The 012 Unbalanced Ternary Causal Growth System: Intrinsic Convergence Prescriptions and Conditional Emergence of the Relativistic Equations/012 不平衡三进制因果生长系统:内禀 收敛规约与相对论方程的条件性涌现

AbstractThis paper formulates the intrinsic coarse-graining, lineage-projection, andstationary-convergence prescriptions required for a discrete causal-growth sector ofthe 012 unbalanced ternary system to enter a continuum relativistic branch. Theconstruction retains C001, C002, and C003 as its foundational axioms. Its intrinsicprescriptions use only lineage markers, claim events, port activity, coherence load,topological charge, lineage drift, and their discrete response. No external scalar field,presupposed action, or independent matter field is introduced. These prescriptionsdefine and select the relativistic continuum branch; they are not unique logicalconsequences of C001–C003 for every causal-growth sector.At the discrete level, claim throttling and topological-charge conservation provide aconserved accumulation structure for event response, while finite group-valuedWilson updates accumulate local charge response into connection transport. Thepositive fixed point of stationary nonadditive feedback identifies the lineage restscalar \(m_0\). Under the intrinsic convergence prescriptions A1–A8, the discreteconnection, matter second moments, and test-lineage transport possess consistentcontinuum limits. If the continuum geometric response is local, symmetric,diffeomorphism covariant, divergence-free, and constructed from at most secondderivatives of the metric, the four-dimensional Lovelock classification restricts it to acombination of the Einstein tensor and the metric. Unit-charge normalization andexclusion of an independent homogeneous response then yield\(G_{\mu\nu}=\kappa T_{\mu\nu},\quad \nabla^\mu T_{\mu\nu}=0.\)Independently, the stationary fixed point \(q^*=\iota^*=m_0\), the definition offour-momentum, and four-velocity normalization imply exactly\(E^2=p^2c^2+m_0^2c^4,\quad E_0=m_0c^2,\quad E=\gamma m_0c^2.\) Theclassical relativistic equations therefore arise as exact special cases in a designatedstationary continuum branch of the 012 system. This result establishes a conditionalbranch-emergence theorem: relativity is a special continuum stationary branchwithin the 012 system, rather than a unique logical consequence of the threefoundational axioms in all admissible causal growth sectors.Keywords: 012 unbalanced ternary system; intrinsic coarse-graining; stationaryconvergence; lineage projection; Einstein field equations; mass–energy relation 摘要本文在 012 不平衡三进制因果生长系统的 C001、C002、C003 公理基底上,建立稳态谱系由离散因果生长进入连续相对论分支所需的内禀粗粒、谱系投影和收敛规约,并推导该分支中的 Einstein 场方程与质能关系。内禀规约只使用谱系标记、认领事件、口岸活性、相干负荷、拓扑荷、谱系漂移及其离散响应,不引入外加标量场、预置作用量或独立物质场。它们构成相对论连续分支的定义与选择条件,而不是 C001—C003 对所有生长扇区的唯一推论。离散层面,认领节流和拓扑荷守恒给出事件响应的守恒累积结构;有限群值Wilson 更新将局域荷响应累积为连接运输;稳态非加性反馈的正不动点将谱系静息标量确定为 \(m_0\)。在 A1—A8 内禀收敛规约下,离散连接、物质二阶矩和测试谱系运输具有一致连续极限。连续几何响应若为局域、对称、微分同胚协变、无散度且至多依赖度规二阶导数的张量,则由四维 Lovelock 分类确定为Einstein 张量与度规项的组合。单位荷归一化及齐次响应排除条件进一步给出\(G_{\mu\nu}=\kappa T_{\mu\nu},\quad \nabla^\mu T_{\mu\nu}=0.\) 另一方面,稳态不动点 \(q^*=\iota^*=m_0\)、四动量定义和四速度归一化严格给出\(E^2=p^2c^2+m_0^2c^4,\quad E_0=m_0c^2,\quad E=\gamma m_0c^2.\)因此,经典相对论方程构成 012 系统在指定稳态连续分支中的精确特例。本文证明的是完整条件下的分支涌现,不主张三条基础公理单独唯一导出相对论。关键词:012 不平衡三进制;内禀粗粒化;谱系投影;稳态收敛;Einstein 场方程;质能关系