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Adjacency Theory markAdjacency Theory

Overview

Adjacency Theory and the Relational Distance Hypothesis

One umbrella programme, one core hypothesis, and a strict separation between what is known, what is debated, and what we are speculating.

The hypothesis

Effective separation as a derived quantity

The Relational Distance Hypothesis (RDH) proposes that the separation between two systems is not a primitive of the description, but a function of the relational structure that binds them. Under RDH, asking “how far apart are A and B?” is a question about relations, and geometry is the answer that those relations happen to produce.

D(A, B) = F(R)   ⟶   δD = (∂F/∂R) · δR
A controlled perturbation δR would have to correspond to a physically meaningful δD without violating causality or any known constraint. Whether such a correspondence exists at all is exactly what is unproven.

What the hypothesis does not say

  • It does not say that distance can be edited. It says that if distance is derived, then the question of editing it becomes well-posed rather than incoherent.
  • It does not treat entanglement as a channel. Entanglement alone carries no signal, and no result on this site contradicts that.
  • It does not claim that any graph on this site is spacetime. The graph is a sandbox for validating our own software and reasoning.

The toy transform

AT-0 represents the relational system as a weighted graph G = (V, E) with couplings 0 < R_ij ≤ 1, mapped to an effective edge distance and closed under shortest weighted path.

d_ij = −L · ln(R_ij)   |   D(A,B) = min over paths Σ d_ij
This mapping is a modelling convention chosen because it is monotone, additive along paths, and hand-checkable. It is not a derived law.

Later stages replace arbitrary R with quantities motivated by information theory — for example the mutual information I(A:B) = S_A + S_B − S_AB — while explicitly testing whether the resulting construction has the properties a metric requires.