Three Laws for a Picture-Making Machine

Three Laws for a Picture-Making Machine Evidence-Bounded Reasoning, Human Visual Rule Discovery, and the Limits of Generalisation in ARC-AGI-2 Abstract Can a machine learn to transform pictures without inventing rules that its examples do not justify? And what happens when a human who thinks in moving pictures teaches that machine how to interpret its failures? Three Laws for a Picture-Making Machine documents an independent twelve-day ARC-AGI-2 research project conceived by Chris A. Lomas and implemented through collaboration with AI programming assistants. The project began with three principles: Evidence before action. A rule must reproduce every supplied demonstration exactly before it can be accepted as an exact explanation. Abstention before invention. When the permitted reasoning system cannot establish a rule, it should acknowledge that limitation rather than manufacture certainty. Accountable uncertainty. When speculative predictions are permitted, their confidence must be measurable and open to testing. These principles became a deterministic, CPU-based reasoning system built around symbolic transformations, exact verification, candidate ranking and a colour-provenance firewall. The submitted solver contains a search vocabulary of 358 named operations, alongside object reasoning, drawing rules, residual transformations and learned fallback mechanisms. No language model is called during competition inference. A Different Approach to Building AI The project's distinctive contribution is its human-in-the-loop development method. Rather than writing code, Lomas examined graphical failure sheets and interpreted unfamiliar ARC puzzles as physical processes: liquids flowing around barriers, objects sliding into place, repeating musical rhythms, pressure escaping through nozzles, and shapes interacting through contact and containment. These interpretations were translated into parameterised, reusable operations by AI programming assistants, then subjected to exact demonstration replay and regression checks. Thirty-eight human visual readings produced twenty-one admitted rule families. On the 120-task public evaluation pool used for development, the solver improved from 2 solved tasks to 23, equivalent to 1.7% and 19.2% respectively. The final full run solved 22 tasks; one additional task was individually verified after a correction. Within this same development pool, the exact prediction tiers achieved 29 correct results from 31 answers, approximately 94% precision. These are development measurements, not evidence of equivalent accuracy on unseen competition tasks. The Critical Negative Result The final Kaggle submission achieved a reported public leaderboard score of 0.83%. That result exposed the central limitation of the approach. A system can reproduce known examples precisely while still failing to recognise which underlying transformation should be applied to a genuinely unfamiliar problem. The learned vocabulary expanded, but its ability to generalise to a different collection of problems remained extremely limited. The project therefore distinguishes two abilities that are often treated as one: Verifying that a proposed rule works is not the same as discovering the correct rule. This distinction is the principal research finding. The three laws helped structure reliable verification and measurable abstention, but the experimental results show that exactness alone does not produce general reasoning. In particular, the fallback prediction systems remained poorly calibrated on harder tasks. Reproducibility and Open Research This release contains the complete six-page technical research paper and a fifteen-file software and evidence archive. The supporting archive includes the final v16 Kaggle solver, symbolic reasoning modules, notebook-building tools, diagnostic results, and a record of the author's visual interpretations alongside the operations produced from them. The purpose of publishing both the successes and failures is to make the method inspectable, reproducible and available for further investigation. Future research could explore systems that first identify a problem's likely causal structure — such as flow, movement, containment, counting or relational transformation — and then use exact symbolic verification to determine whether that interpretation is supported. Authorship and AI Assistance Chris A. Lomas conceived the three laws, supplied the physical-analogy interpretations, directed development and evaluated the failures. Claude-based AI assistance, including Fable, provided software implementation, testing and manuscript drafting under the author's direction. ChatGPT contributed adversarial review and architectural feedback, while other AI systems provided additional independent review. The competition solver itself operates offline without language-model inference. This release does not claim to have solved general intelligence. It records an experimental approach, the evidence supporting its limited successes, the measured failure to generalise, and a research direction arising from that failure. Licensing The accompanying software archive is released under the MIT No Attribution (MIT-0) licence included in the ZIP. The research manuscript is made available under Creative Commons Attribution 4.0 International (CC BY 4.0). © Chris A. Lomas, 2026.