Repository: https://github.com/Lukadud/configuration-graphs
Numerical verification suite for the preprint:
"Configuration Graphs with Real and Complex Path Weights: A Pedagogical Synthesis of Order-Theoretic Kinematics and Path-Sum Dynamics, with a Reproducible Simulation Suite" — Luka Dudkin, 2026 (draft v2, revised after three rounds of internal adversarial review).
This is a synthesis note, not a claims paper: it assembles known results (causal-set kinematics, the Feynman–Kac / quantum-walk dichotomy, Gleason's theorem, Myrheim–Meyer dimension estimation) in one minimal four-axiom setting and verifies every quantitative statement with the code in this repository. Priority on the physical results is explicitly disclaimed; see the preprint's demarcation table.
| # | Script | What it shows | Key number |
|---|---|---|---|
| E1 | configuration_engine.py |
Two-path interference formula P = a²+b²+2ab·cos Δφ (algebraic check) | matches to 1e-12 (IEEE-754 check only) |
| E2 | configuration_engine.py |
Double slit, two-path continuum sum (not a graph — see E9): fringes iff Γ ∈ ℂ | 7 fringes vs 1 smooth maximum |
| E3 | configuration_engine.py |
Same chain: ballistic (ℂ) vs diffusive (ℝ₊) spreading | exponents 1.000 vs 0.500 |
| E4 | configuration_engine.py |
Dimension from pure order (Myrheim–Meyer) | 0.5064/0.2268/0.0992 vs analytic 0.5/0.2286/0.1 |
| E5 | experiment_E5.py |
No continuous reversible dynamics for finite Markov chains; real matrix exponentials, determinant checked against Liouville's formula | max det 0.293 < 1; Liouville gap 2.5e-16 |
| E6 | experiment_E6.py |
Density-inhomogeneity detection from order statistics (not a curvature measurement; illustrative, 4 trials; confounded with the dimension estimator — measured and reported) | link fraction 0.028 → 0.084 |
| E7 | experiment_E7.py |
Lattice dispersion v_g = 2J·sin(k); Planck-scale phenomenology honestly untestable | sim vs theory 4e-4; Δv/c ≈ 8.4e-38 (15.9 orders below GRB timing) |
| E8 | experiment_E8.py |
Gleason illustration: additivity over bases forces quadratic probability rules (within an l ≤ 4 real-harmonic ansatz) | null space exactly 5-dim; l=4 sector excluded (min σ 2.81) |
| E9 | experiment_E9.py |
The framework end-to-end: graph built from the admissibility operator B, all 4096 paths enumerated, both codomains on identical edges | enumeration = DP to 3.6e-16; binomial (ℝ₊) vs interference with 4 near-zeros (ℂ) |
Two deliberately reported failures are preserved in the history: an early version of E6 conflated curvature with window shape, and an early version of E5 assumed the identity it claimed to verify. Both are documented in the preprint and fixed here.
pip install -r requirements.txt
python run_all.py # writes JSONs and PNGs into results/All random seeds are fixed (42, 7, 123, 2026); outputs should match the reference files in results/ up to floating-point noise. No seed sweep has been performed (3–4 trials per statistic in E4/E6 — treat those numbers as illustrative, as the preprint states).
Hilbert-space kinematics, unitarity, non-contextuality, the Hamiltonians of E3/E7, and lattice regularity are inputs, not derived from the axioms. The probability postulate carries no intrinsic normalization (E9 normalizes explicitly). No new testable prediction is offered; the one computed deviation (E7) is ~16 orders of magnitude below experimental reach.
The conception of the theory, its axiomatic core, the research direction, the interpretation of results, and all scientific conclusions are the author's; the author takes full responsibility for the entire content. AI tools (Claude, Anthropic) were used as a working instrument under the author's direction in preparing the manuscript, including assistance with the mathematical formalization, drafting, numerical implementation, and internal consistency review.
MIT — see LICENSE.
The accompanying manuscript is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. 10.5281/zenodo.21445011