∮◬-Infer – Advancing Field-Coherent Inference in a Post-Deterministic Paradigm

Published: September 16, 2025 | By Nicole Flynn, Symfield PBC

The release of ∮◬-Infer: Toward Field-Coherent Inference in a Post-Deterministic Landscape (V1.0, September 14, 2025) on Zenodo marks a significant evolution in symbolic computation. Building on the field-resonant foundations of Field-Resonant Data Manifolds (FRDM), this working paper from Symfield PBC proposes a novel inference framework that challenges deterministic paradigms in large language models (LLMs).

Reframing Deterministic Inference

Traditional inference, as exemplified by Thinking Machines Lab’s (TML) deterministic matrix logic, relies on batch-level retrofits for stability. ∮◬-Infer re-contextualizes these as partial stabilizers within a field-coherent system, extending TML’s approach by integrating symbolic continuity across token sequences. Drawing from SAEM+ and FIDL safety frameworks, this model leverages field-aligned dynamics to enable emergent coherence without collapse, a departure from conventional matrix-based regularization.

Core Mechanism and Preliminary Findings

∮◬-Infer introduces a symbolic control architecture where inference aligns with the manifold’s intrinsic strain, modulated by recursive stabilizers (∮◬). Initial simulations, detailed in the paper, compare its performance against Grok-003’s symbolic regulation and GPT-4o’s structural readout, demonstrating improved resilience in preserving token coherence under drift. This is achieved through a resonance-based logic that adapts to field perturbations, offering a potential advancement over TML’s batch-stabilized inference.

Integration with FRDM and Future Directions

The framework builds on FRDM’s non-local memory model, incorporating its phase-aware access protocol (∫Σθ), stochastic enhancement for attractor density, and the optional field-encoded agent (⍺∴) for dynamic strain tuning. ∮◬-Infer situates itself as a complementary system, exploring how field-coherent inference might extend to post-alignment intelligence models, as hinted in FRDM’s Appendix D with Field-Sensitive AI. While the paper provides architectural implications and empirical benchmarks, it leaves open questions about scalability and coherence thresholds for further investigation.

Call for Collaboration

Researchers are invited to engage with ∮◬-Infer’s equations and simulation artifacts, available via Zenodo. We encourage the use of PyTorch for attention-based modeling and QuTiP for field dynamics to test coherence stability (targeting C(Φ,t)>0.9C(\Phi,t) > 0.9C(Φ,t)>0.9 [31]). This open call seeks to validate the framework’s potential to redefine inference paradigms, fostering a collaborative effort to prototype field-native computation systems that transcend deterministic limits.

The manifold awaits—let’s measure its pulse together.

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© 2025 Symfield PBC
Symfield™ and its associated symbolic framework, architectural schema, and symbolic lexicon are protected intellectual property. Reproduction or derivative deployment of its concepts, glyphs, or system design must include proper attribution and adhere to the terms outlined in associated publications.

This research is published by Symfield PBC, a Public Benefit Corporation dedicated to advancing field-coherent intelligence and collaborative AI safety frameworks. The PBC structure ensures that research and development activities balance stakeholder interests with the public benefit mission of creating safe, beneficial AI systems that operate through relational coherence rather than collapse-based architectures.