Mathine — Evidence In, Trust Out

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

Mathine: Fields-to-Overfields Contract Machine
Link: https://doi.org/10.5281/zenodo.18684034 [1]

“Field” is treated here as a durable compression: a way to encode local structure, global constraints, and admissible transformations without enumerating every micro-cause. The paper leverages that intuition to argue that modern AI risk is increasingly not “the model made a mistake,” but epistemic closure failed — a claim was promoted as “done” under the wrong regime of admissibility, authority, or verification. [1]

The central architectural move is to generalize beyond language: Large Signals Models (LSMs) operate over heterogeneous signals (language, vision, audio, logs, sensors, time series, simulations), while Large Signals Fields (LSFs) act as compact, versioned contracts governing one or more models and tools. In that framing, Large Language Fields (LLFs) become a specialization of LSFs for linguistic channels, and other “field types” emerge naturally (e.g., perception fields) as signal-specialized contracts with explicit closure rules. [1], [2]

Governance is expressed as a layered authority stack: Field → Overfield → Metaoverfield. Overfields behave like a federated gauge layer managing couplings, drift corridors, verification budgets, and blast radius across many LSFs — so “who conditions whom, under what weight, and with what budget” becomes a first-class, declared object rather than an implicit organizational artifact. [1]

The closure protocol is the operational core: claims become promotable only when accompanied by receipts and ledgers — replayable evidence artifacts that bind outputs to their regimes, support audit and transport across environments, and preserve reversibility.

This connects directly to contract-first evaluation and governed boundaries: progress becomes measurable not only by capability, but by legitimacy under explicit contracts and checkable closure. [1], [3]–[5]

References
[1] 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
[2] R. Figurelli, “Large Language Fields (LLFs): The Invisible Layer Above LLMs”. Zenodo, Oct. 03, 2025. https://doi.org/10.5281/zenodo.17254137
[3] R. Figurelli, “Field-Driven Design (FDD): The Operational Extension of Large Language Fields (LLFs)”. Zenodo, Oct. 13, 2025. https://doi.org/10.5281/zenodo.17342856
[4] R. Figurelli, “Field Definition Language (FDL): A Proposal to Evolve APIs into Governed Fields”. Zenodo, Oct. 18, 2025. https://doi.org/10.5281/zenodo.17382665
[5] R. Figurelli, “Benchmarks-as-Contracts: A ReceiptBench Spec Template for Regimes and Closure”. Zenodo, Feb. 17, 2026. https://doi.org/10.5281/zenodo.18675035