# 2. Invariants and the Sector Model

## Why use invariants?

The project needs a stable set of environmental variables that can be compared across sectors and historical periods. The word **invariant** means a recurring analytical parameter, not a variable that literally never changes.

Two nine-item lists currently exist. They should be treated as two layers rather than competing final versions.

## Layer A: derived civilizational pressures

The original seed names these higher-level effects:

1. Thermodynamic gradient
2. Solar insolation curve
3. Latitude resource bell curve
4. Population-density decay
5. Tributary empire limit
6. Panopticon communication threshold
7. Water-scarcity organization
8. Seasonality cognitive pressure
9. Geophysical bottlenecks

These are useful for describing how physical conditions may become social and institutional pressure.

## Layer B: measurable environmental variables

The more operational template uses:

1. **Solar insolation** — kWh/m²/day; affects agricultural and energy ceilings.
2. **Precipitation and water budget** — mm/year and seasonal distribution; affects carrying capacity, storage, and disease ecology.
3. **Elevation relief** — meters and slope; affects flow, defensibility, mining, temperature, and transport.
4. **Soil carbon and mineral matrix** — a documented soil-quality composite; affects agricultural surplus.
5. **Geological mineral concentration** — ore grade or resource density; affects technology and extraction incentives.
6. **Biome primary productivity** — ecological productivity; affects food, fuel, and population possibilities.
7. **Atmospheric circulation cell** — Hadley, Ferrel, polar, monsoon, and related circulation; affects wind, rainfall, and navigation.
8. **Tidal amplitude** — meters; affects harbor timing, fishing, and coastal infrastructure.
9. **Seismic and volcanic activity** — frequency or hazard index; affects construction, fertility pulses, geothermal opportunity, and sudden destruction.

This layer is preferable for actual analysis because it can be tied to sources, units, uncertainty, and sampling decisions.

## Relational parameters

A sector cannot be understood in isolation. Proposed neighbor and corridor variables include:

- elevation gradient;
- climate-zone difference;
- watershed flow direction;
- wind-corridor channeling;
- resource complementarity;
- migration-route viability;
- fire-spread potential;
- transport and communication access;
- distance to ports, passes, rivers, and energy infrastructure.

These variables turn a static map into a system of pressures and flows.

## Four emergent sector types

The template proposes four provisional types:

| Type | Signature | Possible pattern |
|---|---|---|
| Exporter | unusually high mineral, energy, or biological surplus | extraction zone, protected trade hub, low or uneven population |
| Importer | high density with resource deficit or low local complementarity | manufacturing, services, supply dependence, innovation pressure |
| Transit corridor | watershed, wind, maritime, rail, or mountain chokepoint | taxation node, strategic contest, cultural mixing |
| Isolated microgrid | low migration viability plus high environmental difference | local adaptation, late integration, distinctive institutions |

These are analytical labels. They should not be treated as fixed identities.

## Sector record

A complete sector record should eventually include:

```text
sector_id
coordinates and boundaries
physical variables with units and source provenance
neighbor relationships
resource and energy profile
population and settlement history
transport and communication links
historical energy regime
comprehension indicators
quadrant trajectory
confidence and missingness fields
counterexamples
```

## Water as a cross-cutting variable

Water is not just one invariant. It links:

- precipitation;
- soil and agriculture;
- river direction;
- settlement density;
- hydraulic engineering;
- disease and health;
- energy generation;
- migration;
- political coordination.

The Anthrocybernetic Water Systems module provides a related systems vocabulary: input, storage, release, transformation, return, observation, and safety boundary. That vocabulary can help describe infrastructure without claiming that water stores semantic memory.

## Evidence discipline

Every sector variable should be marked as:

- measured or directly sourced;
- modeled from a stated proxy;
- historically inferred;
- uncertain or missing;
- interpretive.

A colorful map with complete-looking cells must not be allowed to imply complete knowledge.