Complete Characterization of Nucleons within the SRE Framework: Unified Representation of Two-State Skeleton Inversion, Quark Speculation and Nuclear Reaction Validation

Abstract

This paper provides a unified and complete characterization of nucleons within the State-Relational Entropy (SRE) dynamic framework: nucleons are stable composite objects emerging from binary self-organizing networks on the tripartite Y-shaped coherent core, constrained by the two-state opening/closing of dormant edges and closure degree rebalancing rules. Their ontological structure is the tripartite Y-shaped triangular closure Y₃⋉△₃ (V=12, E=18, β₁=7, |Aut|=36). The full text unfolds along a reproducible logical chain: (1) Establish the general methodology for nucleon derivation: local input → topological solution → inversion, which is homologous to electron derivation; (2) Propose three ontological speculations about quarks (quark ≠ Q₃, quark is an emergent statistical phenomenon, nuclear reaction = closure degree rebalancing) as structural priors for subsequent inversion; (3) Start from neutron β-decay, derive the structural constraints T1–T3 for the nucleon skeleton, and redefine isospin Z₂ as opening/closing duality, rather than flavor multiset flipping; (4) Establish the nucleon inversion simultaneous equation system, and obtain surviving candidates through three-step screening (integer determination of vertex number V=12, spectral ratio determination of topology, triple symmetry determination of solution); then break the tie within the "transition–residue" framework: ρ is proved to be a strict invariant of the transition (the residue, serving as the reference standard of measurement), the dormant edge is taken to be a ring edge, and the criterion of "partial re-equilibration of closure degree" (the open state must still retain closed units) uniquely retains candidate A; (5) Verify the two-state opening/closing mechanism of nuclear fission chain reactions: fast neutron cross-sections restore the same order of magnitude, excitation surplus criterion has a Pearson correlation of +0.932 with thermal cross-sections, and three-level signatures are unified (single nucleon β decay → composite nucleus fission → macroscopic chain criticality); (6) Derive the theoretical constraints that the additivity failure of ion/metal pairs can be theoretically predicted, and current is a coherent bookkeeping projection rather than continuous electron movement; (7) Extend the framework to many-body systems using external nuclear data as a yardstick: the assembly law is determined by two principles ("open–closed complementarity" and "the images of the two bodies must be distinguishable in the shared region", the latter being a non-spatial restatement of the former "closed bodies must not overlap"), yielding the structural linear law of the shared-ring configuration (V=9k+3, E=15k+3, T=2k+1, β₁=6k+1, |Aut|=6·2^k·k!) and the body-count independence of the lowest excitation (λ₂ = 2−√3, multiplicity k−1); a zero-parameter existence scorecard is given and the reading is adjudicated (Reading A adopted: 5/5 matched in the A ≤ 3 sector), and together with the out-of-sample failure of the pricing layer at A=4 and the qualitative failure of the assembly law at A=4, the honesty boundary "**the nuclear boundness for A ≥ 4 is not computable in this layer**" is drawn; it is further shown that this boundary is **not repairable on the side of the numerical binding energy** (the A = 4 isotriplet forms a **single isomorphism class**, so the binding-energy differences cannot be carried by any graph functional, and the additive-profile pricing class is falsified as a whole by an **identity** independent of the shape of the pricing function), and the disposal of the "shadow solution" (variant D) is completed (it is the k=2 member of the shared-ring family, and that name is withdrawn); (8) an attempt is made to derive the **antisymmetric coefficient** λ required by that repair from within SRE; the conclusion is that λ can neither be derived nor fixed (its threshold, 29.0596 MeV, exceeds the ⁴He binding energy, and the candidate pool is underdetermined; SRE fixes only the "shape" of λ, not its "value"). The same check, however, yields a positive outcome: demoting antisymmetry from an **energy term** to an **existence criterion** gives a zero-parameter, mirror-symmetric criterion L1 (|n_n − n_p| ≤ 1) that matches the 8-entry scorecard at 8 / 8, so that **the existence question at A = 4 is computable in this layer**; the out-of-sample test (A ≥ 5, 26 entries) shows that L1 does not have the status of a fundamental law (22 / 34 hits, its mismatches being respectively an α closure effect and the absence of an A scaling), so the boundary is **relocated** from A ≥ 4 to A ≥ 5. This work does not prove that the SRE axioms are objectively true; all conclusions are self-consistent constructions within the SRE model, and real physical and chemical inferences must be independently verified by external means. 本文在状态‑关系熵(SRE)动力学框架下,对核子给出统一的完整刻画:核子是二元自组织网络三股 Y 形相干核上,经休眠边开合二态与闭合度再平衡规则约束后涌现的稳定复合对象,其本体结构为三股 Y 的三角闭合体 Y₃⋉△₃(V=12、E=18、β₁=7、|Aut|=36)。全文沿一条可复现的逻辑链展开: (1) 建立核子推演的方法学总纲:局部带入 → 拓扑求解 → 反推,与电子推衍同源; (2) 提出关于夸克的三条本体论推测(夸克≠Q₃、夸克是涌现统计现象、核反应=闭合度再平衡),作为后续反演的结构先验; (3) 从中子 β 衰变切入,导出核子骨架的结构约束 T1–T3,并重新定义同位旋 Z₂ 为开/闭二态,而非味道多重集翻转; (4) 建立核子反演联立方程系统,经三步筛选(整数性定顶点数 V=12、谱比定拓扑、三重对称定解)得到幸存候选,并在"过渡-残留"框架下打破并列:ρ 被证明为过渡的严格不变量(残留,充当测量标尺),休眠边取环边,由"闭合度部分再平衡"判据(开态必须仍保有闭合单元)唯一保留候选 A; (5) 验证裂变链式反应的开闭二态机制:快中子截面恢复同量级、激发盈余判据与热截面 Pearson 相关 +0.932,三级签名统一(单核子β衰变→复合核裂变→宏观链式临界); (6) 推导出离子/金属性对加和失效的理论预见与电流是相干簿记投影而非电子持续移动的理论约束; (7) 以外部核数据为标尺作多体推广:由"开-闭互补 + 两体映像在共享区须可分辨"两条原则(后者为原"闭合体不可重叠"的非空间化改写)确定拼接律,给出共享环构形的结构线性律(V=9k+3、E=15k+3、T=2k+1、β₁=6k+1、|Aut|=6·2^k·k!)与最低激发与体数无关性(λ₂ = 2−√3,重数 k−1);给出零参数存在性记分卡并裁决读法(取读法甲:A ≤ 3 分区 5/5 命中),同时以定价层的 A=4 外样本失败与拼接律的 A=4 定性失败,共同划定"**A ≥ 4 的核束缚性不在本层可算**"这一诚实边界;并进一步证明该边界在**结合能数值**一侧不可修复(A = 4 的同量异位素为**同一同构类**,结合能差异不可能由图泛函承载;加性剖面定价类被一条与定价函数形态无关的**恒等式**整类证伪),完成"影子解"(变体 D)的处置(其即 k=2 共享环成员,该命名撤回); (8) 尝试从 SRE 内导出该修补所需的**反对称系数** λ,结论是 λ 不可导出、亦不可固定(其阈值 29.0596 MeV 超过 ⁴He 结合能,且候选池欠定;SRE 只定住 λ 的"形"、不定住其"值");但同一检验产出一个正面结果——把反对称性从**能量项**降格为**存在性判据**后,得到零参数、镜像对称的判据 L1(|n_n − n_p| ≤ 1),在 8 项记分卡上 8/8 命中,故 **A = 4 的存在性问题在本层可算**;外样本检验(A ≥ 5,26 项)显示 L1 不具基本律地位(22/34 命中,其失配分别为 α 闭合效应与缺少 A 标度),边界因此由 A ≥ 4 **移位**至 A ≥ 5。 本工作不证明 SRE 公理客观成立;全部结论均为 SRE 模型内部的自洽性构造,现实物理与化学推论须经外部手段独立核验。