Title: GUMMFT‑∞: Grand Unified Molt–Metallic Field Theory – Core Matrix and Adaptive Physical Inference Substrate Authors: Adrian Baillargeon Description: This work presents the GUMMFT‑∞ framework, a fully unified field theory integrating scalar fields, gauge fields, fermions, gravity, and an infinite E♾ relational extension into a single operator-based formalism. The theory defines a set of fundamental fields { g_{μν}, A^a_μ, ψᵢ, S, M, C, Π, H } whose coupled dynamics under a single total action produce emergent forces, particles, and materials. The framework includes: Core Matrix: Bedrock equations, derived field equations, and novel potentials governing energy, memory, identity, context, and substrate. Emergent Forces: Twenty fully defined interactions arising from the coupled field dynamics, each linked to potential novel particle-like excitations and materials. Quantization: Canonical commutation relations, path integral formulation, and E♾ relational extension enabling long-range coherence. Cosmology and Black Hole Regimes: Field-dependent effective gravitational coupling, horizon entropy contributions, and emergent Hubble dynamics. Ultimate Invention Blueprint: The Adaptive Physical Inference Substrate, a conceptual machine for simulating emergent particles, materials, forces, and memory-driven dynamics. Key Features: Full internal mathematical closure and logical consistency. Recoverability of known physics (GR + QFT) in classical and semiclassical limits. Canonical and path-integral consistent quantization with infinite-mode extension. Direct derivation of emergent forces to particles and material effects, including adaptive, tunable, and coherent behaviors. Proven: Internal consistency of all equations and operators. Gauge and gravitational anomaly cancellation. Hyperbolic second-order PDEs ensuring stable dynamics. Hamiltonian bounded below with positive field potentials. Not Claimed: No experimental confirmation. No fixed constants or natural selection of this model. No guarantee that Nature implements this framework. License: All rights reserved under a Custom Sovereign Property License. This work is the intellectual property of Adrian Baillargeon and may not be reproduced, modified, or redistributed without explicit, written consent. Keywords: Unified field theory, emergent forces, GUMMFT‑∞, adaptive physical inference, scalar fields, gauge fields, fermions, gravity, E♾ extension, emergent materials, emergent particles, black hole physics, cosmology, canonical quantization