The End of Exhaustive Search: A General Theory of Solving Hard Problems by Certified Transport
Mathine: Certified Transport Proof-Carrying Machine
Link: https://doi.org/10.5281/zenodo.18460311 [1]
Exhaustive search fails at scale not only because the search space explodes, but because solutions often don’t travel: the reason an instance is “solved” can collapse when the instance is transformed, encoded, reduced, or verified under a different environment. This paper proposes a general alternative: solving by certified transport. [1]
Progress is defined as producing transportable certificates—finite verifiers with explicit obligations—rather than accelerating exploration. Each admissible transformation must come with replayable evidence artifacts that remain independently checkable under bounded resources, so closure survives movement across toolchains, encodings, and verification contexts. This aligns with the broader “receipt-first” discipline that later becomes explicit in benchmark governance. [1], [3]
The technical hinge is κ-margin preservation: each step maintains a quantitative safety gap that prevents a claim from “closing to zero” under transport. When the margin cannot be preserved, the system must abstain rather than overclaim, turning honest partial closure into a first-class outcome—an idea that fits naturally with zero-trust closure protocols and obligation accounting. [1], [2]
Operationally, the paper’s thesis becomes a blueprint for portable trust: closure is not an authority statement; it’s a checkable state transition. That same portability logic recurs in layered governance stacks (field → overfield → metaoverfield), where a claim may need to remain checkable across authority boundaries, time horizons, and regime changes. [2], [4], [5]
The reframing is blunt: if your success metric is “instances closed,” you optimize the wrong thing. If your success metric is “closures that survive transport,” you get a path to cumulative progress that does not depend on brute force as the default mode of truth. [1], [4]
References
[1] R. Figurelli, “The End of Exhaustive Search: A General Theory of Solving Hard Problems by Certified Transport”. Zenodo, Feb. 2, 2026. https://doi.org/10.5281/zenodo.18460311
[2] R. Figurelli, “Math Machines: The Systems Architecture of Mathematical Trust”. Zenodo, Feb. 6, 2026. https://doi.org/10.5281/zenodo.18511647
[3] R. Figurelli, “From Scores to Receipts: Introducing ReceiptBench, a Typed-Receipt Protocol for Governance-Ready Evaluation”. Zenodo, Feb. 16, 2026. https://doi.org/10.5281/zenodo.18661829
[4] R. Figurelli, “Layered Field Collapse: Executable Collapse Signatures from Benchmarks to Metaoverfields”. Zenodo, Feb. 17, 2026. https://doi.org/10.5281/zenodo.18675054
[5] R. Figurelli, “Fields as the Contract Layer for AI/AGI/ASI: From Physical Fields to Large Signals Fields (LSFs) and Large Language Fields (LLFs) — Architecture, Governance, and Receipt-Based Closure”. Zenodo, Feb. 18, 2026. https://doi.org/10.5281/zenodo.18684034
Mathine — Evidence In, Trust Out 