How the Index is worked out.

Three numbers multiplied, not added.

The Index reads one city at a time, set against the natural region it sits in. At time $t$ it is the product of three terms drawn from the twenty-cell Full-Stack Metrics matrix: four pillars across five scales, from a neighbourhood to the natural region:

Multiplying matters. A city full of fab labs that still imports everything scores low, because DIDO alone is not enough. A city that imports little because it has stopped doing much scores low too. Only the combination counts: the capacity to make, a real drop in what comes in and goes out, and readings that turn into action. The $(1-\mathrm{PITO}_t)$ term turns PITO from a load into the distance a city has moved away from buying far and throwing away near.

The version that answers the pledge is the change in the score over time, $\Delta\mathrm{FCI}/\Delta t$, which is why the Index needs sources that update at least every quarter, and why nodes exist. That quarterly change is what a PLANETAI node reports.

PITO and DIDO.

Every city takes things in and puts things out. PITO, Products In, Trash Out, is the old, one-way version: buy what you need far away and throw it away nearby. PITO measures what the city receives and rejects: imports of products, energy, food and raw materials; exports of waste, emissions and pollution sent elsewhere. It is a stock variable in $[0,1]$; high PITO means a city that mostly buys far and throws away near.

DIDO, Data In, Data Out, runs the other way: sense what is happening, share designs and know-how, make more nearby. DIDO measures what the city generates and circulates: open data infrastructure, fab-lab activity, distributed manufacturing capacity, recycling and remanufacturing capacity, community sensing, institutional transparency, and the policy, research and innovation layer that lets the city act on what it knows. High DIDO means the city has built, and uses, the capacity to replace imported products with local design and local making.

The terms were coined by Vicente Guallart and Neil Gershenfeld in the early Barcelona Fab City period, and are documented in the 2014 and 2016 Fab City white papers (Diez). We are not inventing them. We are operationalising them.

Why both axes, why not collapse to one. A city can have very high DIDO and still very high PITO (Barcelona is closer to this than people would like). A city can have low DIDO and low PITO for bad reasons: too few sensors hiding both flows. The two-axis frame keeps the diagnostic crisp. A single-number index hides this; the original 37/100 is a single number and its weakness is exactly that you cannot tell what is happening underneath.

From cell scores to the two numbers.

Here is how the twenty cell scores become the two numbers, and then the index. Each cell $c$ produces a normalised score $s_c \in [0,1]$ using the rule Boeing used: priority × self-sufficiency where formal data exists; documented proxy where it does not, marked live, partial or mock, so a reader always knows how far to trust it. Every score lands in one cell file, in the format fci-cells-v0. PITO and DIDO at time $t$ are weighted means of cell scores under their respective weight assignments:

$s_c^{\text{extractive}}$ is the cell's score interpreted as throughput; $s_c^{\text{capacity}}$ is the same cell's score interpreted as regenerative capacity. Both indices are bounded in $[0,1]$. Most cells contribute to one side meaningfully and the other faintly, in proportion to their weights; only Economic × City (0.5 / 0.5) and Environmental × Community (0.5 / 0.5) contribute to both axes equally.

Missing data is weighed in the DIDO column (v0). DIDO is how much a place senses and shares, so a cell with no open data counts 0 there, and its DIDO weight stays in the sum: a city that publishes nothing about a cell loses that cell's share of DIDO. A cell nobody has measured drops out of PITO instead, so the absence of data is never read as throughput. Lack of data is therefore not a gap in the Index but one of its weights. A worked example, Barcelona, is under Scores so far.

Why Paris and Hamburg both got 37.

Boeing's Hamburg score and Utopies' Paris score are both one cell, one moment: Economic × Region (or × City, depending on data scope), with no DIDO term and $\rho$ taken as 1.

Set every weight to zero except that one cell, drop ρ, and compute self-sufficiency only:

The derivation also exposes the structural reason both cities scored ~37: at Economic × Region with public data only and no dynamic component, the most diversified Western metros land at the same bound because the underlying material flows are governed by global supply-chain structure, not local policy. The way to move the number is by activating DIDO and ρ: exactly what the Index measures.

ρ: does anything happen?

$\rho_t$ is a number between 0 and 1. It is the share of what a place learns that somebody responds to within a set time. At 1, every reading gets a response in time. At 0, readings are made and nothing is done. Paris and Hamburg were scored as if ρ were 1, because a one-off study has no way to measure it. A node measures it every day: node #1 in Bali counts each thing it flagged and whether anyone acknowledged or acted on it within 24 hours, and publishes the result. The exact rule and the current number live on the node.

What is not settled.

1. Twelve of twenty cells have real content. The region scale and governance at region and natural-region scale are the thinnest.
2. The weight table is v0; three cells need a stronger argument.
3. The Hamburg check is sketched, not worked through on public NACE and COICOP data. That worked example is owed.
4. The ρ rule is drafted on the node; how ρ is weighted across scales, and what counts when a council says no, are open.
5. Vivanco's matrix is a working paper and a 2025 thesis, not yet peer reviewed on its own.
6. Utopies' LOCAL SHIFT and LOCAL FOOTPRINT are proprietary; we cite the published method and the 2018 numbers, not their simulator.