I was debugging a polygon-overlap test that worked locally and failed on the server. Same code. Same input. Different answer.

The function deciding the answer was small. Three points A, B, C; return the sign of (B - A) cross (C - A). That sign tells you whether a vertex is convex or reflex, whether a diagonal stays inside the polygon, whether a point is above a line or below. On x86, LLVM had folded the multiply and the subtract into a single fma — one rounding step instead of two. On WASM there is no FMA, so two roundings. A vertex sitting in the epsilon neighborhood of zero fell on opposite sides. From one bit of disagreement, the whole decomposition forked.

This wasn't a bug in my code. It was IEEE 754 working as advertised. The standard pins down the storage format. It does not pin down behavior. Reassociation, FMA contraction, x87 registers at 80 bits, denormal flush flags — four separate ways to get a different answer from the same inputs. Tightening tolerances doesn't help: convex decomposition is discrete. A vertex is reflex or it isn't. An epsilon at the input is a binary difference at the output.

So I wrote exact-poly, a 2D geometry library that uses no floats at all.

A 10-vertex star decomposed into 5 convex parts. Vertex labels (v0–v9) match input order; part labels (p0.0–p5.3) are emitted by the cascade. Sum of part areas equals the ring area, exactly.

A friend of mine drew the same coastline four times before he registered the parcel. Each time he zoomed in to look at the boundary he disliked something — a kink, a corner that veered wrong, a strip he'd forgotten. He kept fiddling. He didn't buy.

This is the standard problem with property platforms. You can't customize until you own. And owning, on most chains, is a chore: connect a wallet, fund it, sign a transaction, watch a confirmation, hope the tile renders. You spend the first thirty minutes proving you're worthy of expressing yourself. By the time the system lets you draw, you're tired, and you've already decided whether you care.

That order is wrong.

Imagine a global map simulation, a distributed land registry, or a radio frequency allocator. They all share one unbreakable rule: two people cannot own the exact same space. Polygons must not overlap.

Traditional GIS solved this decades ago. But doing it on-chain—inside a strictly consensus-driven network without external servers—has long been considered impossible. Compute limits were simply too strict.

I wrote Mercator, an open-source spatial indexing library for Sui. It lets you register polygons of any shape directly in a smart contract, mathematically guaranteeing zero overlap.

Registering a 4-vertex polygon in Mercator costs about $0.0065. Registering twenty polygons costs exactly the same. The system scales logarithmically, not linearly. To achieve this, I didn't invent anything new. I just borrowed algorithms from 1990s game engines: the Separating Axis Theorem (SAT) for collision detection, and the Morton Z-curve for indexing.

Why are these classic tools only becoming smart contract primitives now? The answer lies in data model architecture. This code simply will not run on EVM, Solana, or Aptos. Here is why.

Enough theory. The map is live.

Open merca.earth today, pick a place, draw a parcel, register it on Sui mainnet. Buy someone else's parcel. Expand your territory. Collect tax from places inside it. Shape the visual layer with a name, description, and artwork.

This is not a waitlist. Not a whitepaper promise. People are already claiming, competing, and making meaning on the map.

Marvin Hagler defended the middleweight title twelve times over seven years. By the end, the belt had absorbed something — not literally, but in the way that objects accumulate history. Every challenger who came and failed was in the record. Every fight where Hagler got hurt and kept going was in the record. The belt was evidence of something real.

Now imagine someone prints an identical belt. Same design, same weight, same gold. He puts it on and calls himself champion. He's never fought. He's never been hit. He's never had to get up off the canvas.

Nobody believes him.

The difference isn't the belt. It's not talent, and it's not the declaration. It's whether the title can be taken away. Hagler's belt could be taken — that's exactly why it carried weight. The printed copy can't be taken because it was never earned through contest. A title that can't be lost can't mean anything.

A spatial index is, at first glance, just a mapping: coordinates go in, parcel IDs come out. The data structure is straightforward. On testnet, though, grid cell dynamic fields consumed 68% of per-parcel insertion cost. Storage was 94–96% of total transaction cost. The data structure was fine. The storage cost wasn't.

Testnet, March 2026. We measured.

Storage was 94–96% of every transaction's cost. Grid cell dynamic fields consumed 68% of per-parcel insertion cost. As we derived in our Dynamic Fields article, the dominant cost term in the insertion formula is $2.7\text{M} \times K$, where K is the number of grid cells a parcel covers:

$$ \text{Cost} = 1\text{M} + 2.7\text{M} \times K + 3\text{M} + 0.5\text{M} \times m \quad (\text{MIST}) $$

A parcel spanning 36 cells paid 97.2M MIST in cell entries alone. That's 97% of the $2.7\text{M} \times K$ term — the dominant cost component, not 97% of total gas. The other terms (base overhead, geometry storage) were fixed. K was the variable. K scaled with geographic size.

This article is about the five approaches we analyzed to cut K. Four of them failed. The fifth — a hierarchical quadtree with depth-prefixed Morton keys — reduced K from up to 36 to exactly 1. This is the story of how we found it.

George Everest never saw the mountain named after him. He retired from India in 1843. The peak was identified as the world's highest in 1852 — nine years after he left. In 1865, the Royal Geographical Society named it after him anyway, over his own objection. Everest had argued that local names should be preserved. The Society disagreed.

That's one name. The mountain has at least two more.

A new parcel arrives on-chain. Before the protocol writes it to the Index, it must answer one question: does this shape overlap anything already registered? A naive answer is to compare the newcomer against every existing parcel — but that's O(N), and N grows with every registration. On a blockchain, O(N) means gas that grows with the map's popularity. The more successful the protocol, the more expensive it becomes to use.

Eminent domain.

In most countries, governments hold the power to take private property for public purposes — a highway, a dam, a railway — and pay what they determine is fair. You receive compensation. You don't receive a choice. The state decided. The state is taking it.

Most people find this unsettling, even when they accept the logic. But at least the shape is recognizable: a government acts, a legal process unfolds, there's a stated reason, and eventually the thing is settled.

Now imagine that power without the government. Anyone — your neighbor, a stranger, someone a continent away who wants a piece of your territory — could take a slice of what you hold, pay you the market rate, and you couldn't refuse.