012 不平衡三进制因果生长系统:从 C001–C003 公理体系推演质能方程与 爱因斯坦场方程/012 Unbalanced Ternary Causal Growth System: Derivation of Mass-Energy Equation and Einstein Field Equation from C001–C003 Axioms

本文从公理化离散因果生长理论——012 不平衡三进制因果生长系统——出发,沿正向演绎主线给出两条推导链:由"生、持、消"三相不平衡公理与认领节流机制(C003)内生导出质能方程 E = γm₀c²;由同一公理集生成的因果序几何,经离 散 Regge 结 构 的 连 续 读 出 极 限 , 同 构 匹 配 爱 因 斯 坦 场 方 程 G_μν =(8πG/c⁴)T_μν,其中宇宙学常数读数与零一致(探测上限 5×10⁻³)。全部推导以十二条内生公理为唯一起点;连续几何、洛伦兹协变与引力动力学均为读出层的极限结构,其匹配条件与适用边界显式给出。文末给出两条区别于广义相对论的可检验观测预言。关键词:012 不平衡三进制;因果生长系统;认领节流;相干极限;离散 Regge几何;质能方程;爱因斯坦场方程Starting from an axiomatic discrete causal growth theory — the 012 Unbalanced Ternary CausalGrowth System — this paper presents two derivation chains along a purely deductive mainline.First, the mass-energy equation E = γ m ₀ c ² is derived endogenously from the unbalancedgeneration – maintenance – elimination axioms together with the Claim Throttling mechanism(C003). Second, the causal-order geometry generated by the same axioms is shown to match, inthe continuous readout limit of a discrete Regge structure, Einstein's field equation G_μν = (8πG/c⁴ )T_μν, with the cosmological-constant readout consistent with zero (detection upperbound 5 × 10 ⁻ ³ ). All derivations take twelve endogenous axioms as the sole starting point;continuous geometry, Lorentz covariance, and gravitational dynamics are limit structures of thereadout layer, whose matching conditions and domains of validity are stated explicitly. Twotestable observational predictions, distinct from general relativity, are given at the end.Keywords: 012 unbalanced ternary; causal growth system; claim throttling; coherence limit;discrete Regge geometry; mass-energy equation; Einstein field equation