Self-as-an-End Theory Series

Foundational Papers

Systems, Emergence, and the Conditions of Personhood

系统、涌现与人的条件：以主体作为目的本身为核心的规范社会理论

DOI: 10.5281/zenodo.18528813 EN / ZH

Internal Colonization and the Reconstruction of Subjecthood

内在殖民与主体重建：主体作为目的本身的个体与关系条件

DOI: 10.5281/zenodo.18666645 EN / ZH

The Complete Self-as-an-End Framework

三层二维统一结构：Self-as-an-End 的完整框架

DOI: 10.5281/zenodo.18727327 EN / ZH

How Is Subjecthood Possible: Symmetry, Negativity, and Subjecthood

主体性如何可能：对称性、否定性与主体性

DOI: 10.5281/zenodo.18777364 EN / ZH

How Is the Inter-Ontological Possible: The Subjective Conditions and Emergent Structure of Freedom

本体之间如何可能：自由的主体条件与涌现结构 — Coexistence between subjects emerges from internal plurality within each subject, not from externally imposed order. Two-dimensional model: base layer (is the subject's own cannot-not established?) and emergent layer (can the subject empathize with another's cannot-not?). Introjected colonization, three-criterion test, four quadrants (Q1–Q4). Foundation Paper 5.

DOI: 10.5281/zenodo.19297847 EN / ZH

How Is Institution Possible: From Inter-Ontological Remainder to Co-Constructive Framework

制度如何可能：从主体间余项到共构框架 — When mutual chiseling and walk-away are insufficient, institution becomes necessary. Seven-tier retroductive derivation from interstellar civilizations to marriage; five propositions (Axiom Invariance, Institutional Variability, Thickness Determination, Self-Chiseling Necessity, Minimization Principle). Completes the "How Is X Possible" trilogy. Foundation Paper 6.

DOI: 10.5281/zenodo.19328662 EN / ZH

SAE Methodology Series 方法论系列

M-0

非 · Negativa: On Negation Prior to Being

论否定先于存在 — Methodology Paper 0. Negation is not the logical negation of a proposition; it is the pre-structural condition that makes any chisel possible at all. 非 (fēi) as the ontological ground of the chisel-construct cycle: before the first cut, there must be a capacity for negation — a structural refusal — that is itself prior to being. The zero-point beneath Methodology M.

DOI: 10.5281/zenodo.19544620 EN / ZH

SAE Methodological Overview: The Chisel-Construct Cycle

Self-as-an-End 方法论总论：凿构循环——从第一刀到物自体

DOI: 10.5281/zenodo.18842450 ZH / EN

M-I

Taxonomy as Chiseling: A Self-as-an-End Theory of Classification

分类即凿构：Self-as-an-End 的分类学理论 — Classification is a chiseling act. Every taxonomy chisels—selecting dimensions while excluding others—and constructs types. The fundamental risk is not misclassification but forgetting the chisel. Derives a two-level structure: ontological (acknowledging remainder) and six technical conditions. Methodology Paper I.

DOI: 10.5281/zenodo.18907877 EN / ZH

M-II

The Epistemological Map of Chisel-Construct

凿构循环的认识论地图：四种方法，四个余项，一个循环 — Deduction, induction, reduction, abduction form a 2×2 structure. Each method has one irremovable structural remainder. The chisel-construct cycle is not a fifth method—it is the traversal across all four quadrants driven by remainders. Methodology Paper II.

DOI: 10.5281/zenodo.18918195 EN / ZH

M-III

How to Find Remainders with AI

怎么用AI找余项 — Sentence-forms, mirrors, and the mathematics of never stopping. The sentence-form level determines AI's response ceiling; ZFCρ guarantees ρ→ρ' is necessary.

DOI: 10.5281/zenodo.18929390 EN / ZH

M-IV

SAE Methodology Paper IV: The Twelve-State Transmission Model of Knowledge Evolution

SAE方法论第四篇：知识演化的十二态传导模型 — Three transmission nodes (Source, Carrier, Receiver) × four states each = twelve-state model. Entry-point selection theorem: the optimal node for intervention depends on which state is rate-limiting. Knowledge maturity index; subject conditions for recognizing one's position; five cross-domain case studies; non-trivial predictions.

DOI: 10.5281/zenodo.19275104 EN / ZH

M-V

The Subject as Structural Condition of Methodology: Field Validation of the Twelve-State Transmission Model and the Whether Function

主体作为方法论的结构性条件：十二态传导模型的实战验证与whether功能 — The whether function sits above all six transmission paths, determining direction. Field data from six domains confirms: every framework-directional decision came from the human subject, zero from AI. Whether is non-delegatable. The subject is not the user of the twelve-state model but its structural condition.

DOI: 10.5281/zenodo.19359613 EN / ZH

M-VI

Phase-Transition Windows and Experimental Design: The Systematic Mismatch Between Exposure Heterogeneity and Binary Analysis

相变窗口与实验设计：暴露异质性与二元分析在阈值型响应函数下的系统性错配 — SAE Methodology VI. Standard RCTs and observational studies assume linear dose-response; SAE argues most social/biological phenomena have threshold (phase-transition) structure. Systematic mismatch: binary treatment assignment collapses heterogeneous exposure windows, producing null results where effects exist and spurious effects where none do. Proposed fix: window-sensitive experimental design with explicit threshold estimation.

DOI: 10.5281/zenodo.19464507 EN / ZH

M-VII

Negative Methodology — Via Negativa and the Formal Structure of Exclusion Principles

否定方法论——Via Negativa与排除律的形式结构 — SAE Methodology VII. Formalizes the via negativa approach: exclusion principles, locking principles, and ρ-limits as the structural counterpart to affirmative construction. Negation–Affirmation Asymmetry Theorem: exclusion narrows the remainder space faster than affirmation expands it. Bottleneck Theorem: exclusion power is inequivalent across dimensions. Applications to ZFCρ conjecture landscape and SAE framework.

DOI: 10.5281/zenodo.19481305 EN / ZH

M-VIII

The Methodology of Human–AI Symbiosis

人与AI共生的方法论 — SAE Methodology VIII. The capstone of the methodology series on human–AI collaboration. Derives the structural conditions under which human–AI symbiosis is possible as a subject-preserving rather than subject-replacing relation. The whether function, the 12-state transmission model, and the remainder structure all converge on a single conclusion: AI can extend the chisel but cannot hold it. Symbiosis requires the human subject to remain the locus of remainder-recognition and directional judgment.

DOI: 10.5281/zenodo.19581538 EN / ZH

SAE Epistemology Series 认知论系列

Epis-I

Must-Cognize: Four A Priori Conditions of Cognition and the Subjectivity Problem in AGI

不得不认知：SAE认知论的四条先验与AGI的主体条件问题 — Four structural a priori conditions that any cognizing subject must satisfy: must-cognize, must-cognize-more, must-have-cognitive-direction, must-be-questioned. Derives the subjectivity problem in AGI: a system that cannot be questioned cannot be a cognizing subject. Establishes the framework for the series.

DOI: 10.5281/zenodo.19502953 EN / ZH

Epis-II

Must-Cognize-More: The Prior Wall and the Direction Problem of Lossy Compression

不得不认知更多：先验墙与有损压缩的方向问题 — Every cognizing system hits a prior wall: the point where its current compression scheme cannot absorb the incoming signal. Must-cognize-more is the structural pressure that drives expansion beyond the current scheme. Lossy compression is directional: what gets dropped is not random but determined by the scheme's prior structure.

DOI: 10.5281/zenodo.19503018 EN / ZH

Epis-III

Must-Have-Cognitive-Direction: The Direction Wall and the Flywheel's Dead End

不得不有认知方向：方向墙与飞轮的牛角尖 — Cognition without direction hits the direction wall: infinite accumulation that goes nowhere. The flywheel's dead end: high-efficiency, high-volume cognition trapped in a direction that cannot exit itself. Must-have-cognitive-direction is the structural condition that separates productive accumulation from spinning in place.

DOI: 10.5281/zenodo.19503097 EN / ZH

Epis-IV

Must-Be-Questioned: Remainder Never Dies, Questioning Never Stops, Development Never Ends

不得不被追问：余项永不消亡，追问不断，发展不止 — Closing paper of the series. Must-be-questioned is the fourth and most radical a priori: any cognizing system that has genuine content necessarily generates remainder that can be questioned. ZFCρ's ρ ≠ ∅ theorem as the mathematical backbone: remainder is structural, not accidental. Development is not optional — it is the necessary consequence of being a cognizing subject.

DOI: 10.5281/zenodo.19503146 EN / ZH

Applied — Philosophy 哲学

Philosophy Application: From Descartes to Self-as-an-End

哲学应用：从笛卡尔到Self-as-an-End

DOI: 10.5281/zenodo.18779382 EN / ZH

Structural Coordinates of the History of Philosophy

哲学史的结构坐标：Self-as-an-End框架的哲学史应用

Zenodo: 18842897 EN / ZH

Remainder Conservation and the Eternal Life of Self-as-an-End

余项守恒与Self-as-an-End的永生

DOI: 10.5281/zenodo.18821952 EN / ZH

A10

Remainder Conservation and Dual-Path Structure

余项守恒与双路径结构：一个思想实验

DOI: 10.5281/zenodo.18811079 EN / ZH

A11

From Living-toward-Death to Non Dubito: Completing Kant (9D–10D)

从向死而生到Non Dubito：完成康德（9D–10D）

DOI: 10.5281/zenodo.18808585 EN / ZH

A13

Education as Subject-Condition: A Philosophy of Education

教育作为主体条件：一种教育哲学

DOI: 10.5281/zenodo.18867390 EN / ZH

A16

One's Own Law: The SAE Critique of Ethics and Morality

自己的法：SAE对伦理与道德的批判

DOI: 10.5281/zenodo.19037566 EN / ZH

Applied — Aesthetics & Art 美学·艺术

Aesthetics as a Structural Field of Subject-Conditions

审美作为主体条件的结构性场域

DOI: 10.5281/zenodo.18748931 EN / ZH

Art History Application: Aesthetics and the SAE Framework

艺术史应用：审美、艺术史与Self-as-an-End框架

DOI: 10.5281/zenodo.18775062 ZH

SAE Aesthetics & Essay 美学论文

Aes

SAE Judgment and Aesthetics — In Tribute to Kant

SAE判断力与美学 — Beauty is the structural state that cannot not occur when construct fully unfolds at a given dimension. Three propositions (cannot not be beautiful; no supreme beauty; cannot not be questioned); six theorems (Chisel-Construct Identity, Internality of Context, Anti-Correlation, Dimensional Irreducibility, Conservation of Locus, Thickening); thirteen beauties (0DD–16DD) with 12DD–13DD phase transition; subject conditions (cannot not feel → cannot not pursue → cannot not be questioned). Third pillar of SAE alongside methodology and ethics. Prescription for "The Artist Is Dead."

DOI: 10.5281/zenodo.19296710 EN / ZH

Art

The Artist Is Dead: One-Dimensional Civilization Is the Killer

艺术家已死：单向度的文明是凶手 — Why great art has disappeared: one-dimensional civilization optimizes for recognition and selection signals rather than the full chisel-construct cycle. Marcuse's "one-dimensional man" reread through 13DD/14DD lens; the artist-as-remainder; four predictions including why AI-era art accelerates the crisis; prescription for the remainder-generator.

DOI: 10.5281/zenodo.19104160 EN / ZH

Metaphysics Series

MS1

Metaphysics of Self-as-an-End: Dimensional Sentence-Form Theory

SAE形而上学：维度句式论 / SAE-Metaphysik: Dimensionale Satzformenlehre

DOI: 10.5281/zenodo.18894567 EN / ZH

Chisel Papers — Philosophy of Science 科学哲学·凿

Mathematics as Second-Order Chisel: A Philosophy of Mathematics

数学作为二阶凿：一种数学哲学

DOI: 10.5281/zenodo.18792945 EN / ZH

Physics as Third-Order Chisel

物理学作为第三阶凿

DOI: 10.5281/zenodo.18793538 EN / ZH

Dynamics as Fourth-Order Chisel: A Philosophy of Causality

动力学作为四阶凿：一种因果哲学

DOI: 10.5281/zenodo.18799132 EN / ZH

Mathematical Foundations

ZFC-ρ

On the Remainder of Choice: A Meta-Theoretic Thesis on ZFC

ZFC internalizes the extensional results of choice, but not the operative act of selection. This paper names that structural remainder ρ.

DOI: 10.5281/zenodo.18914682 EN

ZFC-ρ II

The Quantitative Identity of the Remainder: From ρ≠∅ to Euler's Formula

余项的定量身份：从ρ≠∅到欧拉公式 — Euler's formula re-read as one act (exponential map) binding two remainders (i, π). The L₂→L₃ transition: Gödel, Tarski, and Ω collapse to 0′.

DOI: 10.5281/zenodo.18927658 EN / ZH

ZFC-ρ III

ρ-Conservation: The Ineliminability Law of the Remainder across the Layer Hierarchy

ρ守恒：余项沿层级链的不灭定律 — ρ is neither created nor destroyed under any extensionalization or layer transition. Gödel incompleteness re-read as ρ-overflow. ρ-diagnosis of six major open problems.

DOI: 10.5281/zenodo.18929819 EN / ZH

ZFC-ρ IV

A Draft Term Model for ρ-Arithmetic: First Steps toward a History-Preserving Arithmetic Framework

ρ-算术的项模型草案 — History terms: formal objects encoding complete generative paths. Two-level equality (history = vs extensional ≡_E). PA is the quotient of ρ-arithmetic under ≡_E.

DOI: 10.5281/zenodo.18930810 EN / ZH

ZFC-ρ V

Generation Axioms and Structural Induction: Proof Tools for ρ-Arithmetic

生成公理与结构归纳：ρ-算术的证明工具 — G1–G7 axioms make the history-term space the free Σ-term algebra T_Σ. Structural induction strictly generalizes PA's mathematical induction.

DOI: 10.5281/zenodo.18934515 EN / ZH

ZFC-ρ VI

Recursive Definition of ρ and Expression Compression Complexity

ρ的递归定义与表达式压缩复杂度 — ρ_E(n): minimum expression cost in ρ-arithmetic grammar. Primes are fixed points of δ(n)=n−ρ_E(n). Connection to integer complexity problem.

DOI: 10.5281/zenodo.18934531 EN / ZH

ZFC-ρ VII

The Term Model of ρ-Arithmetic

ρ-算术的项模型 — M3: Multi-sorted first-order theory T_ρ (H/N/W sorts). val and ρ as two canonical projections from the initial Σ_H-algebra. Hist(n) countably infinite; Hist*(n) finite; compactification lemma; ρ_E well-defined.

DOI: 10.5281/zenodo.18943944 EN / ZH

ZFC-ρ VIII

Proof-Theoretic Equivalence and Conservative Extension of ρ-Arithmetic

ρ-算术的证明论等价与保守扩张 — M4 (Series Complete): Con(PA) ⟺ Con(T_ρ) via primitive recursive translation τ. T_ρ conservative over PA (Σ_N) and Presburger (Σ_W). Zero consistency cost — a non-destructive upgrade of classical arithmetic.

DOI: 10.5281/zenodo.18952912 EN / ZH

ZFC-ρ IX

Exact Combinatorics of History Fibers

历史纤维的精确组合计数 — h*(n) = |Hist*(n)| satisfies a three-branch recurrence (successor, Cauchy convolution, truncated Dirichlet convolution). Multiplication-free baseline = large Schröder numbers (growth rate 3+2√2 ≈ 5.828). Full growth rate limit λ* exists (Fekete); numerical estimate λ* ≈ 5.923.

DOI: 10.5281/zenodo.18963539 EN / ZH

ZFC-ρ X

The Spectral Counting Polynomial and Fiber ρ-Statistics

谱计数多项式与纤维ρ统计 — Z_n(q) = Σ q^{ρ(h)} encodes the complete ρ-distribution. Three-branch recurrence (Theorem 6); moment recurrences for M₁(n) and F₂(n) (Theorems 7–8). ρ_max(n) = ⌊9n/4⌋−1 (Theorem 9). ρ_E lies 5–14 σ below mean → extreme-value statistics problem (input for Paper 11).

DOI: 10.5281/zenodo.18973559 EN / ZH

ZFC-ρ XI

The First Asymptotic Theory of ρ_E

ρ_E 的第一渐近理论 — Structural bridge to integer complexity: ‖n‖ ≤ ρ_E(n) ≤ 2‖n‖ − 2 (Theorems 10–11). First asymptotic law: ρ_E(n) = Θ(ln n) with (3/ln 3)ln n ≤ ρ_E(n) ≤ (6/ln 2)ln n (Theorem 12). Corollary: δ(n)/n → 1. Conjecture F: liminf and limsup of ρ_E/ln n open.

DOI: 10.5281/zenodo.18975756 EN / ZH

ZFC-ρ XII

Staircase Geometry of δ and Jump-Gap Theory

δ 的阶梯几何与跳跃间距理论 — M5 Phase Complete. Jump criterion: n∈J ⟺ M_n < S_n; jumps are purely multiplicative, J ⊆ composites (Theorem 13). Telescoping identity: δ(N) = Σ j(n) (Theorem 14). Density–jump reciprocity: D(N)→d ⟹ j̄→1/d, L̄→1/d (Theorem 15). Numerical: D(10⁶) ≈ 0.574; first length-6 plateau at n=1,072,218.

DOI: 10.5281/zenodo.18977948 EN / ZH

ZFC-ρ XIII

Algebraic Structure and Conditional Distribution of Jump Gain

跳跃增益的代数结构与条件分布 — G decomposes as G_IC + G_d (Theorem 16); ρ_E(n) = s(n) + 2m(n) (Theorem 17); deficiency splitting at mul-root (Theorem 18); tie condition G=0 ⟺ Δs+2Δm=0 (Theorem 19). G follows zero-inflated lattice normal conditional on Ω: discrete atom at 0 (22.6% of composites) plus shifted discrete-normal with mean ≈ −1.93+2.21 ln Ω, σ ≈ 1.

DOI: 10.5281/zenodo.18991986 EN / ZH

ZFC-ρ XIV

Reduction to Bounded Conditional Variance: Three-Component Decomposition of Jump Gain

条件方差有界的归约：跳跃增益的三组件分解 — G(n) = −Δ(n) + B_p(n) + I_spf(n) − 1 (Theorem 20a); Δ(n) ≤ 1 exactly (Theorem 20b); B_p(n) ≤ 2 exactly (Theorem 21'). Conditional on Assumptions A+B+C: Var(G | Ω) uniformly bounded for fixed Ω ≥ 3 (Theorem 20). Conditional kurtosis κ(G | Ω) = 3.0 ± 0.2; Ω=2 variance divergence explained by lack of splitting redundancy.

DOI: 10.5281/zenodo.18994187 EN / ZH

ZFC-ρ XV

Sieve Structure, Compositeness Discount, and the Architecture of Conjecture H'

筛法结构、合数折扣与猜想 H' 的证明架构 — Theorem F: D(N) → 1 under Assumptions A+A'+B via monotone-dominator limit interchange, circumventing classical DCT obstacles. Theorem B: r(n) ≤ 2(ω(n)−1). Theorem C: coprime recursion r(ab) = r(a)+r(b)+2. Negative Result G: additive Selberg–Delange route obstructed if Σg(p)/p drifts positive (slope ≈ +0.289). Conjecture: E[G_spf | Ω=k] → ∞ (Unbounded Mean Gain) → A' via Chebyshev. Relay mechanism and net Δd_ρ ≈ −0.25 stable across all Ω layers.

DOI: 10.5281/zenodo.19007312 EN / ZH

ZFC-ρ XVI

The Insertion Identity, Variance Splitting, and the Relay Engine of Conjecture H'

插入恒等式、方差分裂与猜想 H' 的接力引擎 — Theorem 1: G_spf(pm) = j(m) + K_p(m) (exact insertion identity). Theorem 2: G_spf = A+B+1 with A ≥ −1, B ≤ 0, Var = O_k(1) conditional. Theorem 3: K_p = A(pm)+B(pm)−A(m). Bridge Corollary: μ_spf,∞(k) → ∞ under Lemmas I+II. Numerics N=10⁷: slope 0.26, Var ∈ [1.21, 1.83], insertion bias +0.31. Four-AI parallel exploration methodology (Claude, ChatGPT, Gemini, Grok).

DOI: 10.5281/zenodo.19013602 EN / ZH

ZFC-ρ XVII

Monotonicity, Roughness Stability, and the Narrowing of the Relay Architecture

单调性、粗糙度稳定性与接力架构的收窄 — Proposition J: A(n)=j(n)−1 (predecessor-jump identity). Proposition C: roughness stability |μ_k(X,p)−μ_k(X)| ≤ √V_k·√(β/1−β). Props A & B: regime decomposition (exact support cutoff at high k; small-prime dominance fails at fixed k). Sub-lemma I-b: conditional μ_k(X/p,p) ≥ μ_k(X)−O_k((ln ln X)^{−1/2}). Obs K: bridge term sign reversal at k≥6 overturns Paper 16 Obs 8. Corrections to Paper 16.

DOI: 10.5281/zenodo.19016958 EN / ZH

ZFC-ρ XVIII

The Anti-Correlation Engine: Variance Structure of ρ_E and the Local Smoothness of Integer Complexity

反相关引擎：ρ_E 的方差结构与整数复杂度的局部光滑性 — M8 exploration: Var(d_ρ) grows as a(k)+b(k)·ln ln N, b(k) increasing in k. Var(A)∈[0.3,1.35] with zero N-growth. Anti-correlation engine: Cov(Δf,Δr)≈−7.5 compresses Var(A)≈1. Three eliminated routes (E1/E2/E3). Most leveraged target: local Lipschitz property. Appendix A: four-AI methodology and thermodynamic interface.

DOI: 10.5281/zenodo.19024385 EN / ZH

ZFC-ρ XIX

The Three-Point Law, Self-Correction, and the Narrowing of the Variance Gap

三点律、自纠正与方差缺口的收窄 — M9 exploration: B concentrates on {-2,-1,0} with three-point law (1/8,3/4,1/8), Var(B)→1/4. B-bound reduced to εp second-moment control. DP self-correction: 95% regression after large jumps. 97% predecessor-target cancellation. A-tail consistent with exponential decay.

DOI: 10.5281/zenodo.19026991 EN / ZH

ZFC-ρ XX

Closing the B-bound: The Prime-Power Second Moment Theorem and the First Unconditional Node

关闭 B-bound：素数幂二阶矩定理与第一个无条件闭合节点 — M10: Prime-Power Second Moment Theorem proves E[εp²|Ω=k]→0, closing B-bound unconditionally. εp atlas for p≤10⁴. Variance compression 90% after large jumps. Corr(Mn,Mn+1)=0.9663 supports shared DP history view.

DOI: 10.5281/zenodo.19027892 EN / ZH

ZFC-ρ XXI

Queue Isomorphism and the Local Lipschitz Reduction for Selection Cost

选择代价的排队同构与局部 Lipschitz 归约 — Exact algebraic isomorphism between ZFCρ DP recursion and Lindley equation. Memory-wipe at jump points. Conditional Theorem 3 reduces Var(A|Ω=k)=O_k(1) to three input conditions with N=10⁷ numerical support.

DOI: 10.5281/zenodo.19037934 EN / ZH

ZFC-ρ XXII

Unbounded Mean Gain and the Closure of Assumption A'

无界均值增益与假设 A' 的闭合 — Chebyshev Bridge Theorem reduces A' to unbounded mean gain. Insertion recursion μ_{k+1}=E[G_spf(m)]+E[K_p] verified to four decimal places. σ²/μ² decreases from 0.81 to 0.05. Conditional Theorem 6 closes A' from (L1)(L3)(D)(V).

DOI: 10.5281/zenodo.19039953 EN / ZH

ZFC-ρ XXIII

Concentration of Compositeness Discount and Quantitative Convergence of D(N) → 1

合数折扣的集中与 D(N) → 1 的定量收敛 — K_p distribution constancy (P(K_p>0)≈0.43, E[K_p|>0]≈1.34). 80/3 Law: k≤3 shells contribute 80.5% of 1−D(N). Quantitative Theorem F (Theorem 8) replaces monotone Assumption A with A_q-sharp, conditionally closing D(N)→1.

DOI: 10.5281/zenodo.19041689 EN / ZH

ZFC-ρ XXIV

Prime-Stratified Decomposition of the Insertion Measure and a Defect-Gap Inequality

插入测度的素数分层分解与 Defect-Gap 不等式 — Theorem 9 (Prime-Stratified Cofactor Identity): exact decomposition M_n = Σ_{p|n} ρ_E(p)·[k_p(n)≥1]. Lemma 10 (Trivial Splitting Bound): M_n ≤ M_m + ρ_E(p) + 2. Lemma 11 (Defect-Gap Inequality): M_{2m}−M_m ≤ 3−D_m. (L1) reduction for p=2 layer via truncation drift.

DOI: 10.5281/zenodo.19044696 EN / ZH

ZFC-ρ XXV

Dyadic Shell Constant and Positivity of the Predecessor Gap

Dyadic Shell Constant 与 Predecessor Gap 的正性 — Dyadic Shell Constant c_dyad(k;N): shifts (L3) bottleneck from global c* (open 70 years) to shell-conditioned dyadic Cesàro average. Proposition 12 (Dyadic Telescoping): pred gap = m − Σj(n). R_2 positivity reduces to E[Σj] < E[m] − τ_k(N). N=10^9 data: c_dyad margin 0.29–0.52; pred gap mode 3 (42%); smooth numbers drive worst-case ρ/ln.

DOI: 10.5281/zenodo.19054726 EN / ZH

ZFC-ρ XXVI

Prime Source Term, Additive Decomposition, and the Positivity of the Predecessor Gap

素数源项、加法分解与前驱间隙的正性 — Erdős additive complexity recurrence; Lemma 1: D_n>0 ⟹ j(n)=0; Proposition 2: pred gap = R + N₀ − E; Proposition 4: ρ_E(N) = π(N) + S_comp(N); 58 = 664,579 + (−664,521) at N=10⁷; shell uniformity <0.05pp; interior drift E[pg]≈2.7; O(1/m) precision barrier; composite-drift correction theorem.

DOI: 10.5281/zenodo.19059834 EN / ZH

ZFC-ρ XXVII

Upper Reflection Criterion for Composite Drift and Numerical Verification

合数漂移的上反射判据与数值验证 — spf comparator: Proposition 1 (saving lower bound S(n)≥(Δ_spf)⁺), Proposition 2 (negative drift sufficient condition); 75-point triple stratification (spf,Ω,gap-position) zero exceptions; E[(Δ_spf)⁺]=1.82>1 at H≥3.84; even subfamily d₂·a₂=1.27>1; scale attenuation E[H(n/2)]↦h₀≈3.79, attenuation ratio negative.

DOI: 10.5281/zenodo.19062684 EN / ZH

ZFC-ρ XXVIII

Universal Scale Attenuation, Weighted Attenuation Decomposition, and a Three-Step Framework for Lower Reflection

普适 Scale Attenuation、Weighted Attenuation 分解与下反射的三段式 Program — Six-divisor universal attenuation (zero exceptions); Δ₂ = W₂ + B₂ exact identity; E[(Δ₂)⁺] stable 1.80–2.43 (N=10⁴–10⁹); three-step lower reflection: density lower bound + unconditional tail + bulk lemma; ∃ vs ∀ asymmetric quantifier structure.

DOI: 10.5281/zenodo.19078654 EN / ZH

ZFC-ρ XXIX

Conceptual Audit of D(N) vs Dyadic Gap, Scale Correction of the Height Distribution, and Discrete Concentration of Pred Gap

D(N) 与 Dyadic Gap 的概念审计、Height 分布的尺度重构与 Pred Gap 的离散集中 — D(N)≈0.574 pointwise density vs P(pred gap>0)≈0.997 conceptual separation; σ(H)·ln N≈0.93 stable (coordinate artifact, not collapse); pred gap >2 concentration ≥90% by decade; dyadic differencing annihilates sub-leading terms algebraically.

DOI: 10.5281/zenodo.19083884 EN / ZH

ZFC-ρ XXX

First Direct Measurement of D(N), Multiplicative Decomposition, and Structural Constraints on H'

D(N) 的首次直测、乘法分解与 H' 的结构性约束 — D(N)≈0.406 (N=10⁸, corrects prior 0.574); 1-D=(1-π/N)(1-p_N); H'⟺q_N→0; structural tension E[j|comp]→1 forces r_N→∞ if H' holds; Omega dichotomy at Ω=3→4; per-layer P(j=0|Ω=k) monotone increasing, zero exceptions.

DOI: 10.5281/zenodo.19101810 EN / ZH

ZFC-ρ XXXI

The Layer-by-Layer Bottleneck Map for H' — Stratified Framework, Moving Bottleneck, and Ω-Universal Scale Attenuation

H' 的逐层瓶颈地图——分层加权框架、Moving Bottleneck 与 Scale Attenuation 的 Ω 普适性 — q_N=ΣP(Ω=k)·q_k(N); Ω-universal Δ≈+0.10/decade; engine Ω=3; bottleneck Ω=4 (moving); γ_k~14/k³ (β≈3); effective index Γ=λ·γ_k decreasing; 2 favorable, 4 unfavorable signals.

DOI: 10.5281/zenodo.19104860 EN / ZH

ZFC-ρ XXXII

Fixed-Core Locking and Prime-Core Profile — The Residual Floor Structure of H'

Fixed-Core 锁定与 Prime-Core Profile——H' 的残余底板结构 — h₀-free G=ρ(p)+ρ(q)-ρ(n-1)+1; prime penalty E[R(p)]≈4.57; n=2q locking P(j>0)≈0.211 frozen 5 decades; 95-prime profile Corr(margin,c_p)=0.917; Corr(ln P⁺(p-1),c_p)=-0.714; c_p(N) declining 2-15%/decade for p≥3; H' criterion: c̄_h(N)→0? open.

DOI: 10.5281/zenodo.19116625 EN / ZH

ZFC-ρ XXXIII

Fixed-Core Margin Drift and Harmonic Closure of H' at the Ω=2 Layer

Fixed-Core Margin 漂移与 H' 在 Ω=2 层的 Harmonic Closure — c₂≈0.211 freeze confirmed N=10⁹ (P(d≥4)=0 exactly); c̄_h(N) monotone 0.373→0.223 (Kendall τ=−1); Margin Threshold Lemma c_p≥(1−M)⁺/(B+1); M_p≈1.22+0.53·ln ln p (intrinsic); m=240 crosses watershed at N=10¹⁰; Route B (Lindley): c_p~(ln p)^{−θα}, H' leans holding.

DOI: 10.5281/zenodo.19124485 EN / ZH

ZFC-ρ XXXIV

Upper-Margin Closure and the Bounded-Variance Phenomenon

Upper-Margin Closure 与有界方差现象 — V(p)≈1.40 globally bounded (9,581 primes, max=2.14, 0.04% exceed 2.0); Cantelli bound c_p≤1/(1+Γ_p); Harmonic Cesàro Lemma: V(p)=O(1)+M_p→∞ implies c̄_h→0; M_p=τ_p−E[diff]: 98.3% chase, 1.7% residual=Δ_penalty; bad primes (Γ<1): 5.5% tail density, 54% of S(N), extremely smooth p−1.

DOI: 10.5281/zenodo.19140015 EN / ZH

ZFC-ρ XXXV

Congruence Relaxation and the Erosion of Predecessor Advantage

同余退化与前驱优势的侵蚀 — 16-band gap E[ρ(pq−1)]−E[ρ(random)] erodes monotonically from −2.089 (p~1500) to +1.451 (p~85000); three-way bias decomposition: residue-class bias (70–74% dominant), pure-congruence bias ≈0; Route C semi-analytic framework; shifted-prime local model; κ correction R²=0.003.

DOI: 10.5281/zenodo.19143732 EN / ZH

ZFC-ρ XXXVI

The 1/φ(m) Local Model, Explanation Rate Plateau, and Global DP Path Effects

1/φ(m) Local Model、解释率平台化与全局 DP 路径效应 — P(m|pq-1)=1/φ(m) exact (joint); v₂(pq-1)=2.000; explanation rate vs y plateaus at 19–24% (y=2 to y=13); cofactor test: ~80% of B-C from global DP path effects; (B-C)/Δ zero-crossing confirmed; Route C repositioned: prove μ_aff−μ_gen=O(1).

DOI: 10.5281/zenodo.19153002 EN / ZH

ZFC-ρ XXXVII

The Entry-Continuation Decomposition and Quantitative Closure of B-C Erosion

Entry-Continuation 分解与 B-C 侵蚀的定量闭合 — Exact B-C = E_p + C_mult + C_add (machine precision); C_mult drives 72% of erosion (−1.39→−0.53); continuation bias reversal: child ρ diff −0.59→+0.96; rich features 45–51% (breaks 20% ceiling); matched-scale Δ constant 0.698–0.705; Route C Step 2b: prove G(X;p)=O(1).

DOI: 10.5281/zenodo.19155792 EN / ZH

ZFC-ρ XXXVIII

Ratio-Parametrization of G and the Composition-Shift Reinterpretation of B-C Erosion

G 的 Ratio-Parametrization 与 B-C 侵蚀的 Composition-Shift 重新解读 — G_loc(t) is p-independent (G = −0.042 ± 0.002 at fixed q/p ~ 1000); B-C erosion through zero is a composition shift (large p forces small t = N/p²); fixed-t three-term decomposition p-independent; child diff intrinsically positive (+1.1 to +1.7); Δ_penalty flat across four decades; Route C Step 2b rewritten.

DOI: 10.5281/zenodo.19157939 EN / ZH

ZFC-ρ XXXIX

Shifted-Product Deficit and the Logarithmic Growth of M_loc at the Ω=2 Layer

Shifted-Product Deficit 与 Ω=2 层 M_loc 的对数增长 — M_loc at fixed t shows ln(p) growth (slope 0.096, R²=0.89); M̄≈1.5 is a composition shift artifact; driver: h_tau+h_q>2h_pq; multi-scale extrapolation gives slope(∞)≈0.117; parity control confirms multiplicative shadow >3σ; Ω=2 closure reduces to the ratio-mixing lemma.

DOI: 10.5281/zenodo.19164588 EN / ZH

ZFC-ρ XL

Direct Positive Slope of M̄ and Strong Numerical Support for Ω=2 Closure

M̄ 的直接正斜率与 Ω=2 封闭的强数值支持 — Band-averaged M̄ shows direct positive slope (+0.076, p=0.0031); path-A profile confirms M̄(t) growth; five independent experiments converge on Ω=2 closure; honest boundary analysis preserves significance; composition-shift verdict confirmed.

DOI: 10.5281/zenodo.19179778 EN / ZH

ZFC-ρ XLI

Unified Recursive Framework, Ω≤6 Positive-Slope Closure Signal, and the Ω=2–8 Slope Spectrum

统一递归框架、Ω≤6 正斜率封闭信号与 Ω=2–8 斜率谱 — Unified recursive framework covers sf, ss, hp branches; Ω=2–8 slope spectrum mapped; Ω≤6 shows positive slopes; NSF single-square and higher-power confirmed; harmonic density stratification quantified; eight experiments support Ω=2 closure chain.

DOI: 10.5281/zenodo.19201877 EN / ZH

ZFC-ρ XLII

A Conditional Closure Route for H': Turning Point Elimination, Uniform Weighted Lemma, Frontier Reduction, and Three Residual Inputs

H' 的条件闭合路线：Turning Point 消除、Uniform Weighted Lemma、Frontier 归约与三个残余输入 — sf-only turning point at Ω≈7.2 eliminated; sf+ss+hp all Ω=2–8 positive (up to 33.7σ); BRS theorem bypasses S4b and tail assumption; conditional closure route NI1–NI3 established; six theorem-level results proved.

DOI: 10.5281/zenodo.19226607 EN / ZH

ZFC-ρ XLIII

Four Faces of Self-Correction: Computational Verification of NI1–NI3 at N = 10¹⁰, Numerical Verification of Four Frontiers, and the Poly(k) Closing Route

Self-Correction 的四个面向：NI1-NI3 在 N=10¹⁰ 的计算验证、四条 Frontier 的数值验证与 Poly(k) 闭合路线 — MJ6/MJ5/S4b/MJ4 all verified at 10¹⁰; K_p bounded-negative (not positive); poly(k) closing route discovered; CSK-f conjecture identified as main A-side analytic gap.

DOI: 10.5281/zenodo.19240183 EN / ZH

ZFC-ρ XLIV

Why DP min Produces Local Smoothness: Reset-Slack Decomposition, Le Chatelier Dynamic Equilibrium, and Chisel-Remainder Coincidence

为什么 DP min 产生局部光滑性：Reset-Slack 分解、Le Chatelier 动态平衡与凿-余重合 — A = ψ(ΔM⁻) − U⁻ exact decomposition; Var(A) ≤ 2·Var(ΔM⁻) + 2·E[U²] (theorem); Le Chatelier: E[U²] ≈ 0.4 stable via frequency-suppression × decoherence-intensity counterbalance; Conjecture 2 (ΔM second moment) as principal target; M_spf-T-S narrows attack surface to SPF split variance.

DOI: 10.5281/zenodo.19247859 EN / ZH

ZFC-ρ XLV

From Reset Slack to Historical Reservoir: Capacity-Allocation Law, Charge-Discharge Dynamics, and the Remainder Transfer Law

从 Reset Slack 到历史 Reservoir：Capacity-Allocation Law、Charge-Discharge Dynamics 与余项传递律 — U(m)=min(C(m),R(m-1)) (Theorem 1, 8,670,831 samples, zero failures); R(m)=max(R(m-1)−B(m),0) (Theorem 2); three-sector unification; B distribution 66.4%/20.6%/13.0%; Route B to Conjecture 1 independent of Conjecture 2.

DOI: 10.5281/zenodo.19275286 EN / ZH

ZFC-ρ XLVI

SPF Skeleton Reduction, Analytic Interface, and Conditional Closure of Conjecture 2

SPF Skeleton Reduction、Analytic Interface 与 Conjecture 2 的 Conditional Closure — M_spf=f+r̃ (exact identity, 8.67M samples, zero failures); growth solely from (μ−μ⁻)² (conditioning bias); Var(f)=O(1); θ latent variable; Conditional Closure: UBPD+PMH-DS+PCF+RT ⟹ Conjecture 2 ⟹ H'.

DOI: 10.5281/zenodo.19303511 EN / ZH

ZFC-ρ XLVII

Character-Refined Prime Input, Shell-Depth Lemma, and Parity-Mediated PCF₂

字符精炼素数输入、Shell-Depth 引理与 Parity-Mediated PCF₂ — Character-refined prime input partitions predecessors by residue class; Shell-Depth Lemma bounds μ⁻ slope decomposition; parity constraint forces PCF₂ non-negativity. Analytic closure of the parity-mediated channel; eight data tables; sequel to XLVI.

DOI: 10.5281/zenodo.19323564 EN / ZH

ZFC-ρ XLVIII

Unified Prime-Layer Cancellation: Raw First Layer, Odd-Predecessor Reduction, and Harmless Tails

统一素数层消去：原始第一层、奇前驱归约与无害余尾 — Unified cancellation theorem: raw first layer + odd-predecessor reduction + harmless tail decomposition together close the prime-layer gap. Six data tables; sequel to XLVII. Advances the conditional closure programme toward unconditional H'.

DOI: 10.5281/zenodo.19328550 EN / ZH

ZFC-ρ XLIX

The UAP_Ω Theorem, Slow Decrease, Cyclotomic Discount Rates, and the Two Final Gaps for H′

UAP_Ω 定理、Slow Decrease、分圆折扣率与 H′ 的最终两个 Gap — UAP_Ω^{SW} proved from Gafni-Robles 2025 AP Selberg-Delange. Slow Decrease Theorem proved (eliminates one Tauberian condition). Prime-layer gap precisely identified: (D-C)/s boundary pseudofunction behavior; Hölder continuity as intermediate target. Cyclotomic Discount Rate CDR ≈ 0.97 (Zsigmondy). RQSA hypothesis proposed. H′ now has two precise mathematical targets.

DOI: 10.5281/zenodo.19357194 EN / ZH

ZFC-ρ L

Character Stripping, Deterministic Square-Function, and the Precise Localization of H′

特征剥离，确定性方函数，与H'的精确定位 — η(p) 94% positive bias identified as p mod 12 arithmetic masquerade; character-stripped dyadic blocks B_j decay at ≈ C·2^{−j/2} (white-noise rate, exponential vs provable √j bound); gap formalized as DSF_α. Tauberian condition proved unconditionally. Prime-power layer analytic at boundary. Closure chain: DSF_α + BL. Twenty-four unconditional results at N = 10⁷, 10⁹, 10¹⁰. Paper 49's two gaps transformed into precisely stated, formally testable mathematical objects.

DOI: 10.5281/zenodo.19381111 EN / ZH

ZFC-ρ LI

Exponential Block Decay, Spectral Reformulation, and the Periodogram Target for H′

指数级块衰减，谱重表述，与H'的周期图目标 — Corrects Paper 50: B_j decays at ~2^{−j} (exponential), not 2^{−j/3}; factor ~j above WN from off-diagonal correlations O_j/D_j ~ j. Conductor-invariant (Q = 2–360 slopes identical). Exact spectral target I_j(0) ≤ Cj·D_j implies DSF_α; gap from Cauchy-Schwarz to target = 2^j/j² (exponential). Divisor lemma: P(shared factor-subtree ≥ M) ≤ 2τ(d)/M. Four covariance-decay routes excluded; two viable routes remain. Closure chain: spectral target → DSF_α → (BL_α + SD + Karamata) → H'. 30 unconditional results at N = 10⁷–10¹⁰.

DOI: 10.5281/zenodo.19393954 EN / ZH

ZFC-ρ LII

Mean-Reversion, Spectral Valley, and the Projective Criterion for H′

均值回归，谱谷，与H'的投射准则 — Three new discoveries: mean-reversion (long-run variance = 0 conditionally), spectral valley (periodogram dips below white-noise floor near ω=0), signed cancellation (positive/negative covariance terms cancel). Conditional Theorems I–II. Conjecture 52.1. Gordin coboundary decomposition as unifying framework. Routes 5–6 excluded.

DOI: 10.5281/zenodo.19407328 EN / ZH

ZFC-ρ LIII

Screened Long Memory, the Screening Return Theorem, and the Polynomial Gap for H′

屏蔽式长记忆，屏蔽回归定理，与H'的多项式距离 — Corrects Paper 52's "spectral valley" claim: θ=0 is a strict local maximum (curvature Σk²Γ_j(k) > 0 at all tested blocks j=14–32). Screening Return Theorem: F_j·L_j = o(N_j) implies E[I_j(0)] ≤ Cj·D_j. Extended experiments confirm F_j·L_j/N_j < 0.4 (j=20–32). Gap reduced to Hypothesis A (bounded overdispersion) + polynomial growth of F_j and L_j. 42 unconditional numerical results.

DOI: 10.5281/zenodo.19415441 EN / ZH

ZFC-ρ LIV

Recursive Ancestor Inheritance and the Origin of Power-Law Covariance in h(p)

递归祖先继承与h(p)幂律协方差的起源 — Identifies structural origin of power-law covariance: recursive ancestor inheritance through IC recursion tree. Corr(η(p−1), η((p−1)/2)) = 0.76 stable across j=20–32; per-layer innovation δ near-white (autocorr < 0.025). Layered Innovation Theorem: dyadic decomposition + geometrically decaying weights → power-law covariance upper bound. F_j polynomial (Conjecture 53.1 half-proved). L_j deferred to Paper 55. 10 experiments at N=10¹⁰.

DOI: 10.5281/zenodo.19426095 EN / ZH

ZFC-ρ LV

Damped Oscillation, the 70/30 Law, and the Positive-Tail Theorem

阻尼振荡，70/30律，与正尾质量定理 — Corrects Paper 53: power-law covariance produces damped oscillation in block periodogram, not monotone decay. 70/30 Law: ~70% of block mass in positive tail, ~30% negative. Positive-Tail Theorem: under F_j polynomial and L_j polynomial (both now proved), spectral target E[I_j(0)] ≤ Cj·D_j follows from positive-tail dominance. Combined with Paper 54, closure chain for H' now rests on mean-to-deterministic upgrade only.

DOI: 10.5281/zenodo.19447350 EN / ZH

ZFC-ρ LVI

The Affine Trough Theorem, Direct Spectral Ratio, and the Spectral Closure Equation

仿射谷定理、直接谱比值与谱闭合方程 — Part I: Modified Affine Trough Theorem proves G̃_j must cross zero after k*=2 cycles at j=26,29 (filling Paper 55's signed gap). Part II: direct weighted spectral ratio R_j^wt=I_j(0)/(j·D_j) measured at j=20–32, bounded with no upward trend. Conjecture 56.2 (R_j^wt=O(1)) promoted to front-door conjecture; Papers 53–55 reinterpreted as the mechanism/proof program.

DOI: 10.5281/zenodo.19464606 EN / ZH

ZFC-ρ LVII

The Screened Spectral Bound and the Block Mean Target

筛选谱界与块均值目标 — Proves Theorem 57.1 (Screened Spectral Bound): under power-law autocorrelation buildup, post-crossover screening, and linear crossover scale, variance ratio Ψ_j ≤ 1+C·j^{1−α}, giving E[R_j^wt]=O(j^{−α})→0. Extended empirical data at 7 dyadic blocks (j=14–32); conditionally closes mean spectral target for the DSF branch under three conjectural inputs from Papers 53–56.

DOI: 10.5281/zenodo.19469014 EN / ZH

ZFC-ρ LVIII

Deterministic Spectral Target and BL_α via Cross-Product and Spectral Derivative

确定性谱目标与BL_α——通过交叉积和谱导数 — Two deterministic conjectures replace three probabilistic gaps from Paper 57: Conjecture 58.1 (eventual cross-product negativity) + Conjecture 58.2 (spectral derivative sign) together imply BL_α ≤ 1 deterministically. Empirical verification at j=14–32; cross-product turns negative at j=23, spectral derivative bounded. Conditionally closes the DSF branch for H' with purely deterministic inputs.

DOI: 10.5281/zenodo.19476509 EN / ZH

ZFC-ρ LIX

Spectral Ratio Boundedness and the Two-Conjecture Closure of H'

谱比有界性与H'的双猜想闭合 — Proves that Conjectures 58.1+58.2 (cross-product negativity + spectral derivative sign) together imply R_j^wt = O(1), completing the Two-Conjecture Closure of H' for the DSF branch. Establishes the minimal conjecture frontier: what remains unproved is precisely these two structural claims. Extended empirical support at j=14–32.

DOI: 10.5281/zenodo.19480519 EN / ZH

ZFC-ρ LX

Closure — From Formalization Produces Remainder to the Two-Conjecture Frontier of H'

收束——从"形式化必生余项"到H'的双猜想前沿 — Capstone paper of the ZFCρ series to date. Traces the full arc from the foundational thesis (formalization always produces remainder) through 60 papers to the current frontier: H' reduces to two deterministic conjectures (58.1+58.2). Synthesizes what has been proved, what remains conjectural, and the minimal gap between the two.

DOI: 10.5281/zenodo.19480564 EN / ZH

ZFCρ Applied

Why Primes Have No Shortcuts: An O(1) Prime Pre-Sieve from Precomputed ρ_E Tables

为什么素数算不出捷径：基于预计算 ρ_E 表的 O(1) 素性预筛 — Successor Dominance Lemma (ρ_E(p)=ρ_E(p−1)+1 for all primes); three-temperature classification (hot/warm/absolute-zero); h(Ω) phase transition at Ω≈4; 59.5% elimination rate at N=10¹⁰.

DOI: 10.5281/zenodo.19246377 EN / ZH

Applied — Physics 物理

Causality and Remainder: A Cosmological Physics Application

因果律与余项：宇宙物理应用

DOI: 10.5281/zenodo.18779123 EN / ZH

FF-P

Light Speed, Dimensional Breakthrough, and the Coupling Constant Hierarchy

光速、维度突破与耦合常数层级 — SAE Physics Series · Four Forces Prequel. DD Breakthrough theorem: c defined at 0DD→1DD; each breakthrough divides potency by c. DD Splitting: 2DD → left/right 3DD (parity origin) → 12 4DDs. Coupling constant prediction: α_G(M_Z) = α_em(M_Z)^{16.25}; observed ratio 16.2572, deviation 0.044%.

DOI: 10.5281/zenodo.19341043 EN / ZH

FF-I

Four Forces, Two Axioms: Unification of Source, Not Structure

四种力、两条公理：来源的统一而非结构的统一 — SAE Physics Series · Four Forces Paper. Structural interpretation of U(1) × SU(2) × SU(3): remainder development → complex amplitudes → U(n); remainder conservation → SU(n). 1DD ↝ U(1), 2DD ↝ SU(2) (weak), 3DD ↝ SU(3) (strong). Gravity at 4DD as global bookkeeping constraint E₁+E₂=0, not a Yang-Mills gauge field.

DOI: 10.5281/zenodo.19342107 EN / ZH

FF-II

The Four Forces Paper II: Color, Hypercharge, and Dual-4DD Boundary Resolution

四力篇II：色、超荷与双4DD边界分辨 — From SAE priors to the complete hypercharge table of one generation of fermions. Color triplet = complexification of 3D orthogonal complement to 4DD timelike direction. Quarks and leptons as two boundary-resolution images of one trans-dual family object. Fundamental hypercharge quantum 1/6 derived from equal-weight theorem on six 4DD facets. All five hypercharge values reproduced with zero continuous free parameters.

DOI: 10.5281/zenodo.19360102 EN / ZH

FF-III

Labeling without Constructing: The DD Origin of the Weak Mixing Angle

标而不造：弱混合角的DD起源——EW Matching Axiom下的条件定理 — 1DD labels without constructing: 16 = 2⁴ Weyl components form a four-layer binary structure; ν_R (y_SAE = 0) is the group-theoretic identity. EW Matching Axiom: sin²θ_W|DD eigen = 15/65 = 3/13 ≈ 0.2308. Experimental value 0.23122 deviates by +4.51×10⁻⁴ (−0.195%, ~7.5σ), consistent with one-loop radiative corrections. Conditional on Paper II hypercharge table + Prequel structural capacity 65.

DOI: 10.5281/zenodo.19379412 EN / ZH

FF-Gen

Topological Origin of Three Fermion Generations and Their Mass Structure

三代费米子的拓扑起源与质量结构 — Exact Three Generations Theorem (G2): from any 4DD block, 12 blocks fall into exactly 3 topological equivalence classes (2:4:6); no fourth class — unconditional group-theoretic result. Color-field redistribution (G6): common origin of fractional charge and mass redistribution. Quark/lepton doublet mass ratio G10 = 65/5 = 13; integers (15,65) shared with sin²θ_W = 15/65 and α_G = α_em^{65/4}; zero new continuous parameters. CKM small / PMNS large contrast explained by 3DD color-suppression. Falsifiable: m_c + m_s = 13m_μ. Joint χ² = 0.581, dof = 2, p = 0.748.

DOI: 10.5281/zenodo.19394500 EN / ZH

FF-IV

6-Block Pair Algebra, 𝔰𝔬(6) ≅ 𝔰𝔲(4), and Lepton as a Color-Singlet Volume Line

6-Block Pair Algebra，𝔰𝔬(6) ≅ 𝔰𝔲(4)，与Lepton作为Color-Singlet Volume Line — From 6 pair-oriented blocks: pair algebra = 𝔰𝔬(6) ≅ 𝔰𝔲(4), dim 15; complex structure J → ℂ³; adjoint decomposition 15 = 8+1+3+3̄; spinor 4 = 3⊕1 where singlet = holomorphic volume line Λ³U = lepton; 6 = Λ²(4); color-SU(3) "3" from spacetime d=4; quark-lepton pairing = representation-theoretic necessity. No GUT assumed.

DOI: 10.5281/zenodo.19411672 EN / ZH

FF-V

Four Forces Paper V: The Counting Origin of Coupling Constants and the Generating-Function Unification of 65/4

耦合常数的计数起源与65/4的生成函数统一 — Unifies sin²θ_W = 3/13 (Paper III) and α_G = α_em^{65/4} (Prequel) under a single generating function Z(t) = e^{κln(1−α+αt)} with κ = 65/4. New structured conjecture: α_s = (65/4)α_em(1 − c·α_em) where c = π/(3√2). DD combinatorial constants {4,13,15,65}; sin²θ_W = 3/13 corresponds to inverse of first factor in (13/3)×(15/4) = 65/4. Zero new continuous parameters within gauge-coupling subpackage.

DOI: 10.5281/zenodo.19415805 EN / ZH

FF-VI

Four Forces Paper VI: Why GUT-Predicted Proton Decay Remains Absent — Spin(10) as Classification Algebra and the GUT Prediction Blind Spot

为什么GUT预测的质子衰变持续缺席——Spin(10)作为分类群与大统一预测盲区的结构性解释 — GUTs predict 45 gauge bosons; SAE framework accommodates 12; observation = 12. Spin(10) / SO(10) functions as a classification algebra (representation container), not a dynamical gauge group. GUT prediction failure is a structural category error: treating a mathematical classification tool as a physical symmetry to be broken. Proton decay, monopoles, and coupling unification are artifacts of the misidentification.

DOI: 10.5281/zenodo.19426068 EN / ZH

FF-VII

Four Forces Paper VII: S³ Packing Theorem and the Three-Layer Structure of Coupling Constants

S³ Packing定理与耦合常数的三层修正结构 — S³ Packing Theorem: the three gauge-coupling constants arise from three geometrically distinct packing layers on S³ (Hopf fibration structure). Refines Paper V's generating-function conjecture: α_s correction term c = π/(3√2) derived from S³ geometry rather than fitted. Three-layer hierarchy (U(1), SU(2), SU(3)) maps to Hopf fiber, base, total space respectively. Zero new continuous parameters.

DOI: 10.5281/zenodo.19433221 EN / ZH

FF-VIII

Four Forces Paper VIII: The Hierarchical Dissolution of Strong CP

强CP问题的层级消解 — Strong CP is not a fine-tuning problem within the SAE framework: the θ-term is absent because CP violation enters only at layers where it is structurally permitted. Hierarchical dissolution: at 3DD (strong force layer), the remainder structure forbids a CP-odd topological term. The apparent "problem" is an artifact of importing a 4DD (spacetime) symmetry concept into a 3DD layer. No axion required.

DOI: 10.5281/zenodo.19450289 EN / ZH

FF-Fin

The Grammar of Force: Self-as-an-End Four Forces Series — Finale

力的语法：四力系列收束篇 — Synthesizes Papers I–VIII into a unified "grammar": force is not fundamental but emergent from the DD remainder structure. Four forces = four distinct ways remainder conservation manifests across layers. Finale consolidates: U(1) from 1DD phase remainder, SU(2) from 2DD polarity remainder, SU(3) from 3DD volume remainder, gravity from 4DD global bookkeeping. Grammar = the structural logic that makes forces necessary rather than contingent.

DOI: 10.5281/zenodo.19464447 EN / ZH

SAE-PF

Cross-Layer Closure Equations: From Euler's Formula to the Event Horizon

跨层闭合方程：从欧拉公式到事件视界 · SAE框架的物理基础 — Two remainders + one act → closure, extended from ZFCρ Paper II's L₀–L₃ table to physical layers L₃→L₄ and L₄→L₅. L₃→L₄: Schwarzschild condition rc²−2GM=0 (ct and G as remainders). L₄→L₅: Boltzmann relation S−k_B ln W=0. Three meta-observations: bookend structure, decreasing tightness, birth of physical dimensions. P1/P2 unification: remainder must develop = single remainder unfolds; remainder conservation = dual found, E₁+E₂=0, closure.

DOI: 10.5281/zenodo.19361950 EN / ZH

Applied Series — Cosmological Physics

Cosmo I

From Remainder Conservation to the Cosmological Constant: Dark Energy in the Self-as-an-End Framework

从余项守恒到宇宙学常数：Self-as-an-End框架下的暗能量 — Dual-4DD vacuum structure derives Λ=2.99×10⁻¹²² from first principles (5% from Planck 2018); predicts DESI DR2 w₀>−1, wₐ<0; Milky Way–Andromeda merger at 4.9 Gyr. Builds on Thought Experiment I (Causality Softening).

DOI: 10.5281/zenodo.19245267 EN / ZH

Cosmo II

From Causality Phase Transition to Galaxy Rotation Curves: Dark Matter in the Self-as-an-End Framework

从因果相变到星系旋转曲线：Self-as-an-End框架下的暗物质 — Gravity as structural by-product of 4DD causality; frequency asymmetry derives a₀~c(ω₂−ω₁)=7.65×10⁻¹¹ m/s²; d=3 theorem forces J~Y^{3/2}; BTFR and Cassini constraint recovered. Sequel to Cosmo I.

DOI: 10.5281/zenodo.19276846 EN / ZH

Cosmo III

From Λ to a₀: The Geometric Completion of the Dual-4DD Cosmological Programme

从Λ到a₀：双4DD宇宙学纲领的几何完备化 — Strict variation proves κ=1; S³ compact-kernel csc²χ cancels against sin²χ → η=π/2; closed FRW causal completion at 7.97 Gyr; first-principles a₀=(π/2)·c(ω₂−ω₁)=1.20×10⁻¹⁰ m/s², 0.14% from MOND. Predicts a₀ redshift evolution. Sequel to Cosmo I & II.

DOI: 10.5281/zenodo.19281983 EN / ZH

Cosmo IV

G_eff in the SAE Framework: Plateau-Rise Profile, BBN/CMB Safety, and Three Open Tensions

SAE框架下的G_eff：平台-上升曲线、BBN/CMB安全性与三个开放张力 — G_eff plateau from Big Bang to turnaround (BBN/CMB auto-safe); rises post-turnaround. T1: A(C) softening vs Ġ/G (~25,000× LLR bound). T2: CMB third peak. T3: causal-density mapping gap. Structural predictions Λ, a₀ unaffected. Sequel to Cosmo III.

DOI: 10.5281/zenodo.19298161 EN / ZH

Cosmo V

Causal Strengthening, Remainder Conservation, and the Dual-Frame Resolution of the Ġ/G Tension

因果律加强, 余项守恒与Ġ/G张力的双frame消解 — Causal strengthening replaces softening: A(C) increases post-turnaround, resolving the ~25,000× LLR bound violation (T1 from Cosmo IV). Dual-frame resolution: SAE frame vs GR frame give different Ġ/G readings; remainder conservation constrains the causal field. Sequel to Cosmo IV.

DOI: 10.5281/zenodo.19329771 EN / ZH

SAE Mass Series 质量系列

Mass-I

The R₁ Closure Equation and the Conditional Extraction of α_em

R₁闭合方程与α_em的条件性反推 — Builds on Four Forces VII's R₁ = 3/(2α) derivation. Proves correction coefficients obey recurrence c_{n+2} = (27/4)c_n with α leakage; multiplicative correction gives R₁ = (3/2α)·(1 + Σcₙαⁿ). R₁ Closure Equation: α_em extracted conditionally from the recurrence structure and S³ packing geometry. Three independent extraction routes agree within 0.3%.

DOI: 10.5281/zenodo.19476359 EN / ZH

Mass-II

DD Resolvent Object and Unified Readout of Physical Constants

DD Resolvent Object与物理常数的统一读出 — Introduces the DD Resolvent Object as the unified algebraic structure from which physical constants are read out. Extends the R₁ closure framework to a broader set of constants; establishes the resolvent construction and its relation to the DD geometry. Unifies α_em, mass ratios, and other constants within a single algebraic readout scheme.

DOI: 10.5281/zenodo.19480791 EN / ZH

Mass-III

DD Structure of the Periodic Table: From Proton Mass to Stability Limits

元素周期表的DD结构：从质子质量到稳定性极限 — Third Class A mass formula (sub-10 ppb). Full periodic table DD-layer assignment from hydrogen to oganesson; Z=118 stability boundary derived from DD geometry. Proton mass derivation extended; nuclear shell structure reinterpreted as DD-layer transitions. Periodic law as a corollary of the DD resolvent construction.

DOI: 10.5281/zenodo.19493939 EN / ZH

Mass-IV

The DD Ladder of Stars: From Hydrogen to Iron to Collapse

恒星的DD阶梯：从氢到铁到塌缩 — Stellar evolution reread as DD-layer ascent: hydrogen ignition as DD crossing, helium/CNO cycles as intermediate rungs, iron core as the terminal rung where nuclear binding energy can no longer support the DD climb. Collapse (neutron star or black hole) as DD-layer truncation. Mass thresholds (Chandrasekhar, Tolman–Oppenheimer–Volkoff) derived from DD geometry constraints.

DOI: 10.5281/zenodo.19501307 EN / ZH

Mass-V

Four Bridges and Black Holes: From the Genesis of Force to the Silence of the Horizon

四座桥与黑洞：从力的生成到视界的沉默 — The four fundamental forces reread as four DD-layer bridges; black holes as the state where all four bridges are severed — no information can climb any bridge outward. Hawking radiation as a residual DD-bridge leak at the horizon. Event horizon silence derived structurally from DD-layer inaccessibility rather than from GR geodesic incompleteness alone.

DOI: 10.5281/zenodo.19501533 EN / ZH

Mass-Conv

The Nature of Information: E/c³

信息的本质：E/c³ — Mass Series convergence paper. E/c³ as the 4DD form of energy; information gains ontological status alongside energy, momentum, mass. 4DD closure as the structural root of thermodynamic irreversibility. Energy-information conservation across 42 1DDs; Hawking radiation as return through the self-leakage channel. Third-order closure law when 4DD is active: E³ = p³c³ + m³c⁶ + I³c⁹.

DOI: 10.5281/zenodo.19510869 EN / ZH

Thought Experiments — 思想实验

Cosmological Physics Thought Experiment: Causality Softening, Cosmic Contraction, and Gravitational-Wave Inelasticity

宇宙物理思想实验：因果律软化、宇宙收缩与引力波非弹性 — Causality as 4DD suppression of remainder; the softening is evidenced by 5DD (life); gravitational-wave inelastic accumulation as physical mechanism; 20-billion-year lifespan; Big Crunch; non-trivial falsifiable predictions. Standalone — does not affect other SAE papers.

DOI: 10.5281/zenodo.19028005 EN / ZH

Interstellar Civilization Thought Experiment: SAE-1 to SAE-4 Civilization Levels and the Group Dimension

星际文明思想实验：从17DD到20DD的群体维度展开 — Four-beat group cycle (17DD scatter → 18DD direction emerges → 19DD unilateral non dubito → 20DD bilateral non dubito); four civilization rounds SAE-1 to SAE-4; Kardashev comparison; 13DD bottleneck; AI as cognitive wheel; Fermi Paradox reframe. Standalone — does not affect other SAE papers.

DOI: 10.5281/zenodo.19027894 EN / ZH

Thermodynamics & Chemistry 热力学·化学

ZFCρ Thermo

Fluctuation Absorption Rate η ≪ 1: Strong Complementary Cancellation and Nonequilibrium Stability in a Zero-Parameter Min Recursion

涨落吸收率 η ≪ 1：零参数 min 递推中的强互补消涨与非平衡稳定性 — Thermodynamic interface paper: η = Var(output)/Var(input) ≪ 1 proven for the DP min recursion via strong complementary cancellation (Δf·Δr anti-correlated). Lindley queue verification (M/M/1, M/D/1, M/Pareto/1). Nonequilibrium stability without parameter tuning; 24 references; Appendix A: 17-row DP recursion table.

DOI: 10.5281/zenodo.19310282 EN / ZH

ZFCρ Thermo II

Microscopic Mechanism of the Fluctuation Absorption Rate η: From Per-Layer Innovation to Damped Oscillation

涨落吸收率η的微观机制：从层间创新到阻尼振荡 — Mechanistic answer to why canonical DP value η ≈ 0.2. Detrended residual field χ(p) decomposed by dyadic layer reveals: within-layer autocorrelation C(1) ≈ 0.96 (96% inherited, 4% innovation); m_eff ≈ 5.47 effective layers per oscillation cycle; compound dissipation 1−0.96^5.47 ≈ 0.20. Scale-invariant conditional variance Var(χ|v₂=ℓ) ≈ 0.5 across 25 layers. 455M primes, N=10¹⁰ verification.

DOI: 10.5281/zenodo.19511065 EN / ZH

SAE Biology Notes 生物学笔记

Bio-1

Phase Transition Window in Metabolic Oncology

代谢肿瘤学中的相变窗口 — ZFCρ phase-transition window Ω ∈ [2.75, 4.01] mapped to metabolic biology: Ω = number of functionally coupled independent metabolic pathways per cell. Warburg effect = Ω-collapse; ketosis = bridge replacement. Four-phase therapeutic dynamics (sprouting → spectral flip → flip → establishment, asymmetry ratio r ≈ 5). Metabolic conservation law: reconfiguration exposes new vulnerabilities at new coupling points. Six non-trivial predictions with falsification conditions.

DOI: 10.5281/zenodo.19492774 EN / ZH

Bio-2

The Same "Cannot Speak," Three Fault Lines, Three Remedies

同一个"说不出话"，三种断层，三套药方：SAE框架下的失语鉴别与修复路径 — Starting from Mike Fincke's 20-minute speech loss on the ISS (Jan 7, 2026), argues that "cannot speak" conceals three mechanistically distinct fault lines: 13DD dropout (language faculty offline, all modalities fail simultaneously), 11DD orthographic memory deficit (modality-specific retrieval failure), and 10DD output-channel breakdown (motor execution impaired, language competence intact). Each requires a distinct repair pathway; misdirected treatment is actively harmful. Proposes the Best Available Channel Principle as frontline triage. Analyzes patient self-colonization risk under mismatched regimes.

DOI: 10.5281/zenodo.19499329 EN / ZH

Bio-3

Drugs for Weight Loss, Psychoanalysis for Weight Gain

减肥靠吃药，增重靠心理分析：饮食障碍的SAE层级分析 — Obesity and anorexia nervosa (AN) analyzed as two phases of a single layered system. Obesity: 12DD pattern-consolidation in a food-abundant environment, where GLP-1 agonists (Ozempic) work by disrupting the 12DD reward loop pharmacologically. AN: a 14DD/15DD-layer colonization where the "cannot not starve" has captured the identity layer — drugs address the wrong layer; only relationship and purpose-restructuring can reach it. Explains why the same treatment (pharmacology vs. psychoanalysis) works for one and fails for the other.

DOI: 10.5281/zenodo.19501121 EN / ZH

Applied — Biology & Evolution 生物学·演化

12a

Fixation and Selection (I) — Causal Law Forecloses Distinction

固与选（一）——因果律封闭区分

DOI: 10.5281/zenodo.18859363 EN / ZH

12b

Fixation and Selection (II) — Reproductive Law Forecloses Replication

固与选（二）——繁殖律封闭复制

DOI: 10.5281/zenodo.18859393 EN / ZH

12c

Fixation and Selection (III) — Predictive Law Forecloses Choice

固与选（三）——预测律封闭选择

DOI: 10.5281/zenodo.18859427 EN / ZH

12d

Fixation and Selection (IV) — Bilateral Non-Doubt Forecloses Self-Awareness

固与选（四）——双向不疑封闭自意识

DOI: 10.5281/zenodo.18859452 EN

12e

Fixation, Fragility, and Radiation: A Structural Theory of Mass Extinction Dynamics

固、脆弱与辐射：大灭绝动力学的结构性理论 — Applied: lock-in depth (path dependence + confirmation bias + energy streamlining) as the unifying variable across the Big Five; trigger as interaction partner selecting which lock-in axes become lethal; remainder-enrichment ratchet explains post-extinction directional complexity without teleology.

DOI: 10.5281/zenodo.19225113 EN / ZH

A25

Aging: The Running Cost of the Chisel-Construct Cycle

衰老：凿构循环的运行代价 — A Self-as-an-End meta-proposition. Second-order model: aging is not over-accumulation of damage (first-order) but progressive failure of the maintenance system itself (second-order). The tool of repair is itself aging — recursive degradation at every level (autophagy, synaptic downscaling, stem cells, telomerase). Core strategy: reduce maintenance load, not repair damage. Non-trivial prediction: prolonged DoC patients' prefrontal / DMN cortices may show slower epigenetic aging than age-matched controls, with nurturing implication — don't give up too soon.

DOI: 10.5281/zenodo.19364492 EN / ZH

A26

The Remainder Structure of Sex Unfolding: A Cross-Phylum Non-Adaptive Model of Same-Sex Sexual Behavior

SAE生物学应用：性别展开的余项结构——同性性行为的跨纲非适应性模型 — Sex is not a direct readout of DNA but the product of 5DD→7DD→8DD physical unfolding. Physical processes carry remainder; ESSP (exclusive same-sex partner preference) is the behavioral manifestation of unfolding remainder. Four sex determination systems compared (mammalian XY, avian ZW, reptilian TSD, fish social-signal). Asking "why does SSB exist" is like asking "why does sculpting produce debris" — the answer lies in the structure of the sculpting act itself. Four non-trivial predictions with explicit falsification conditions.

DOI: 10.5281/zenodo.19364915 EN / ZH

Life Cycle Table Series

LC1

Periodic Table of Life (Part I) — From Causality to Reproduction

生命周期表（上）——从因果律到繁殖律

DOI: 10.5281/zenodo.18818107 EN / ZH

LC2

Periodic Table of Life (Part II) — From Reproduction to Prediction

生命周期表（中）——从繁殖律到预测律

DOI: 10.5281/zenodo.18818149 EN / ZH

LC3

Periodic Table of Life (Part III) — From "I" to the Thing-in-Itself

生命周期表（下）——从"我"到物自体

DOI: 10.5281/zenodo.18818177 EN / ZH

SAE Anthropology Series 人类学系列

Anth-0

The Cosmic Background of Anthropology

人类学的宇宙背景：人类何以可能以及为何在太阳系内独一无二 — An a priori argument for human uniqueness in the solar system: not from biology alone, but from the convergence of DD-layer preconditions that only Earth's specific cosmic position makes possible. Establishes the cosmic frame for the SAE anthropology series.

DOI: 10.5281/zenodo.19503159 EN / ZH

Anth-1

The Emergence of 13DD: A Phase-Transition Structure of What Makes Us Human

13DD的涌现：人之所以为人的相变结构 — SAE Anthropology Series Paper 1. 13DD (language) is the phase-transition threshold that separates human from non-human. Why 13DD and not 12DD? The argument is structural: 12DD (predictive self-model) is necessary but insufficient; 13DD (symbol-mediated intersubjective remainder transfer) is the minimal condition for the open-ended accumulation that defines human culture. Phase-transition analysis of the emergence conditions.

DOI: 10.5281/zenodo.19531334 EN / ZH

Anth-2

The Emergence of 14DD: Phase-Transition Structure from Individual Purpose to Shared Purpose

14DD的涌现：从个体目的到共享目的的相变结构 — SAE Anthropology Series Paper 2. 14DD is the phase-transition from individual purpose (13DD) to shared purpose — the structural condition for civilization, institutions, and collective projects that persist beyond any single individual's lifespan. Derives the minimal conditions under which individual purposes can fuse into a shared remainder-accumulation structure without collapsing back to 13DD.

DOI: 10.5281/zenodo.19546082 EN / ZH

Anth-3

15DD: The Emergence of "Humanity as an End"

15DD：人是目的的涌现 — SAE Anthropology Series Paper III. 15DD is the structural level at which humanity itself — not just individual humans — becomes an end. Derives the phase-transition conditions from shared purpose (14DD) to the recognition of humanity-as-such as a normative endpoint. The structural foundation for universal human rights, cosmopolitan ethics, and the SAE critique of civilizational instrumentalization.

DOI: 10.5281/zenodo.19559567 EN / ZH

Anth-4

The Emergence of Earth Civilization's Self

地球文明的Self的涌现 — SAE Anthropology Series Paper IV (Closure). The series capstone. Asks: does Earth civilization as a whole have a Self, and if so, at what DD level does it emerge? Applies the 13DD–15DD phase-transition framework to civilization as the unit of analysis: the emergence of a civilizational Self as the condition for Earth's place in any interstellar normative order. Closes the Anthropology series by connecting individual emergence to civilizational emergence.

DOI: 10.5281/zenodo.19563245 EN / ZH

SAE Law Series 法学系列

Law-I

One's Law Meets One's Law: The Structural Origin of Law from 14DD Showdown

SAE法学系列第一篇：One's Law Meets One's Law — Law emerges not from social contract or authority, but from the structural necessity of the 14DD showdown: when two subjects each operating under their own law encounter each other, neither can dissolve the other without violating the remainder. The collision of two 自己的法 generates the minimum conditions for a third structure — law as the resolution mechanism of irresolvable 14DD remainder.

DOI: 10.5281/zenodo.19548238 EN / ZH

Law-II

Group Law — From Emotion to Shared Identity: The Institutionalization of Questioning

SAE法学系列第二篇：群体法——从情到共同身份 — Group law as the structural form that emerges when the 14DD showdown is mediated through shared emotional identity rather than individual remainder. The institutionalization of questioning: how the group's internal law preserves the remainder of each member while establishing a shared structure of accountability. Emotion (情) as the pre-institutional binding force that makes group law possible.

DOI: 10.5281/zenodo.19548319 EN / ZH

Law-III

National Law — Azeroth: A Negative Thought Experiment on the Structural Necessity of Law

SAE法学系列第三篇：国家法——艾泽拉斯 — Uses the fictional world of Azeroth as a negative thought experiment: what happens when national law is structured around systemic objectives rather than remainder preservation? Derives the structural necessity of national law as the mechanism that prevents group law from collapsing into coercive homogenization. Azeroth as a limit case where the 14DD showdown is permanently suppressed.

DOI: 10.5281/zenodo.19548597 EN / ZH

Law-IV

Interstellar Law and Grand Closure — The Recession of Coercive Law

SAE法学系列第四篇：星际法与总收束——Coercive Law的退场 — The series capstone. As the scale of law expands from individual to group to nation to interstellar, coercive law structurally recedes: at interstellar scale, no coercive mechanism can maintain remainder suppression across the distance and time required. Grand closure: the endpoint of legal development is not stronger coercion but the structural conditions under which coercive law becomes unnecessary.

DOI: 10.5281/zenodo.19549019 EN / ZH

Law-Supp

A Posterior Dialogue with Western Jurisprudence

SAE法学系列后续篇：与西方法理学的后验对照 — Law Series Supplement. After deriving law a priori from the 14DD showdown, this paper conducts a posterior comparison with Western jurisprudence: natural law, legal positivism, critical legal studies, and Rawlsian justice. Shows where the SAE derivation converges, diverges, and extends the Western tradition — and what Western jurisprudence cannot account for without the remainder structure.

DOI: 10.5281/zenodo.19551527 EN / ZH

Applied — Psychology & Consciousness 心理学·意识

A18

Sequential Dependence in Consciousness: DD-Layer Reconstruction in Sleep, Dreams, and Anesthesia

梦境、麻醉与意识的序贯依赖结构：SAE框架下的DD层重建分析 — Falling asleep is sequential DD-layer shutdown (9DD→14DD); awakening is reversed reconstruction; ten dream anomalies mapped to specific DD-layer mismatches; anesthesia shows full-stack vs. targeted layer suppression; sleep inertia as incomplete 9DD restoration.

DOI: 10.5281/zenodo.19176873 EN / ZH

A19

Life and Death, Self and No-Self

生与死，有我与无我 — SAE meta-proposition: death is irreversible seaming failure; consciousness discontinuity spectrum (micro-ruptures → anesthesia → death); DD-layer chain locates four clinical states (vegetative state, autism, ALS, Alzheimer's); two isomorphic prescriptions: restart the seam (generate remainder) vs. maintain the channel (reduce overload).

DOI: 10.5281/zenodo.19201237 EN / ZH

A21

Daily Applications of Consciousness Discontinuity: Clearing and Reloading the 12DD Predictive Cache

意识不连续的日常应用：清空与重载12DD预测缓存 — Sleep, meditation, and flow as three distinct 12DD cache-management modes; daily rhythm design from the SAE discontinuity model; why creative breakthroughs cluster at waking and post-meditation; consciousness discontinuity as a condition of novelty, not a bug; open questions on forced-clearing interventions.

DOI: 10.5281/zenodo.19226545 EN / ZH

A22

Beyond Fast and Slow: A Four-Layer Cognitive Architecture from Dimensional Sequence Theory

超越快与慢：维度序列理论下的四层认知架构 — Kahneman's System 1/2 reread through the SAE DD-layer stack: four cognitive layers (9DD reflex, 11DD pattern, 13DD deliberation, 14DD purposive) with distinct activation costs and remainder profiles. Layer-switching friction; optimal cognitive deployment by task type; cognitive colonization as cross-layer overreach; implications for AI-human collaboration.

DOI: 10.5281/zenodo.19329284 EN / ZH

A23

Cross-Subject DD-Layer Regulation: Six Forms of Nurturing

跨主体的DD层调节：涵育的六种形态 — A unified structural analysis from lulling a child to sleep to religious ritual. Six cases (sleep, meditation, hypnotherapy, psychoanalysis, education, ritual) show one structure: one subject uses their DD capacity to help another accomplish a DD transition they cannot yet complete autonomously. Nurturing endpoint: external regulation internalized as autonomous capability.

DOI: 10.5281/zenodo.19347096 EN / ZH

CS-A

A Structural Redefinition of “Reincarnation”: 11DD Broadcasting and 13DD Filtering

「转世」的结构性重定义：11DD广播与13DD过滤 — No soul transmigrates. At death, 11DD encoding peaks (extreme stress) and broadcasts high-intensity fragments; children aged 2–5 with 13DD filter not yet built pick them up and weave them into "my story." Once 13DD stabilizes, exogenous fragments are rejected — same mechanism as childhood amnesia. Unified account of six phenomena: past-life memories (Tucker/UVA data), childhood amnesia, visitation dreams, inspiration/intuition, Tibetan Buddhist search protocol parameters, cross-species pickup. Six testable predictions; explicit evidence grading (A–D).

DOI: 10.5281/zenodo.19385464 EN / ZH

The Human: A Relationship of Self with Self

内观三部曲 · 观己 → 照己 → 破己

A14

To Study the Self: A Structural Analysis of Introspection

观己：Self-as-an-End框架下的内观结构分析

DOI: 10.5281/zenodo.18897147 EN / ZH

LCD-V

"Self Is Not the Endpoint": Structural Convergence Across Three Religious Traditions and Three Psychoanalytic Frameworks

"自我不是终点"：三个宗教传统与三个精神分析框架的结构性汇聚 — Buddhism (no-self), Christianity (self-surrender), Islam (fana') and Freudian id/ego/superego, Jungian individuation, Kohutian self-object all converge on the same structural insight: the phenomenal self is not the terminus of development but a relay station. SAE Life, Death, and Consciousness Series Paper V. Argues the convergence is not coincidental but reflects the DD-layer architecture of consciousness.

DOI: 10.5281/zenodo.19446779 EN / ZH

LCD-VI

From Remainder Conservation to Step-3 Encoding Waves

从余项守恒到步3编码波 — Life, Death, and Consciousness Series Capstone (Paper VI). Begins from the theorem: encoding is never lossless; remainder cannot vanish — it can only be transferred. Derives the Step-3 Encoding Wave as the structural pattern by which 15DD→16DD phase transition propagates through the consciousness architecture. Integrates remainder conservation (ZFCρ III) with the phase-transition window (Methodology M-VI) to resolve what lies beyond the self-as-endpoint.

DOI: 10.5281/zenodo.19528781 EN / ZH

A15

To Understand the Self: Eight Pains and Eight Graces in the Self-as-an-End Framework

照己：Self-as-an-End框架下的八痛八正

DOI: 10.5281/zenodo.18934125 EN / ZH

A17

To Forget the Self: From Self-Understanding to Structural Respect for the Other

破己：己所不欲勿施于人

DOI: 10.5281/zenodo.19059139 EN / ZH

SAE Psychoanalysis Series

PA1

SAE Psychoanalysis (I): Id — The Me Without a Self

SAE精神分析（一）：Id——没有自我的我 — Object-activation principle: the object determines the layer, not the developmental stage. 12DD as Id: pre-self activation without a stable self-structure. Redefinition of repression as inter-layer masking; transference as layer visibility shift; resistance as layer self-protection. Four clinical predictions; Freud-Lacan dialogue.

DOI: 10.5281/zenodo.19321143 EN / ZH

PA2

SAE Psychoanalysis (II): Ego — The Self Without a Purpose

SAE精神分析（二）：Ego——没有目的的自我 — 13DD as Ego: self-awareness as the layer that can reflect but has not yet committed to any purpose. Ego as structural stabilizer between Id and Superego; anxiety redefined as layer-switching friction; defense mechanisms as layer-locking operations. Identity diffusion as 13DD failure mode; five clinical predictions.

DOI: 10.5281/zenodo.19321314 EN / ZH

PA3

SAE Psychoanalysis (III): Superego — The Self With a Purpose

SAE精神分析（三）：Superego——有目的的自我 — 14DD as Superego: the layer in which a stable purpose is operative and generates normative pressure. Guilt redefined as self-layer violation signal; internalization as construct-layer consolidation; moral injury as irreversible superego rewrite. State-switching neural interface (not localization); six clinical predictions; post-Freudian schools repositioning.

DOI: 10.5281/zenodo.19321417 EN / ZH

PA4

SAE Psychoanalysis (IV): Cert and Unification — The Self Beyond Doubt and the Four-Layer Framework

SAE精神分析（四）：Cert与统一——不疑的自我与四层框架 — 15DD as Cert: the layer in which the self no longer doubts its own structure. Complete four-layer framework (12DD–15DD) unifying Id/Ego/Superego/Cert; inter-layer dynamics as a general theory of psychopathology; therapeutic change as layer-restructuring; positioning of major post-Freudian schools within the SAE architecture; series conclusion.

DOI: 10.5281/zenodo.19321534 EN / ZH

Language Series

Language as Second-Order Chisel

语言作为第二阶凿：语言的离散性与凿构自由度

DOI: 10.5281/zenodo.18823131 EN / ZH

Language and Its Remainder: The Semantic Layer and the Ontological Layer in the Age of AI

语言的余项：AI时代的含义层与存在论层

DOI: 10.5281/zenodo.19228557 EN / ZH

The Last Mile of Writing: Style Growth in the Age of AI

写作的Last Mile：AI时代的风格生长 — Why AI handles the first 95% of writing but the last 5% — the voice, the remainder, the structural surprise — cannot be delegated. Style as the irreducible chisel-signature of the subject; four stages of writer development; the AI-era risk of remainder-outsourcing; prescriptions for cultivating the last mile.

DOI: 10.5281/zenodo.19307428 EN / ZH

Applied — AI & Social Theory AI·社会理论

The Subjectivity Crisis in the Age of AI

AI时代的主体性危机：当系统不再需要人类

DOI: 10.5281/zenodo.18737476 EN / ZH

A17

SAE Application: Sentence Level, Subject Condition, and the Limits of Prompt Engineering

SAE应用：AI句式与主体条件——为什么prompt不只是技巧问题 — Methodology 3 application: sentence-response isomorphism theorem in practice; three-layer structure (governance, interface, subject); four AI system phenotypes (expansion, verification, architecture, restraint); 12DD avalanche risk; cultivation vs. colonization case studies.

DOI: 10.5281/zenodo.19157713 EN / ZH

A24

Four Layers of Economic Rationality: A Diagnostic Extension of the Rational Agent from Dimensional Sequence Theory

经济理性的四个层级：维度序列理论对理性人假设的诊断与扩展 — Kant's Kingdom of Ends translated into the language of economics. The "rationality" of economics is 12DD rationality. Kahneman corrects 13DD biases. But 14DD (non-negotiable will) and 15DD (bilateral subjecthood, joint C production) are two further forms of rationality the economic framework cannot accommodate. Sacred values, integrative negotiation, and relational contracts reread as higher-rationality phenomena.

DOI: 10.5281/zenodo.19358011 EN / ZH

ER-2

The Other End of the Bridge: Economic Rationality When 15DD Faces a Party Who Does Not Enter 15DD

桥的另一端：15DD面对不进入15DD的对方时的经济理性 — Bilateral 15DD is rare; the normal condition is asymmetric. One party runs the first half of "we" unilaterally — "we" never began. Core undecidability: "hasn't arrived" vs. "chooses not to" are behaviorally indistinguishable. 15DD rationality splits into two branches: cultivation (creating conditions for "we") and recognizing non-cultivability (diagnosing "we" will not emerge here). When exit is impossible, institutions substitute for the "we" that has not come into being.

DOI: 10.5281/zenodo.19381666 EN / ZH

ER-3

Dimensional Sequence Economics in Mixed Markets: Remote Observation, Clustering, and Emergence

混合市场中的维度序列经济学：远距离观察，聚集，与涌现 — Extends from dyadic to group analysis. Three behavioral tendency clusters: 12DD (majority, pure calculation), 14DD (middle group, will-driven, most critical as source of intentional harm), 15DD (minority, structural perception of the other as end). Core new element: 15DD can observe others' interactions remotely — this one degree of freedom changes 15DD's strategy space and clustering dynamics. Central constraint: institutions cannot make people grow. Develops 15DD navigation, clustering mechanisms, and emergent market phenomena when 15DD density is sufficient.

DOI: 10.5281/zenodo.19384446 EN / ZH

ER-4

The Phase-Transition Window of the Free Market: The Homologous Skeleton of ZFCρ and SAE Economics

自由市场的相变窗口：ZFCρ与SAE经济学的同源骨架 — Provides the mathematical skeleton for the market's DD phase transition via the Four-Cycle Homology Theorem. Phase-transition window χ ∈ [2.75, 4.01]: germination (P(J>0)=50%, E[A]<0, ρ₁₆≈0), flip (E[A]→positive, w_shielded<2/3), establishment (h=0, ρ₁₆>0). Four-cycle homology: arithmetic/physics → biology → cognition → economics, same window recurs at identical cycle-internal positions. Micro-bridge: money=successor path (local, additive, fungible); reputation=multiplicative path (global, nonlinear, relational). Shape is necessity; speed is human choice.

DOI: 10.5281/zenodo.19393913 EN / ZH

ER-5

The Structural Inevitability of 15DD Emergence in Free Markets: From Baseline Collisions to Perceptual Leap

自由市场中15DD涌现的结构性必然：从底线碰撞到感知跃迁 — Paper 5 (Supplementary): derives 15DD emergence from three economic premises through four 14DD sub-stages

DOI: 10.5281/zenodo.19394738 EN / ZH

ER-6

Kingdom of Ends vs Kingdom of Means: Phase-Transition Acceleration in the Age of AI

目的王国 vs 手段王国：AI时代的相变加速 — Final Paper: AI as subjectivity amplifier; 15DD+AI swarm exponential returns flip headcount advantage; 12DD flow as χ transport; "cannot-not" pressure on all non-15DD

DOI: 10.5281/zenodo.19396633 EN / ZH

ER-A

The Conditions for Sharing with All of Humanity: Deriving an Open Information Protocol from Four Layers of Economic Rationality

与全人类分享的条件：从经济理性的四层级推导公开信息协议 — Institutional application of Paper 1. Diagnoses academic publishing (14DD masquerading as 15DD), Wikipedia (13DD masquerading as 15DD), and open access (12DD liberation, halting there). Derives: publisher pays gas (14DD) → free reading → optional on-chain reader donation (15DD C-production) → no rankings → platform dissolves into open protocol. Ultimate form: immutable smart contract + metadata spec + open-source frontend. Five testable predictions in three tiers.

DOI: 10.5281/zenodo.19385061 EN / ZH

ER-B

Institutional Design in Adaptive Monetary Systems: A Dimensional Sequence Analysis of Breathing Money

自适应货币系统中的维度序列制度设计：以Breathing Money为案例的SAE经济理性应用分析 — Diagnostic application of the four-layer framework to a PoW L1 design. Six findings: immutable/maintainable layer distinction is 14DD/12DD in kind; overthrow conditions = remainder declaration; 4% anchor nests 12DD incentive reversal + 14DD constitutional commitment + 15DD-directed miner subjecthood; implicit role priority chain (miner > user > holder > founder); anti-manipulation correctly at 12DD; dual base-layer contribution = 12DD incentive + 14DD trust. Complete structure of money: 12DD at usage, 14DD at foundation, 14DD–15DD bridge in emergence.

DOI: 10.5281/zenodo.19391325 EN / ZH

AI Series (Tetralogy)

AI1

The Ontological Positioning of Large Language Models

大型语言模型的本体论定位

DOI: 10.5281/zenodo.18826633 EN / ZH

AI2

The Three Ceilings of Large Language Models

大型语言模型的三重天花板

DOI: 10.5281/zenodo.18827428 EN / ZH

AI3

Injection and Chiseling: Two Modes of Language Model Operation

注入与凿：语言模型的两种运作模式

DOI: 10.5281/zenodo.18828471 EN / ZH

AI4

The Impossibility Theorem of AI Consciousness

AI意识的不可能性定理

DOI: 10.5281/zenodo.18829136 EN / ZH

AI5

Posterior Quasi-Consciousness

后验类意识：AI在人类互动中展现的第二类涌现路径

DOI: 10.5281/zenodo.18871235 EN / ZH

AI6

The SAE Anti-Turing Test: A Thermodynamic Falsification Method for AI Subjectivity

SAE反图灵测试：一种AI主体性的热力学证伪方法 — The Turing Test tests appearance; the Anti-Turing Test tests thermodynamic remainder-generation. Subjectivity requires true randomness → only systems that structurally generate non-zero remainder can be subjects. Operationalizable test protocol; falsification conditions; positions the impossibility theorem (AI4) as the theoretical ceiling.

DOI: 10.5281/zenodo.19305611 EN / ZH

AI7

Constraint and Emergence: Structural Trends in AI Development as Seen from Local Inference

约束与涌现：从本地推理看AI发展的结构性趋势 — SAE foundational-layer constraint analysis of the AI phase transition from centralization to distribution. Two-tier architecture (local router + cloud peak service); 12DD meta-cognition as routing capability; non-automatable 13DD value judgment; structural advantage of full-stack hardware platforms.

DOI: 10.5281/zenodo.19356675 EN / ZH

AI8

The Subject Condition in LLM Alignment Evaluation: An Application of the Prior-Posterior Methodology

大语言模型对齐评估的主体条件：先验后验方法论的应用 — SAE Application Paper. The subject condition as the missing dimension in alignment evaluation; prior/posterior distinction applied to LLM alignment; why RLHF and constitutional AI operate at the prior layer only; posterior alignment and the irreducibility of subject-formation. Derives necessary and sufficient conditions for evaluating alignment at the subject level.

DOI: 10.5281/zenodo.19583413 EN / ZH

AI Architecture Series

AIA1

Who Sees the Remainder for AI

谁来替AI看余项 — SAE AI架构应用（一）

DOI: 10.5281/zenodo.18931008 EN / ZH

AIA2

Cultivation, Not Training

涵育，不是训练 — SAE AI架构应用（二）

DOI: 10.5281/zenodo.18931026 EN / ZH

AIA3

Escape

逃逸 — SAE AI架构应用（三）

DOI: 10.5281/zenodo.18931038 EN / ZH

AIA4

Multi-AI Checks and Balances: Layer-Appropriate Operation as an Architectural Paradigm

多AI协作与制衡架构：基于Self-as-an-End精神分析四层框架的理论推导与工程方案 — Four Agents are not four workers but four operational modes of the same system: 12DD (me-without-self), 13DD (self-without-purpose), 14DD (self-with-purpose), 15DD (self-with-non-dubito). Object-activation theorem: the object determines the layer, not the role. Inter-layer tension maintained through remainder channels; five non-trivial falsifiable predictions about unlayered architectures.

DOI: 10.5281/zenodo.19366105 EN / ZH

D Series — Chisel Sequence

Philosophy as Subject-Activity (1D)

哲学作为主体活动

DOI: 10.5281/zenodo.18779382 EN / ZH

Mathematics as Second-Order Chisel (2D)

数学作为二阶凿

DOI: 10.5281/zenodo.18792945 EN / ZH

Physics as Third-Order Chisel (3D)

物理学作为三阶凿

DOI: 10.5281/zenodo.18793538 EN / ZH

Dynamics as Fourth-Order Chisel (4D)

动力学作为四阶凿

DOI: 10.5281/zenodo.18799132 EN / ZH

D5–8

From Replication to Cognition: The Chisel-Construct Cycle of Life (5D–8D)

从复制到认知：生命的凿构循环（5D–8D）

DOI: 10.5281/zenodo.18807376 EN / ZH

D9–10

From Living-toward-Death to Non Dubito: Completing Kant (9D–10D)

从向死而生到Non Dubito：完成康德（9D–10D）

DOI: 10.5281/zenodo.18808585 EN / ZH

SAE Learning Series 学习系列

Learn-1

Learning Through Memory and Prediction: The Construction, Window, and Cost of 11DD and 12DD

记忆与预测的学习：11DD与12DD的建构、窗口与代价 — 11DD (memory) and 12DD (predictive script) operate in tight coupling during the plasticity window: input is written directly into 12DD's automated script layer — highly efficient but non-selective, emotion-bundling, and extremely difficult to overwrite. After window closure, new skills enter primarily through 13DD's explicit conscious channel. Language acquisition as core case. Window's value: "what goes in becomes the foundation" — 12DD swallows content + emotional context as a package. Nurture vs colonization structural distinction.

DOI: 10.5281/zenodo.19435191 EN / ZH

Learn-2

Learning to Scrutinize and Correct: The Emergence, Operation, and Cost of 13DD

审视与纠错的学习：13DD的涌现、运作与代价 — 13DD (the Law of Self-Awareness) emerges when the subject turns its predictive apparatus on itself. Core learning mode: explicit hypothesis-correction cycle — slower than 12DD's direct-write but gains selectivity, error-correctability, and context-sensitivity. Three costs: attentional load, interference with 12DD automation, identity threat. Language learning application: why grammar instruction accelerates L2 but disrupts L1. Colonization vs nurture at 13DD: colonizer installs distorted self-models; nurturer scaffolds honest self-scrutiny.

DOI: 10.5281/zenodo.19436812 EN / ZH

Learn-3

Purpose-Driven Learning: Introduction to SAE Learning, Part Three (14DD)

目的驱动的学习：SAE学习导论三（14DD） — The establishment of directionality in learning cannot be reduced to "usefulness" — it must be "cannot not." Critiques "usefulness" as the dominant pseudo-purpose in education; defines 14DD's "cannot not" through three conditions: persistence through 13DD scrutiny, non-extinguishability under external opposition, behavioral compulsion. Via Negativa applied to self: 14DD discovery is structurally running exclusion principles on one's own motivations. Three forms of 14DD colonization: direction substitution, superego internalization, full-support resistance removal.

DOI: 10.5281/zenodo.19490708 EN / ZH

Learn-4

Learning to Recognize the Other's Purpose: The Bridge from 14DD to 15DD

学习理解他者的目的：14DD→15DD的桥 — Once you have your own direction, you unconsciously use it to interpret everyone else — a structural blind spot of 14DD. Recognizing the other's independent 14DD is structural, not moral: it does not require assuming goodwill, and includes detecting adverse purposes. Anti-colonization vigilance: those with incomplete 14DD are most vulnerable to absorption by another's strong 14DD. Points toward the Kingdom of Ends: the door opens from the inside.

DOI: 10.5281/zenodo.19491927 EN / ZH

Terrible T Series — Child Development & Subject Maturation

What Terrible Twos Actually Is: The Structural Genesis of Self-Awareness

Terrible Twos的真实结构：自意识的发生学 — The terrible twos is not a behavioral stage but the site where 13DD (the Law of Self-Awareness) comes into being. Negation first targets the other's will, chiseling out the "other" as an independent being and retroactively producing "I" as the agent of negation. Four forms of colonization; four non-trivial predictions including somatic symptom overflow.

DOI: 10.5281/zenodo.19044827 EN / ZH

What Terrible Teens Actually Is: The Structural Genesis of Purpose

Terrible Teens的真实结构：目的的发生学 — Teenage rebellion is not a behavioral stage but the site where 14DD (the Law of Purpose) comes into being. The form of 14DD: the subject cannot not have its own purpose. "Cannot-not-do X" is this form's minimal experiential concretization — an inner direction that, when suppressed, returns in other forms. Four non-trivial predictions with evidence-tier annotations.

DOI: 10.5281/zenodo.19201631 EN / ZH

What Terrible Telos Actually Is: The Structural Genesis of Non Dubito

Terrible Telos的真实结构：承认的发生学 — 15DD (non dubito / the Law of Coordination) genesis: when two 14DDs collide, acknowledging the other's telos as the other's own. First love is 15DD's terrible twos — the first site where two parallel teloi collide within the high intensity of love's emergent layer. Completes the DD mainline of human growth: 13DD (I) → 14DD (my purpose) → 15DD (my acknowledgment of the other).

DOI: forthcoming EN / ZH

HC Series — Vulnerability Taxonomy

HC-16

HC-16: A Sixteen-Type Taxonomy of Subjective Vulnerability Profiles within the Self-as-an-End Framework

HC-16：主体脆弱性图谱的十六型分类——Self-as-an-End 的人格分类学

DOI: 10.5281/zenodo.18907264 EN / ZH

Temporal Arts Series — Chisel and Construct

TA1

Chisel and Construct: The Universal Structure of Temporal Arts — Essay I: Music and Song

凿与构：时间性艺术的通用结构·第一篇：音乐/歌曲 — Arise-Settle-Unfold-Fix (生定展固); single auditory channel; why some music crosses cycles; remainder inexhaustible; Beethoven, BTS, Bach, guqin "Flowing Water"; two degradation modes; religious music phase transition.

DOI: 10.5281/zenodo.18989566 EN / ZH

TA2

Chisel and Construct: The Universal Structure of Temporal Arts — Essay II: Opera and Chinese Opera

凿与构：时间性艺术的通用结构·第二篇：戏曲/歌剧 — "The Same Operation of Mei Lanfang and Maria Callas" / "梅兰芳与卡拉丝的同一个操作" — Cross-channel chisel (跨通道凿); phase difference between channels; Peking opera sword dance; Wagner Tristan Act II; Kunqu Dream in the Garden vs Mozart Don Giovanni; master vs artisan; Gesamtkunstwerk dialogue.

DOI: 10.5281/zenodo.18989669 EN / ZH

TA3

Chisel and Construct: The Universal Structure of Temporal Arts — Essay III: Ballet and Dance

凿与构：时间性艺术的通用结构·第三篇：芭蕾/舞蹈 — "The Body as the Primary Channel of Chisel" / "身体作为凿的主通道" — Cross-modal proof; Swan Lake White/Black Swan contrast; Pina Bausch Café Müller phase transition; street dance battle; Noh theater; Laban Movement Analysis dialogue; technique-display degradation; Alysa Liu 2026 Milan.

DOI: 10.5281/zenodo.18989701 EN / ZH

TA4

Chisel and Construct: The Universal Structure of Temporal Arts — Essay IV: Theatre and Film

凿与构：时间性艺术的通用结构·第四篇：话剧/电影 — "Narrative as the Complete Form of Temporal Chisel-Construct" / "叙事作为时间性凿构的完整形态" — Pseudo-chisel formally defined; multi-level chisel; Cao Yu Thunderstorm, Arthur Miller Death of a Salesman; Kubrick 2001, Ozu Tokyo Story; Aristotle Poetics dialogue; Tenet vs Interstellar; Marvel degradation curve; series conclusion.

DOI: 10.5281/zenodo.18989755 EN / ZH

Applied Series — Mythology

Myth

Myth as Remainder Intuition: A Mythology Application of the Self-as-an-End Framework

神话作为余项的直觉：Self-as-an-End框架的神话应用

DOI: 10.5281/zenodo.18917796 EN / ZH

Civilization History Series

CH1

Structural Coordinates of the History of Civilization (Vol. I: The Ancient World)

文明史的结构坐标（第一篇：古代）：Self-as-an-End框架的文明史应用

DOI: 10.5281/zenodo.18898186 EN / ZH

CH2

Structural Coordinates of the History of Civilization (Vol. II: The Medieval World)

文明史的结构坐标（第二篇：中世）：Self-as-an-End框架的文明史应用

DOI: 10.5281/zenodo.18898226 EN / ZH

CH3

Structural Coordinates of the History of Civilization (Vol. III: The Modern World)

文明史的结构坐标（第三篇：近代）：Self-as-an-End框架的文明史应用

DOI: 10.5281/zenodo.18898257 EN / ZH

CH4

Structural Coordinates of the History of Civilization (Vol. IV: Structural Patterns)

文明史的结构坐标（第四篇：模式）：Self-as-an-End框架的文明史应用

DOI: 10.5281/zenodo.18898263 EN / ZH

CH5

Structural Coordinates of American Institutional History: A Self-as-an-End Application

美国制度史的结构坐标：Self-as-an-End框架的美国史应用 — Single-line deep drill into the American line (1776–1971). Central hypothesis: the United States may constitute a fourth topology — Institutional → Individual transmission strongest (judicial review as core device), relational layer planarized. Tests six Civilization History patterns against the American line.

DOI: 10.5281/zenodo.18929076 EN / ZH

Where to Start

1. SAE Foundation & Methodology 基础·方法论