refine

REFINE Protocol v1.0: Contraction Mapping & Fixed-Point Convergence

Absorb → Audit → Iterate → Sweep → Report

This workflow defines the /refine execution loop. The objective is to guide sequence token generation through a series of discrete state transitions (Absorb, Audit, Iterate, Sweep, Report) to systematically reduce the entropy of pre-existing artifacts. The process is modeled as an iterative contraction mapping that halts only when a stable fixed point is verified.

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Philosophy & Mathematical Model

Refining an existing artifact is modeled as finding the unique fixed point $\mathbf{S}^*$ of a state-space contraction mapping. Let $\mathcal{X}$ be the space of artifact configurations, and let $d: \mathcal{X} \times \mathcal{X} \rightarrow \mathbb{R}_{\ge 0}$ be a metric proportional to the residual entropy and count of latent/active flaws. The refinement operator $R: \mathcal{X} \rightarrow \mathcal{X}$ is a contraction if:

$$d(R(\mathbf{A}), R(\mathbf{B})) \le q \cdot d(\mathbf{A}, \mathbf{B})$$

for all $\mathbf{A}, \mathbf{B} \in \mathcal{X}$ and some contraction factor $0 \le q < 1$. By the Banach Fixed-Point Theorem, repeated application of $R$ converges to the unique fixed point:

$$\mathbf{S}^* = \lim_{k \rightarrow \infty} R^k(\mathbf{S}_0)$$

CyberCorrect & Computable Loop Dynamics

To evaluate convergence in real-time, the error metric $e_k$ is computed using a computable proxy metric $d_p(\mathbf{S}_k)$, defined as the count of unresolved (PENDING or IN_PROGRESS) items in REF_LEDGER. The convergence rate is defined as:

$$\rho_k = \frac{d_p(\mathbf{S}k)}{d_p(\mathbf{S}{k-1})}$$

For a true contraction, $\rho_k \le q < 1$. If $d_p(\mathbf{S}_k) \to 0$, the system is Cauchy-convergent. In practical autoregressive generations:

1. Unstable Oscillations (Limit Cycles): If $\rho_k \ge 1$ (active only when $d_p(\mathbf{S}_{k-1}) > 0$ and $d_p(\mathbf{S}_k) > 0$) or if codebase states exhibit exact tracked workspace file hash equality with any prior loop state ($\mathbf{S}_k = \mathbf{S}_j$ for $0 \le j < k$ stored in TRACKED_WORKSPACE_HASHES), the loop has entered an unstable cycle. The system must adapt search parameters (lower generation temperature, inject explicit negative examples, or alter subagent critique rubrics) or execute the rollback protocol to break the attractor basin.
2. Diminishing Returns & Stochastic Cascades: Self-correction exhibits sublinear convergence, where functional errors are corrected early, but sequential, identical sweeps on unchanged code accumulate stochastic LLM noise (false positive critiques). To prevent these cascades, sweep angles must execute in parallel, and any new subagent finding on unchanged code must be ignored unless backed by a deterministic test or static linter failure.