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Overview 

The Morphic Conservation Principle (MCP) posits that all stable computational and physical processes obey a single invariant relationship among energy expenditure, informational structure, and functional correctness. Originating from the Energy–Accuracy–Equivalence (EAE) framework, MCP extends beyond AI optimization into thermodynamics, topology, and quantum information theory. It states that any system capable of transforming information while preserving correctness will spontaneously evolve toward an energy-minimal configuration consistent with its equivalence topology. 

The Morphic Conservation Principle builds on the Energy–Accuracy–Equivalence framework recently submitted to IEEE Transactions on Artificial Intelligence (2025). It extends these results into a cross-domain symmetry law connecting energy, information, and correctness.

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1. Foundational Statement 

For any morphic system M = (S, T, L), where S represents system states, T allowable transformations, and L a correctness operator, the Morphic Conservation Principle requires that: 

L(S) = L(T(S)) and ΔE → min subject to L(S) = true. 

Thus, correctness is invariant under admissible transformations, and energy decreases monotonically toward the Landauer bound. This establishes a quantitative symmetry linking logical equivalence to thermodynamic efficiency. 

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2. Topological and Thermodynamic Invariance 

Each morphic transition functions as a homeomorphism on the information manifold: it preserves global structure while permitting local reconfiguration. In physical terms, this corresponds to adiabatic or reversible evolution, minimizing entropy production. The same invariance class governs both morphic AI models and topological quantum systems, suggesting that computational and physical stability share a common symmetry law. 

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3. Cross-Domain Manifestations 

• Artificial Intelligence: Six-Sigma-grade code synthesis and self-healing verification via Version RAGs. 

• Thermodynamic Computing: Energy-bounded transformation control within Normal Computing’s hardware paradigm. 

• Quantum Information: Path-invariant logic operations analogous to braided topological qubits. 

• Mathematics: Equivalence relations and σ-algebras forming conserved manifolds of correctness. 

• Physics: Near-reversible information flow consistent with Landauer-limited computation. 

 

4. Implications 

MCP suggests a deep unification across computation, physics, and mathematics: 

All systems that transform information correctly do so under conserved energy–equivalence symmetries. 

This bridges AI optimization with fundamental physical law, implying that intelligence itself may be a thermodynamic symmetry phenomenon — a measurable, conservative force maintaining correctness through minimal energetic action. 

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                                                                                                                                                                          John Harby 10/21/2025