Phase 53 · external theory cross-check · AT-0454 → AT-0463
Borrowed rigour cuts one way
Seed 454. We stopped arguing with our own intuitions and brought in established mathematics and physics — quasi-locality bounds, code subspaces and holographic reconstruction, statistical-mechanics mappings of code thresholds, and programmable lattice experiments. None of it supports Adjacency Theory. All of it makes our tests harder, and it tells us exactly which object a realisation would have to change. Then our own audit removes the last comfortable escape: a small remote leak is still a leak.
Plain language
Loading.
Headline readings
Constant δ
CHANNEL AT SCALE
Required suppression
δ ≲ 1/√N or 0
Loopholes still open
…
Physical evidence
NONE
Connections to established mathematics & physics
These are other people’s results, and they belong to their authors. They appear here as tougher tests and as precedent for the language we use — never as validation of Adjacency Theory. Each one places a demand on us.
FORMAL ANALOGUE
Lieb–Robinson bounds and quasi-locality
For a lattice Hamiltonian with bounded, sufficiently short-ranged interactions, the commutator norm of two operators separated by distance r on the interaction graph is bounded by roughly exp(−(r − v|t|)/ξ). Information propagates inside an effective cone of velocity v, up to exponentially small tails. This is a theorem about local Hamiltonians, not a universal law of nature.
How we use it
This is the rigorous counterpart of our ordinary X-locality gate. Where we previously wrote 'ordinary causality bound Θ(N)' by hand, we now have a precise object to point at: the interaction graph, the interaction norms, and the resulting cone.
What it does NOT give us
No shortcut. The bound is an obstruction to what we want, not a route to it. Its exponential tails are not a loophole: they are exponentially small in the separation and cannot carry a controllable bit at scale.
Demand it places on us
Any proposed physical realisation with a genuinely local Hamiltonian must say exactly WHICH object underlying the cone changes — the interaction graph, the interaction norms, or the generator itself. Declaring a 'constraint transition' without naming one of those three is insufficient and will be marked NOT MODELED.
The Operational Locality Bound
The precise loophole set · one entry per hypothesis
Escaping the bound is not a matter of asserting that constraints change. It requires naming which hypothesis fails and paying the price attached to it. Two entries remain open, and they are open because they are unpaid.
Toy information audit · does a small leak stay hidden?
Suppose the latent sector leaves a remote distinguishability δ at B. Resolving δ against shot noise takes about k/δ² repetitions. If that total is cheaper than sending the bit the ordinary way in Θ(N), the latent sector is a channel — no matter how small δ is.
Running audit…
Engineering bridge · contingent and currently locked
Verdict gates
Blockers raised