How to Make Large-Scale Experiments Smarter and Cheaper with AI-Driven Proofs

Abstract

The Asymmetric Self-Consistency Hypothesis reframes scientific falsifiability for the age of AI. By leveraging cross-verification with multiple independent AI formal proof systems (Lean, Coq, GPT-based), we ensure that if a theory passes all self-consistency checks, any experimental discrepancy points not to flaws in the theory itself, but rather to limitations in measurement or the foundational axioms used. This approach is fully reproducible, with open datasets, proof scripts, and CI pipelines available for verification.

1. Introduction: Why AI Verification Changes the Game

Traditional science has always relied on experiments to test theory, with Popper’s falsifiability as a cornerstone. But with the rise of AI — especially formal proof assistants — the very notion of “falsification” shifts. If AI-driven systems independently agree a theory is internally self-consistent, then discrepancies with experiment often reveal issues with experimental setup or unexamined axioms, not with the logic of the theory itself.

Intuitive Example:

Suppose three independent AI “instruments” analyze a theory and all find it self-consistent. If a fourth process disagrees (e.g., an experiment), it’s more likely the outlier is due to external error, not the theory. This is a paradigm shift in scientific logic!

1. Core Hypothesis Statement:

If a theory T is verified as self-consistent by multiple independent AI systems, then any contradiction between T’s predictions and experimental results is most likely due to:

A) Experimental limitations, or

B) Foundational flaws in the axioms
…rather than in T’s internal logic.

1. Formal Framework

Axiomatic Basis
Clearly states all starting axioms (e.g., QFT postulates, symmetries, renormalization).
Example: All fields and couplings are well-defined; symmetry-breaking terms are specified; perturbative expansions converge, etc.
AI-Based Self-Consistency Verification
Three independent proof systems were used:

Lean 4.0 (Proofs.lean)
Coq 8.14 (Proofs.v)
GPT-based checker (gptreport.json)

All check:
If T |= SelfConsistent in AI-verifier V, then ¬(Experiment ∧ ¬T)

In plain English: a failed experiment means there’s either an issue with the experiment or with the starting principles, not with the logic of T.

1. Micro-Axiomatic Case Study: Physics Example

Perturbative Convergence: All calculations (e.g., n-point functions) converge for “reasonable” couplings, as proven in both Lean and Coq.
Two-loop β-Function: Explicit multi-loop calculations (and their formal proofs) are included and can be checked for logical soundness via scripts.

1. Falsifiability: A New Perspective

A prediction is falsifiable if there exists an experimental setup E such that a discrepancy implies either E is flawed, or the axioms are incomplete. This reframes the “meaning” of experimental contradiction.

Quantitative Criteria:

Compare predicted and experimental cross-sections.
Statistically significant deviations trigger re-examination of experimental procedures or foundational theory.

1. Practical Experimental Design

Resonance Windows: Predictions for high-energy collider experiments (HL-LHC, FCC-hh) are precisely given.
Systematic Uncertainties: All major error sources and their sizes are catalogued — model can be stress-tested in real collider settings.

1. Demonstrative First-Principle Adjustment

By tweaking a foundational axiom (e.g., adding a tiny Lorentz-breaking term), the formal proof pipeline checks if the theory’s consistency is still maintained. AI re-verification proves robustness to minimal physical changes.

1. Reproducibility: Proof Scripts & CI for Everyone

All proof scripts, datasets, and logs are open (see Zenodo link).
Full reproducibility via provided Docker environments (build from provided Dockerfile; scripts run Lean, Coq, Python checkers).
SHA256 checksums for all files guarantee integrity.
How to Reproduce:

Download from Zenodo (full dataset)
Build Docker env; run Lean/Coq/GPT scripts
Validate against checksums and reproduce the figures/simulations

1. Results & Impact

AI verification pipeline passed 99.8% of 1000 proof steps, with only 2 minor issues automatically corrected.
Major cost savings: By verifying theory logic before experimental investment, wasted time and resources can be drastically reduced.
Scientific focus is shifted: More energy spent on refining experiments or foundational principles, less on re-running expensive failed experiments.

1. Future Directions

Grid-based Monte Carlo validation (non-perturbative regime, Q3 2025)
Series of micro-adjustment studies (exploring various symmetry-breaking extensions)
Extended cross-verification (lattice, advanced proof systems, etc.)
Manuscript revisions and community feedback cycles

1. Conclusion

The Asymmetric Self-Consistency Hypothesis provides a reproducible, transparent framework for using AI to guarantee theoretical integrity. It shifts scientific methodology, turning AI not just into a “co-author” but into a guardian of scientific logic, allowing humanity to build faster, safer, and with greater confidence.

Full Paper & Dataset on Zenodo
https://zenodo.org/records/15630260