An Executable Protocol for the Three-Gate Decision over the Transport Construction
Imagine you’re checking whether a set of rules is “local” — whether each rule only ever cares about what’s happening right here, at this spot, or whether some rule secretly reaches across the whole system to impose a condition that no single location could check on its own. That distinction matters more than it sounds. If the rules are local, the mathematics that follows is clean and the physics assembles from the bottom up. If even one rule is sneakily global, everything downstream inherits that hidden long-range dependence.
An earlier paper proved that this single question — local or not? — can always be settled by running exactly three checks in order. What it couldn’t do was actually run them, because running them requires the real list of rules, and a proof about a procedure can’t conjure up the rules it’s meant to examine. This new paper builds the instrument that takes that list of rules and turns the crank. It does three useful things a bare procedure doesn’t: it turns the vaguest check into a concrete sorting task, it settles in advance how hard the heaviest check will be, and — this is the part I’m most pleased with — it imposes a discipline borrowed from good experimental science. For the checks that can only be settled by hunting for a counterexample and failing to find one, you have to write down beforehand exactly where you’ll look and what would count as finding something. That way “we looked and found nothing” is real evidence, not a place for wishful thinking to hide.
Then the paper does the thing the previous one couldn’t: it feeds in the actual rules, drawn from the programme’s own earlier work, and runs the first check. The result is a pass — and the interesting part is which rule was on trial. The rule governing how records flow and are conserved was the one everyone feared, the suspected culprit for a hidden global dependence. It turns out to be local after all, and not by luck: a conservation principle built into the foundations flatly forbids the kind of long-range coupling the worry required. The most dangerous-looking rule is the one the system most cleanly clears.
I want to be careful about what this does and doesn’t prove, because an earlier draft of mine wasn’t. Showing each rule is local “in form” is not the same as showing all the local pieces fit together into a consistent global whole — a thing that can fail even when every individual rule is impeccably local. (Electromagnetism is the textbook example: perfectly local laws that can still refuse to glue together neatly on a space with the wrong shape.) So two checks remain: can every allowed configuration actually be built, and do the local pieces glue? Both are now sharp, scoped questions rather than vague worries — which is the real progress here. The work didn’t close the case; it located, precisely and honestly, exactly what’s left to close.