictions, verbatim.**

- P1: Intensity should collapse onto the envelope-to-volume ratio.
- P2: Compact buildings should outperform sprawling ones.
- P3: Glazing should matter less than shape.

**Refutation, verbatim.**

> Intensity tracking floor area at controlled shape would restore the benchmark.

## Operationalisation

- **Unit.** A New York City property with a Local Law 84 energy disclosure for calendar year 2022, 2023 or 2024, and a tax lot in PLUTO. The latest disclosed year per property is kept.
- **Outcome.** Site energy use intensity, converted from kBtu/ft² to kWh/m² per year (× 3.154). "Site" rather than "source" because the claim is about the building, not the supply chain.
- **Shape ratio.** Envelope area ÷ volume, in m⁻¹. Footprint = gross floor area ÷ floor count (PLUTO `bldgarea` and `numfloors`); height = floors × 3.2 m; envelope = perimeter × height + roof, assuming a square footprint; volume = footprint × height.
- **Floor area.** Gross floor area from the disclosure, in m².
- **Controls.** Use type (eight categories), year built, occupancy, number of buildings on the lot.
- **Sample.** EUI 10–600 kWh/m², floor area 200–200,000 m², 1–100 floors, built after 1800, occupancy 5–100%, one of eight use types with at least 200 buildings.

## Pre-specified support and refutation

The test is **supported** if:

1. P1: the shape ratio explains materially more of the variance in log intensity than floor area does, in a model with use-type fixed effects — the difference in R² must exceed 0.05, and it must survive out-of-sample (grouped 5-fold cross-validation by property).
2. P2: at fixed floor area, taller buildings have lower intensity — the coefficient on log floors must be negative with a 95% bootstrap interval excluding zero.
3. The direction is consistent: higher envelope-to-volume means higher intensity (a positive coefficient) when floor area is not controlled.

The **refutation** holds if intensity tracks floor area at controlled shape, i.e. if floor area's coefficient is larger and more precise than the shape ratio's, or if the two cannot be separated.

**P3 is not testable with this dataset.** The disclosure contains no glazing area or window-to-wall ratio. We say so and do not substitute an estimate from another source.

## Named before running: the identification problem

The shape ratio is constructed from floor area and floor count. It is therefore not an independent variable, and a regression containing floor area, floors and shape together is comparing algebraic combinations. The test will report the correlation between the shape ratio and floor area, and will treat near-collinearity as a finding rather than as a nuisance to be controlled away.

## What would change the answer

Measured building footprints and heights (rather than floor area ÷ floors), window-to-wall ratio, and envelope thermal properties. With those, the ratio could be separated from size. Without them, a null result is evidence about the measurement, not about physics.

## Sensitivity analyses (named before running)

1. Exclude multifamily housing, leaving commercial, institutional and warehouse buildings.
2. Restrict to single-building lots.
3. Remove the occupancy control.
4. Split the sample by floor-area decile and compare the taller and lower halves within decile.

Included code and results

• tests/02-building-shape/data.csv
• tests/02-building-shape/results.json
• tests/02-building-shape/run.py