理论成熟度审计报告（公开版）
Theoretical Maturity Audit Report (Public Version)
共 33 项审计模块 · 宪法基准 V3.8.0 · 文档 SGT-000 V3.0
33 Audit Modules · Constitution V3.8.0 · Document SGT-000 V3.0
依据内部多轮严格审计、数学证明、数值验算与极限测试，将理论模块划分为 A 级、A- 级、B+ 级三个成熟等级；所有结论均经过无先验假设检验。
Based on multiple rounds of rigorous internal audits, mathematical proofs, numerical verifications and extreme tests, theoretical modules are divided into maturity levels A, A-, and B+. All conclusions pass priori-free verification.
| 模块 | 核心结论 | 闭合等级 |
|---|---|---|
| 理论基础 | ||
| 拉格朗日作用量 | 完整作用量体系，场方程由变分原理导出 | A |
| 度规-介质分离原则 | 度规方程与介质方程分层独立 | A |
| 场方程 | ||
| 静态场方程 | Ω-A1 解自洽，静态解唯一性定理（P9-A） | A |
| 动态场方程 | 完整协变形式 | A |
| 修正 Friedmann 方程 | FRW 背景下完整变分导出 | A |
| 介质属性 | ||
| 介质物理状态 | 预应力横观各向同性弹性固体 | A |
| 各向异性应力指纹 | Pθ < Pr 全局成立 | A |
| 应变定义 | 度规应变唯一自洽 | A |
| 弹性应变能 W | 完整 3+1 形式公开 | A |
| 弹性常数体系 | 6 常数全闭合（4 独立 + 2 约束） | A- |
| Onsager 互易性 | 精确成立 | A |
| 不可排空性 | ||
| 不可排空性-静态 | Crr → ∞ as χ → 0 | A |
| 不可排空性-动力学 | χ > 0 | A |
| 不可排空性-拓扑 | χ > 0（极端扰动） | B |
| Crr → ∞ ⟺ 不可排空性 | 严格等价命题 | A |
| χ 场结构 | ||
| χ 场本构律 | χ = (1−f)/(1+f²) | A |
| χ(f) 推导链路 | 完整公开 | B+ |
| 冻结分层结构 | 五层 + 冻结锋面 ≈ 光子球 | B+ |
| 动力学 | ||
| 动能项唯一性 | F = 1 精确 | A |
| 变量映射体系 | u/f/ψ 球谐展开严格定义 | A |
| 能量泛函 E | 正定性 + 守恒性 | A |
| Cauchy 适定性（χ ≥ ε） | 双曲系统适定 | A |
| 退化双曲路线图 | 问题精确陈述 + 数学工具推荐 | A |
| 孤立波 | 不存在 | A |
| 因果结构 | ||
| 因果结构定理 | 有效因果锥 + 双曲性 + 因果封闭 | A |
| 内壳层因果性 | 超光速被因果封闭区屏蔽 | A |
| 热力学 | ||
| Hawking 温度 | TH = 0.866 × THGR | A |
| Wald 熵 | SWald = AH/4G | A |
| 第一定律熵 | η1st = 1.66 | B |
| 宇宙学 | ||
| 奇点消除定理 | H(0) = 1.023×10−1 有限 | A |
| 等价定理 | f(0) = 1 ⟺ H(0) < ∞ | A |
| 冻结 de Sitter 相 | 引力冻结驱动极早期膨胀 | B |
| 光学 | ||
| 引力透镜光学 | n = ef，Zeff = Z₀ | A |
| 耦合规则 | ||
| 物质耦合规则 | 普通物质与真空介质耦合分离 | A |
| 微扰与预言 | ||
| QNM 谱 | 含介质修正 | B |
| 回声时延 | Δt ≈ 14.3 M | A |
| 传递函数 F | ψRW = F · ψmedium | B |
| 约束与鲁棒性 | ||
| U(f) 约束定理 | C1–C4 下核心定性结论鲁棒 | A |
| 静态解唯一性定理 | Birkhoff 型证明 | A |
| χ(f) 定性等价性定理 | G1–G5 下核心结论鲁棒 | A- |
| Module | Core Conclusion | Closure Grade |
|---|---|---|
| Theoretical Foundation | ||
| Lagrangian action | Complete action system; field equations from variational principle | A |
| Metric-medium separation | Metric and medium equations layered independently | A |
| Field Equations | ||
| Static field equations | Ω-A1 self-consistent; uniqueness theorem (P9-A) | A |
| Dynamic field equations | Complete covariant form | A |
| Modified Friedmann equations | Full variational derivation in FRW background | A |
| Medium Properties | ||
| Medium physical state | Pre-stressed transversely isotropic elastic solid | A |
| Anisotropic stress fingerprint | Pθ < Pr globally | A |
| Strain definition | Metric strain uniquely self-consistent | A |
| Elastic strain energy W | Complete 3+1 form published | A |
| Elastic constant system | 6 constants fully closed (4 independent + 2 constrained) | A- |
| Onsager reciprocity | Exactly satisfied | A |
| Non-Emptiability | ||
| Non-emptiability (static) | Crr → ∞ as χ → 0 | A |
| Non-emptiability (dynamic) | χ > 0 | A |
| Non-emptiability (topological) | χ > 0 (extreme perturbation) | B |
| Crr → ∞ ⟺ non-emptiability | Strict equivalence proposition | A |
| χ Field Structure | ||
| χ field constitutive law | χ = (1−f)/(1+f²) | A |
| χ(f) derivation chain | Fully published | B+ |
| Frozen layered structure | Five layers + frozen front ≈ photon sphere | B+ |
| Dynamics | ||
| Kinetic term uniqueness | F = 1 exact | A |
| Variable mapping system | u/f/ψ spherical harmonic expansion strictly defined | A |
| Energy functional E | Positivity + conservation | A |
| Cauchy well-posedness (χ ≥ ε) | Hyperbolic system well-posed | A |
| Degenerate hyperbolic roadmap | Precise problem statement + recommended tools | A |
| Solitary waves | Do not exist | A |
| Causal Structure | ||
| Causal structure theorems | Effective causal cone + hyperbolicity + causal closure | A |
| Inner shell causality | Superluminal signals shielded by causally closed region | A |
| Thermodynamics | ||
| Hawking temperature | TH = 0.866 × THGR | A |
| Wald entropy | SWald = AH/4G | A |
| First-law entropy | η1st = 1.66 | B |
| Cosmology | ||
| Singularity elimination theorem | H(0) = 1.023×10−1 finite | A |
| Equivalence theorem | f(0) = 1 ⟺ H(0) < ∞ | A |
| Frozen de Sitter phase | Gravity-frozen driven early expansion | B |
| Optics | ||
| Gravitational lensing optics | n = ef, Zeff = Z₀ | A |
| Coupling Rules | ||
| Matter coupling rules | Ordinary matter and vacuum medium coupling separated | A |
| Perturbation & Predictions | ||
| QNM spectrum | Includes medium corrections | B |
| Echo delay | Δt ≈ 14.3 M | A |
| Transfer function F | ψRW = F · ψmedium | B |
| Constraints & Robustness | ||
| U(f) constraint theorem | Core qualitative conclusions robust under C1–C4 | A |
| Static solution uniqueness | Birkhoff-type proof | A |
| χ(f) qualitative equivalence | Core conclusions robust under G1–G5 | A- |
分级审计结论汇总
Graded Audit Summary
AA 级完全闭合（严格解析证明，体系无漏洞）：拉格朗日作用量、度规-介质分离、静态/动态场方程、修正 Friedmann 方程、介质状态、各向异性应力、应变定义、弹性应变能 W、Onsager 互易性、不可排空性（静态/动力学/等价命题）、χ 场本构律、动能项唯一性、变量映射、能量泛函 E、Cauchy 适定性、退化双曲路线图、孤立波不存在、因果结构定理、内壳层因果性、Hawking 温度、Wald 熵、奇点消除定理、等价定理、引力透镜光学、物质耦合规则、回声时延、U(f) 约束定理、静态解唯一性定理等。
AGrade A — Fully Closed: Lagrangian action, metric-medium separation, static/dynamic field equations, modified Friedmann equations, medium state, anisotropic stress, strain definition, elastic strain energy W, Onsager reciprocity, non-emptiability (static/dynamic/equivalence), χ constitutive law, kinetic term uniqueness, variable mapping, energy functional E, Cauchy well-posedness, degenerate hyperbolic roadmap, no solitary waves, causal structure theorems, inner shell causality, Hawking temperature, Wald entropy, singularity elimination, equivalence theorem, gravitational lensing optics, matter coupling rules, echo delay, U(f) constraint theorem, static solution uniqueness, etc.
A-A- 级基本闭合：弹性常数体系（6 常数全闭合）；χ(f) 定性等价性定理（G1–G5 下核心结论鲁棒）。
A-Grade A- — Basically Closed: Elastic constant system (6 constants fully closed); χ(f) qualitative equivalence theorem (robust under G1–G5).
B+B+ 级定性成立：χ(f) 推导链路完整公开；冻结分层结构（五层 + 冻结锋面 ≈ 光子球）。
B+Grade B+ — Qualitatively Established: χ(f) derivation chain fully published; frozen layered structure (five layers + frozen front ≈ photon sphere).
十一、诚实标注 · 理论负债清单
XI. Honest Labeling · Theoretical Liability Inventory
已清偿的理论负债（P6–P9）
- W 完整形式公开、变量映射严格定义、应变定义唯一自洽、传递函数 F 定量给出
- χ 身份解耦、波速定义统一、有效度规近似标注、μfull 声明、理论闭环状态明确
- βrr < 0 符号 A 级解析证明、非线性稳定性能量证明、弹性常数交叉验证
- Crr → ∞ ⟺ 不可排空性等价命题、U(f) 约束定理、011-A Step4 逻辑缝隙补全
- χ(f) 推导链路公开、退化双曲路线图、静态解唯一性定理（A 级）
- χ(f) 定性等价性定理（A- 级）、奇点消除定理（A 级）、等价定理（A 级）
已清偿核心负债：22 项
Resolved Theoretical Liabilities (P6–P9)
- Complete W form published, variable mapping strictly defined, strain definition uniquely self-consistent, transfer function F quantitatively given
- χ identity decoupled, wave speed definition unified, effective metric approximation labeled, μfull declared, theoretical closure status clarified
- βrr < 0 sign Grade A analytical proof, nonlinear stability energy proof, elastic constant cross-validation
- Crr → ∞ ⟺ non-emptiability equivalence, U(f) constraint theorem, 011-A Step4 logical gap closed
- χ(f) derivation chain published, degenerate hyperbolic roadmap, static solution uniqueness theorem (Grade A)
- χ(f) qualitative equivalence theorem (A-), singularity elimination theorem (A), equivalence theorem (A)
Resolved Core Liabilities: 22 items
仍保留的理论负债（不影响当前自洽性）
- βrr 精确值（−0.75）、Crθ 精确幂律、K 和 fc 微观起源
- Smedium 微观态计数、宇宙学耗散机制、纵波辐射与双星轨道衰减
- 全域 Cauchy 适定性（含 χ → 0 退化）、g(f) = 1+f² 严格唯一性
- SGT 宇宙学扰动理论、冻结 de Sitter 相解冻机制
- 弹性疲劳第一原理推导（C 级）
剩余可控负债：10 项（均为拓展型研究内容，不影响主体体系自洽性）
Remaining Theoretical Liabilities (No Impact on Current Self-Consistency)
- Exact βrr value (−0.75), exact Crθ power law, microscopic origin of K and fc
- Smedium microstate counting, cosmological dissipation mechanism, longitudinal wave radiation and binary orbit decay
- Global Cauchy well-posedness (including χ → 0 degeneration), strict uniqueness of g(f) = 1+f²
- SGT cosmological perturbation theory, frozen de Sitter phase thawing mechanism
- Elastic fatigue first-principle derivation (Grade C)
Remaining Controllable Liabilities: 10 items (all extended research; no impact on main system self-consistency)