Five voters hold fixed ideal points in the plane. A voter strictly prefers the proposal strictly closer in Euclidean distance, an equidistant voter abstains, and one proposal beats another iff more voters prefer it. From the start pin, the page hunts a chain of majority-winning proposals that ends EXACTLY on the target pin, and separately composes that relation over a 1024 by 1024 grid to find the bounded central region that no opening winner can eliminate.
Every figure on this page is derived from the stated coordinates and the stated rule. Nothing is recalled from a table or a paper.
Drag the pins and the voters, or select a pin and use the arrow keys. Blue circle: start. Orange cross: target. Yellow squares: voters. Green: the survivor blob. Blue wash: points that beat the centre. Red wash: points an opening winner beats.
path: waiting for the engine
wasm hash: pending
| battery: waiting for the engine |
battery: waiting for the engine
control: waiting for the engine
planted core: not yet run; press the button
full-size decomposition: not yet run; press Run full grid
The reversed-preference control and the planted-core control are re-runnable with their buttons. The planted control doctors the DATA, not the code: the five ideal points become exactly radially symmetric, where a majority core provably exists, and the same unmodified search must report failure from the core rather than loop.
Two decompositions agreeing rules out a stripe-boundary error and very little else. Every check on this page, in the browser and offline, shares one majority predicate; a shared misreading of the tie rule or of what "reachable" means would pass all of them. Under exact radial symmetry the win set of the core must be EMPTY over all 1,048,576 points: that is Plott's condition, a theorem the grid code was never told, and it is the strongest check here.
The engine and the reference use no transcendental function at all: only sqrt, floor, ceil and popcount, each correctly rounded or exact under IEEE 754 in both wasm and JavaScript. The agreement between the two implementations is therefore a property of this page, not of which browser opened it; no platform Math whose rounding ECMA-262 leaves unspecified is consulted anywhere.
The byte-for-byte rebuild check is offline: your browser cannot compile C. It runs in research/any-destination-if-you-write-the-order/verify-any-destination-if-you-write-the-order.mjs, together with the whole-grid independent recount, the boundedness band, the cross-method recomposition and three negative controls.