DC‑NO.PM: Philosophy of Mathematics · Conjectures and Conceptual Analyses

This is the official preprint in the philosophy of mathematics for the DC‑NO system, conducting metamathematical exploration and foundation around the core meta‑axiom "Measurement‑as‑Non‑Being". Through directed auxiliary exploration, it proposes two meta‑theoretic conceptual analyses: the non‑positive formalizability of pre‑measurement reality, and the absolute independence conjecture of Measurement‑as‑Non‑Being; it argues that if one accepts the definitional equivalence of "formalization as measurement," then Measurement‑as‑Non‑Being is an independent proposition in formal systems containing measurement operations, neither provable nor refutable. This study places Measurement‑as‑Non‑Being into the same structural analogy family of self‑referential theorems as Gödel's incompleteness theorems, Tarski's undefinability theorem, and Turing's halting problem, providing a rigorous philosophical‑mathematical foundation for the system. All conclusions are labeled with proof status and abide by reflexive constraints. The term "violence" as used in the DC‑NO.EP second‑order metaphilosophy of economics is strictly confined to the ontological philosophical level, denoting the structural closure effect imposed by measurement operations upon economic alterity, rather than any physical, institutional, or political violence. The system explicitly distinguishes three levels: ontological violence (the system's core usage), institutional violence (merely for differentiation), and physical violence (not used by the system). This usage is descriptive, aiming to reveal the mechanism by which the irreducible ontological residue Δ arises in economic measurement; it does not constitute a moral condemnation or political accusation against any particular state, political system, social group, or historical practice. The system's critique of "plan" and "market" is symmetrical, as both fall within the framework of "measurement‑alteration"; the system does not take sides with any political camp, and its ethical red line explicitly prohibits using this system for epistemic power suppression. The system itself is also subject to this critique — its own text is likewise a measurement operation that generates ontological residue. This abstract is intended to convey the precise academic meaning of the term to readers, avoiding any misinterpretation divorced from its philosophical context. Mandatory Risk Disclosure: The formalization of the Δ operator, the fixed‑point theorem of audit recursion, the non‑integrability proof of the five‑dimensional gap topology, and the empirical testing of ODR phase transitions are open conjectures that have not received rigorous external mathematical proof. This system is a second‑order metaphilosophy and does not produce first‑order policies or tools; direct use in resource allocation, policy formulation, or performance evaluation is strictly prohibited. All propositions carry embedded falsification conditions; 100 internal deduction rounds do not constitute external validation. τ_crit ≈ 0.42 and the personhood formula P = (RD/3) × (1/(1+CS)) are qualitative heuristic tools only and are prohibited from use as empirical parameters. C‑080 bridging to China's independent economic knowledge system is a strategic‑level extrapolation carrying forced‑association risk, currently unverified. The judgment AI(LT) = 0 is sample‑insufficient (n = 1 < 5); the system may not claim quality compliance. The system prohibits cognitive power suppression, prohibits claiming to stand outside its own meta‑axioms, prohibits using "insufficient samples" as a permanent defense, and prohibits direct binding with performance evaluation, resource allocation, or policy formulation. Reflexive declarations are markers of metaphilosophical honesty only, not additional axioms. This is an architectural boundary, not a disclaimer.