Minimal Core Constants in RCFT/ULRC

Abstract This paper presents a universal and operational framework for quantifying stability, memory, and identity in physical, biological, and symbolic systems, formulated through the Unified Language of Recursive Collapse (ULRC/RCFT). The approach centers on four dimensionless, empirically defined invariants—Symbolic Drift (δΨ), Recursive Fidelity (F), Collapse Entropy (S), and Reentry Delay (τR)—that together form a minimal yet complete set of criteria for diagnosing collapse dynamics and persistence across diverse domains. By rescaling observable quantities into normalized, unit-free form, the protocol enables direct, meaningful comparisons between systems as varied as temperature fields, quantum states, biological signals, and symbolic processes. Each invariant is anchored to standard physical units (SI or Planck), ensuring results are both reproducible and falsifiable. A central contribution is the formalization of a universal “survival law” that translates the persistence of identity from philosophical speculation into a practical, testable condition. Systems that maintain high fidelity, low drift, limited entropy, and bounded reentry time satisfy this empirical criterion for survival; those that do not are at risk of collapse. This framework does not ignore its own limitations. It calls attention to the need for transparent normalization, careful calibration, and honest reporting of reference values. Rather than concealing complexity behind jargon, the protocol emphasizes clarity, practical applicability, and scientific responsibility. By reducing the analysis of persistence and transformation to a handful of universal, empirically validated measures, this work provides a rigorous foundation for cross-domain diagnostics. It offers a clear and testable language for understanding stability and change, unifying approaches from physics and biology to cognition and information theory.摘要 本文通过递归坍缩统一语言（Unified Language of Recursive Collapse，ULRC/RCFT）构建了一套普适且可操作的框架，用于量化物理、生物与符号系统中的稳定性、记忆性与同一性。该方法聚焦于四个经实验定义的无量纲不变量——符号漂移（Symbolic Drift，δΨ）、递归保真度（Recursive Fidelity，F）、坍缩熵（Collapse Entropy，S）与再入延迟（Reentry Delay，τ_R），共同构成了一套极简且完备的判据集，可用于诊断跨多样领域的坍缩动力学与系统存续性。 通过将可观测物理量归一化为无量纲的标准化形式，该协议可实现多样化系统间直接且具实际意义的比较，涵盖温度场、量子态、生物信号与符号过程等场景。每个不变量均锚定标准物理单位（国际单位制SI或普朗克单位制），确保研究结果具备可重复性与可证伪性。 本文的核心贡献在于将普适“存续定律”形式化，该定律将同一性存续的哲学思辨转化为可实践、可检验的条件。维持高保真度、低漂移、低熵与有界再入时间的系统，可满足该经验性存续判据；反之则面临坍散风险。 该框架并未回避自身局限性，而是强调需对归一化过程保持透明、谨慎校准并如实报告参考值。本协议未以行话掩盖复杂性，而是着重强调清晰性、实际应用性与科学责任感。 通过将存续性与变换分析简化为若干普适且经实验验证的度量方式，本文为跨领域诊断提供了严谨的理论基础。它为理解稳定性与变化提供了清晰且可检验的语言，统一了物理学、生物学乃至认知科学与信息论的研究路径。