Locality Causes Tractability? An Intervention Study on the Variable-Interaction Radius in Geometric Random Satisfiability

A widespread intuition holds that real-world computational problems are easybecause their ``causes act locally'': when variables interact only within smallneighbourhoods, constraint solvers should scale well. Observational evidencesupports the intuition, but observation cannot separate locality from the manyother regularities real instances carry. We translate the intuition into afalsifiable, interventional claim: holding the number of variablesfixed, matching clause density relative to each radius's own threshold, andwith clause-content statistics r-invariant by construction, varying only the radius $r$ within which clause variables are drawn from a 2-Dtorus should causally change CDCL solving difficulty. Three findings. (i) The operational satisfiability boundary is not $r$-invariant: itlies below density 2.5 at $r=0.06$ and near the classical ${\approx}4.3$region by $r=0.22$ (a displacement of at least 1.7 density units) ---locality moves the sat/unsat boundary itself --- before becoming unmeasurableat $r\ge 0.3$ under a $10^7$-conflict budget. (ii) At density matched relative to eachradius's own threshold, difficulty spans $3.4$ orders of magnitude across $r$among decided instances (mean $\log_{10}$ conflicts $1.45 \to 4.86$ from$r=0.06$ to $0.22$), and $\ge 4.5$ orders when budget-censored runs arecounted at their lower bound; RM-ANOVA $F(8,216)=2808.5$, $p\approx10^{-213}$;Jonckheere--Terpstra $p\le 10^{-4}$ with FDR $q\le 10^{-4}$; partial$\eta^2 \approx 0.99$. (iii) A degree-preserving swap that destroysspatial locality while keeping every literal's occurrence count exactly fixedraises difficulty by $16$--$68\times$ (Wilcoxon $p\le 7\times10^{-10}$) andflips the satisfiability status of 53 instance pairs; causal mediationattributes ${\sim}94\%$ of the radius effect to community-structurerestructuring (ACME 3.06, bootstrap CI $[2.84, 3.37]$). Locality is not merelycorrelated with tractability --- under our controls it is the causal channel.All claims are scoped to $n=400$, direct CNF encodings, and CDCL-familysolvers; we discuss what this does and does not say about P versus NP. Code,seeds, data, preregistration, and the full audit trail are public. Deposit contents. The package consists of three files: a READMEdescribing the package and its licenses; the paper PDF (journal-formatted,with a structured abstract, five technical appendices including the JAIRReproducibility Checklist, complete threshold tables, per-arm dose--responsedetails, and censoring-sensitivity analyses); and a single tarball containingthe complete research repository --- the LaTeX sources of both the journal andthe compact versions of the paper, the locality-kernel instance generator,the solver and analysis pipeline, all raw result databases and summary JSONfiles, the preregistration chain with its numbered amendments and theprespecification-vs-implementation audit, the experiment log, the full reportin English and Chinese, literature notes, the AI-use disclosure, the testsuite, and a bundled third-party probSAT solver. The snapshot isbyte-identical to the repository state tagged v4.0.0; the complete commithistory is available at https://github.com/essnt/correlation-vs-hardness.