Book Two

The Missing Term

Correcting the Independence Assumption

The Rogue Wave proved the error exists. This book corrects the formula — seven governing equations, seven domains, one measured number inserted in one place.

Rhombus Tech · 2026

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7Governing formulas corrected: supply chains, software SLAs, power grids, polypharmacy, structural engineering, aviation redundancy, climate ensembles.
1The correction is always the same: find the independence assumption, measure d, replace p with dp.
3–7Forty CMIP6 climate models behave like a handful of independent ones (3 to 7 with illustrative correlations). A confidence interval that treats them as independent is 3× too narrow.

The seven corrections

Every formula had the same error

Each domain has a governing equation that institutions trust, regulators enforce, and practitioners use daily. Each one assumes independence. Each one is wrong by dn .

Ch 3 · Supply Chain

The Chain

1 − qn → 1 − (dq)n

Six coupled suppliers at d = 1.8: the model is 34× too optimistic. The 2021 semiconductor shortage cost $210B.

Ch 4 · Software

The Update

1 − fn → 1 − (df)n

Two backups sharing infrastructure with d = 5 give four and a half nines, not six. CrowdStrike took down 8.5 million devices.

Ch 5 · Power Grid

The Grid

∏ qi → ∏ (d·qi)

During Uri, with d = 2.5, ten generators failing together was 9,500× more likely than the standard said. 246 dead. $195B.

Ch 6 · Medicine

The Dose

1 − ∏(1−ri) → 1 − ∏(1−d·ri)

Five drugs sharing CYP3A4 at d = 2: adverse-event rate nearly doubles. Opioid–benzo co-prescription: about 3.9× the overdose-death risk.

Ch 7 · Structural

The Building

(n/m) pm → (n/m) (dp)m

Five coupled columns at d = 3: 243× more likely to fail together. Champlain Towers collapsed in 12 seconds. 98 dead.

Ch 8 · Aviation

The Redundancy

pn → (dp)n

Triplex redundancy with d = 10 gives 10−6, not 10−9 — 1,000× worse than the safety case claims. The 737 MAX safety case leaned on the crew as the backup; 346 died on two flights.

Ch 9 · Climate

The Ensemble

σ/√n → σ/√neff

40 models behave like 3–7 (illustrative correlations). The confidence interval is ~3× too narrow. The correction does not change the central estimate; it widens the tails of ensemble-based projections.

Inside the book

Three parts, twelve chapters

Part I restates the law. Part II corrects seven formulas — each chapter opens with the standard equation, marks the independence assumption, writes the corrected version, asks what would have been different, and names the barrier. Part III turns the correction into practice.

Part I · The Correction

1
The Error
The dn law restated in one chapter.
2
The Crossover
When adding components makes the model worse, not better.

Part II · The Formulas

3
The Chain
Semiconductors. Six suppliers, one coupled system.
4
The Update
CrowdStrike. Total coupling at the kernel.
5
The Grid
Winter Storm Uri. The gas–electric feedback loop.
6
The Dose
Polypharmacy. Five drugs, one enzyme.
7
The Building
Champlain Towers. The phase transition from crack to collapse.
8
The Redundancy
737 MAX. When backups share a failure mode.
9
The Ensemble
Climate models. Forty models, seven independent.

Part III · The Practice

10
The Monitor
A dashboard: one number, updated weekly, that says how wrong the model is right now.
11
The Trend
Coupling is rising. The error is accelerating.
12
The Barrier
Why the correction hasn’t been adopted, and what it would take.

Book Two

Where this book fits

The Rogue Wave proves the error exists and measures it. The Missing Term corrects the formulas. You can read this book on its own: it restates the law in Chapter 1 and gives you everything you need to apply the correction.

Book 1: The Rogue Wave