Ephemeroi: An Innovative Framework for Reconstructing Constraint Solving as a Dynamic Evolutionary System

Ephemeroi is a hybrid reasoning and simulation framework whose core is to redefine traditional constraint-solving problems as dynamic evolutionary systems. Drawing on the mathematical isomorphism of cosmogony, it treats the computation process as a continuous evolutionary process where solutions emerge from physical pressures, energy fields, and phase transitions, challenging the traditional static input-output computing paradigm.

Traditional AI solvers treat computation as a static input-output process. The Ephemeroi framework proposes a new paradigm: constraint solving is a continuously evolving dynamic system, where solutions do not get "computed" but "emerge" from dynamic evolution in the state space, driven by physical pressures, energy fields, and feedback mechanisms—similar to how the universe forms structures from chaos.

The theoretical foundation of Ephemeroi is the mathematical isomorphism between the cosmic formation process and constraint satisfaction problems. Physical processes correspond one-to-one with mathematical objects: formless clumps correspond to random initial assignments, quantum fluctuations correspond to phase amplitudes, dark energy corresponds to the vacuum pressure field, spiral condensation corresponds to the maximum pressure parameter, and vortices/basins correspond to the memory signature of the solution's attraction domain. This isomorphism is a normative specification, where each subsystem corresponds to a physical process of cosmic generation.

Ephemeroi is a discrete dynamic system running in a binary assignment space. Its core equations include: the vacuum pressure equation (calculating the number of unsatisfied constraints), phase field update (tracking the rate of state change), and condensation point selection (selecting the variable with the highest pressure for update). The architecture flow starts from constraint input, goes through the constraint graph engine, energy field layer, multi-agent planetary layer, to the belief layer and reality layer, ensuring modularity and extensibility.

An important architectural innovation of Ephemeroi is the separation of the belief layer and the reality layer (no direct precedent in random local search literature). The belief layer (photon chip) includes phase coherence scores, cavity pressure fields, photon history, etc.; the reality layer directly evaluates constraint satisfaction without trust weights and has absolute veto power over the output of the belief layer. The core insight: high trust ≠ correctness—variables may have high trust but be involved in unsatisfied clauses ("illusion of confidence").

Ephemeroi includes a sanitation system to handle "deceptive coherence" (coexistence of high photon trust and persistent clause violations). It consists of a deceptive coherence detector (marking entries with high trust and involvement in unsatisfied clauses), the Cyrus Decree (adversarial detection to reset trust), and selective memory pressure (accumulating trust only for effective restarts). The hierarchical system: Deception → Hard Lock → Soft Lock → Freedom.

A phase-locking event occurs when the phase field Φ(t) stabilizes, and the solver finds an attractor. The backbone detector identifies invariant variables in the attraction domain (the skeleton of the solution), and locking them reduces the search space and improves efficiency. This simulates physical phase transitions: from maximum entropy chaos through condensation to a crystallized backbone structure.

The Ephemeroi framework's significance goes beyond SAT solving, demonstrating a new computing paradigm (problem solving as physical system evolution). Applicable scenarios include: complex optimization (objective function as energy landscape), belief revision (consistent models for dynamic environments), and adaptive intelligence (pressure feedback to adjust strategies). Its cosmogonic foundation provides a new perspective for computing theory: the essence of computation may be a physical process.