Xiaozhou Zeng

The companion paper Quantum Gravity from One Axiom derived, from the single axiom of Structural Determination Theory, a discrete structure carrying a Planck-scale step measure μ = t_P/|A| whose two continuum limits are the Schrödinger equation (|A| ≫ 1) and Einstein's equation (|A| = 1). It deliberately reserved the dynamics connecting them. This paper supplies that dynamics and develops its consequences to the point of experimental test. We derive, from the action structure alone, the compatibility condition □ψ = (8πG/3)(T − 2ℒ_m)ψ that any admissibility dynamics must satisfy; show that no single-register local rule can satisfy it; and derive the unique two-register form graph-internally from counting structures the formal corpus already contains — placing the gravitational half on the same derive-then-calibrate footing as the quantum half. The resulting three-register update system (U1)–(U3′) is verified numerically in both continuum limits, including exact floor-arrival timing and attractor convergence. Realizing the matter sector as the Standard Model under the weighted coupling, an exact field redefinition decouples free fermions entirely, migrates the coupling into interactions, and — jointly with precision-gravity bounds (Cassini, lunar laser ranging, equivalence principle) — forces the coarse admissibility field to unity at all sub-Planckian densities: the realized theory is exactly general relativity plus the exact Standard Model, with black-hole entropy necessarily boundary-carried and the Hawking spectrum inherited. The theory's one near-term falsifiable prediction follows as a theorem: gravitationally-induced-entanglement experiments of the Bose-Marletto-Vedral class yield a strict null result with matter coherence surviving and no anomalous noise — a previously unoccupied position (fundamentally quantum, mediationally classical) in the live mediation debate, discriminable from graviton-mediated, collapse, postquantum, and semiclassical alternatives.

This document develops the higher-order mathematical structures of the determination dependency graph G_D introduced in Structural Determination Theory (SDT) v6.0, together with the cross-theoretical interfaces that build on G_D's base structure. Working at the level of model theory, category theory, reproducing kernel Hilbert space theory, sheaf cohomology, and Alexandroff topology, it provides the mathematical machinery for which SDT's foundational paper and the companion graph-theoretic and formal-system documents leave room. The principal contributions are: (i) the chain-pair relational geometry of G_D, comprising the antichain spatial structure, predecessor overlap, joint constraint capacity, structural proximity graph, intrinsic light-cone saturation on lightlike pairs, the five-fold tolerance-relation classification of chain pairs, inter-chain information flow as reference-frame invariant, observer-relative simultaneity via common successor, the structural absence of Lorentz-type frame transformations at the meta-level, and the conditional emergence of Lorentz, Galilean, Carrollian, and Conformal synchronization regimes under entity-theoretic axioms (S1, S2, CL1); (ii) confluence predictability for ≺-incomparable chains, with two independent mathematical paths (H2-compatibility reduction; pushout/colimit construction) and Bell correlations as a pre-confluence transient (Section 11.11); (iii) the Jaccard metric on G_D nodes via predecessor cones with Aronszajn–Schölkopf RKHS embedding; (iv) structural entropy from A's monotonic contraction; (v) the token-parameterized time projection interfacing G_D's discrete chain structure with continuum time variables (QM, GR, thermal); (vi) the sheaf-theoretic perspective on the locally single-output subgraph and the multi-product extension to full G_D, with the SDT-KS no-obstruction theorem as the principal sheaf-theoretic result; (vii) the SDT–quantum-mechanics correspondence program, including the four-type classification's quantum-event interpretation, the read-out principle, and the structural alignment with Constructor Theory; (viii) the local-maximum principle for sub-graph identification supporting cross-application structural-pattern recognition. The document is the third in the SDT v6.0 mathematical series; the foundational paper (SDT v6.0), the graph-theoretic formalization (GD v6.0), and the formal system (FS v6.0) are the canonical sources for SDT's main theorems, G_D's graph-theoretic structure, and SDT's proof-theoretic properties respectively. Boundary statements identify what each construction does and does not provide; entity-theoretic content (specific physics, gauge group, particle spectrum, dimension) is consistently distinguished from the meta-structural machinery developed here.

时间问题，量子力学的时间参数 t 与广义相对论的固有时 τ 之间的表观不相容，一直被视为量子引力的根本障碍。本文论证这是一种层次混淆：两种理论都在各自的实体理论框架内定义时间，生成的表观对立在时间被重新定位到元结构层次时即告消失。基于元层时间结构 T_SDT := (V_G, ≺)（Zeng 2026），本文将 QM 时间与 GR 时间形式化为一条统一时间公式的两个投影，由实体理论的记号（token）所参数化。四种记号特殊化恢复对应的时间概念。一条桥梁定理确立所有记号投影的相互相容性。本文构造了双向的 QM-GR 通道（正向：GR 几何到 QM 相位；反向：离散链对到洛伦兹时空），合成自洽闭环。 三条进一步的结果超越消解走向统一。第一，Madelung 桥构造从判定图公理结合连续嵌入（CL1）推导出薛定谔方程，包括希尔伯特空间、酉性、哈密顿量、量子势、Born 规则，无需任何独立的 QM 输入；推导可延伸到克莱因-戈尔登。第二，在离散判定依赖图 G_D 上构造普朗克尺度记号 μ = t_P/|A_{v'}|，其中 |A_{v'}| 为可容许性基数；在 CL1 之下，这一单一步度恢复 QM（|A| ≫ 1）与 GR（|A| = 1）作为其两个连续极限，爱因斯坦方程在经典区域（|A| = 1）经两阶段论证（Benincasa-Dowker 作用量收敛加标准标量-张量变分）得证。精确的量子引力修正推导为带 φ = 1/|A| 的标量-张量方程。第三，无连续嵌入的离散判定图自身构成一个自足的普朗克尺度量子引力理论：拥有良定义的路径积分、有限维 S 矩阵（在 κ = 0 区域为酉，κ > 0 区域为等距；无 UV 发散），保持信息穿过黑洞视界，消解奇点，推导出过去假设，并为规范对称性、霍金辐射、谱维度与自旋-统计关系提供结构性起源。时间问题不仅被消解，而是被一个建构性框架所取代，其中 QM 与 GR 统一为单一离散结构的两个极限。

This paper formalizes a quantum gravity framework derived from Structural Determination Theory (SDT), a single-axiom ontology: reality consists of distinctly differentiated structure. The Problem of Time is dissolved by relocating time from QM's tt t and GR's τ\tau τ to the meta-level structure TSDT:=(VG,≺)T_{\text{SDT}} := (V_G, \prec) TSDT​:=(VG​,≺); QM and GR time emerge as two token-parameterized projections of a single Universal Time Formula, with a Bridge Theorem and a Bidirectional Duality establishing mutual compatibility on the common substrate GD\mathcal{G}_D GD​. Three further results unify QM and GR. (i) A Madelung-bridge construction derives the Schrödinger equation (Hilbert space, complex field, unitarity, Bohm quantum potential, Born rule) from the determination-graph axioms with no QM postulates as inputs; the derivation extends to Klein-Gordon and Dirac. (ii) A Planck-scale token μ=tP/∣Av′∣\mu = t_P/|A_{v'}| μ=tP​/∣Av′​∣ recovers QM (∣A∣≫1|A| \gg 1 ∣A∣≫1) and GR (∣A∣=1|A| = 1 ∣A∣=1) as continuum limits; the modified Einstein equation is derived along two paths: an SDT-native α path (ψ=∣A∣\psi = |A| ψ=∣A∣, gravity enhanced in high-coherence regions), and a CST-compatible β annex (φ=1/∣A∣\varphi = 1/|A| φ=1/∣A∣, gravity diluted). (iii) The discrete determination graph constitutes a self-contained Planck-scale QG framework with UV-finite S-matrix, information preservation across black-hole horizons (decoupled from unitarity via RR R non-retraction), and CL1-conditional resolution of Big Bang and BH singularities. Gravity is positioned ontologically as the structural manifestation of mass-induced AA A-contraction through SDT's R→G→C→AR \to G \to C \to A R→G→C→A chain, not as an autonomous primitive; SDT supplies the structural form, entity theory supplies the content. An empirical program operationalizes the framework through four laboratory- and stellar-scale tests (gravitationally induced entanglement, atom interferometry, BH horizon deviations, GW polarization) and five cosmological-scale tests, with framework-level discrimination between α and β paths projected for 2030–2040. The framework is categorically distinct from string theory, LQG, CST, CDT, and AS across five comparative structural dimensions.

This paper develops a graph-theoretic characterization of consciousness within the determination dependency graph G_D of Structural Determination Theory (SDT). The result is a meta-structural identification criterion with four substantive claims and a cross-chain personal identity criterion. (1) Four-fold equivalence. A sub-graph C of G_D is consciousness if and only if it satisfies sixteen identification conditions IC_1 through IC_16 together with a local-maximum principle. Three extension equivalences add reflection (IC_17), free will (IC_18), and consciousness-level memory (IC_19) as independent extension conditions. (2) Cross-chain personal identity. A cross-chain criterion PI_1 governs diachronic identity between distinct consciousness chains via substrate continuity, formalizing the N9 signature of Biology Identification within the consciousness framework and completing the deferred work of Distributed Identity (§7.1.3). (3) Two-directional strength. The necessity direction is established at mathematical-proof level within the SDT framework, drawing on the consciousness-is-structure derivation of Bounded Free Will (§3.2) and canonicity arguments establishing each IC_i as the unique G_D-formalization of the corresponding ontological commitment. The sufficiency direction is established as the SDT-internal strongest identification claim via structural-space analysis showing that the non-conscious satisfaction space is empty. (4) Coordination and application. The framework yields determinate verdicts on nine boundary cases (persistent vegetative state, split-brain, anesthesia, infants, dementia, mammals, octopus, large language models, mind upload), with concept-level paradigm verification on adult awake human consciousness and instance-level verification through an explicit minimal G_D construction satisfying all sixteen identification conditions jointly. The framework resolves classical personal-identity puzzles (Locke's circularity, Olson's thinking-animal, Parfit's fission, Williams's body-priority, Parfit's "what matters") under a dual-signature framework, and is differentiated from Integrated Information Theory, Global Workspace Theory, Higher-Order Theory, and Predictive Processing. The paper does not address the explanatory aspect of the hard problem (Chalmers 1996) — why conscious structure has phenomenal character lies outside SDT's scope. The ontological aspect, namely what consciousness fundamentally is, is addressed via the IC characterization of the structure that consciousness is (Bounded Free Will §3.2).

This paper develops a distributed account of object identity within Structural Determination Theory (SDT). Three classic puzzles (Black's mirror universe, quantum indistinguishables, and the ship of Theseus) share a tacit assumption: that the identity of an object must be borne by a single structural source. SDT rejects this assumption. Within SDT's formal apparatus, synchronic identity is distributed across three independent levels (the realized-structure set R, the trace set T, and the determination dependency graph G_D), and diachronic identity is borne by G_D-structural signatures whose specific form depends on the kind of object. Two such signatures are deployed: one for biological organisms, one for conscious chains. The Hobbes variant of the Theseus puzzle falls into a case where no determinate signature is available, with the consequence that diachronic identity is ontologically indeterminate rather than epistemically gapped. A parallel substantive commitment on the synchronic axis denies the standard R-member count for entangled quantum states, which SDT treats as single R-members with internal two-particle structure rather than as pairs of indiscernible R-members. The position is contrasted with ontic structural realism, four-dimensionalism, sortal essentialism, and constitution theories.

This paper develops a graph-theoretic characterization of biological organisms within the determination dependency graph G_D of Structural Determination Theory (SDT), and verifies the characterization on a concrete biological instance. Given two antecedent commitments — SDT's meta-structural / entity-theoretic division of labor (Zeng 2026, SDT v5.9) and an ontological prior P1–P6 spanning object-hood, material throughflow, regulatory dynamics, information processing, multi-scale organization, and reproduction–memory — the paper proves that twelve graph-theoretic conditions N_i on G_D, together with a local-maximum principle, constitute the canonical G_D-formalization of P1–P6 (Biological Classification Theorem). Each N_i is shown to be canonical under SDT-grounded constraints R1–R3 (no alternative G_D-formalization of the corresponding ontological arm exists within the paper's scope), necessary by explicit counter-model construction M_{N_i}, and jointly sufficient by structural-space analysis showing that no sub-collection satisfying all twelve conditions fails to be biological. The characterization is verified on a constructed G_D representation of Escherichia coli at functional-module granularity (61 nodes, 98 edges, six ≺-stages). All four existential conditions (N_3, N_6, N_7, N_9) and all eight ratio-based conditions (N_1, N_5, N_8, N_10, N_11, N_12, N_15, N_18) are satisfied, with ratios ranging from 2.07× to infinity above five non-biological baselines (linear physical chains, chemical networks, crystal lattices, vortex structures, and mixed combinations). Under the uniform environment-marker partition, N_3, N_7, and N_9 are cleanly baseline-discriminative; N_6 functions as a structural well-formedness condition. The characterization aligns with biological consensus across single-celled and multi-celled organisms, correctly excludes inanimate dissipative structures such as vortices and crystals, yields partial satisfaction at empirically contested boundaries (viruses, cultural systems), and is compared with autopoiesis, Integrated Information Theory, Constructor Theory, Kauffman's autocatalytic sets, the Free-Energy Principle, and Cavalli-Sforza–Feldman cultural transmission networks. The contribution is a meta-structural characterization in the SDT methodological tradition with concrete instance verification: it gives the graph-theoretic form that biological organisms manifest in G_D, leaving entity-theoretic baseline calibration and algorithmic detection to follow-up work.

This paper advances three substantive claims on the foundational architecture of AI alignment and safety. First, the mainstream distinction between alignment (goal fidelity) and safety (system resilience) is a byproduct of probabilistic frameworks, not a foundational necessity. Probabilistic optimization tools cannot provide hard guarantees and therefore require separate safety mechanisms as backup; the separation reflects tool limitations rather than categorical distinction. Second, in the framework of Structural Determination Theory (SDT), where modal-structural admissible ranges A_v are foundational, alignment and safety are achieved through a single design choice: constraining A_v as a subset of A_intended. Alignment is positively specified, safety is negatively achieved (harmful outputs excluded as logical consequence); the two are logically ordered—alignment-prior, safety-by-consequence. Third, this range-based foundation yields catastrophe prevention (via minimax sufficiency and the dual-layer paradigm of the SDT corpus) and probabilistic optimization efficiency as joint substantive benefits. The paper articulates four mathematical theorems (UA-A1 through UA-A4) formalizing the foundational unification, the probabilistic necessity of separation, the search space reduction, and the modal-structural inevitability of specification gaming. AI safety as a problem domain has a substantive modal-structural footprint—binary catastrophe, worst-case adversarial robustness, structural invariance across deployment—that probabilistic foundations cannot capture without loss. The paper situates Constitutional AI training, Constitutional Classifiers, RLHF, Defense in Depth, and constrained reinforcement learning within this framework, identifying their structural gap and providing foundational justification for their existing complementary deployment. The argument extends a modal-structural categorical-priority methodology to AI safety: such foundations categorically reorganize what entity-theoretic frameworks treat as separate categories.

This paper advances three substantive dimensions of categorical priority on which Structural Determination Theory (SDT) is more foundational than the three principal research programs in spacetime emergence: loop quantum gravity (LQG), causal set theory (CST), and string theory. First, on background independence: SDT is the unique program among LQG, CST, and string theory whose meta-level commits to no spacetime-related structural assumption; CST presupposes spacetime causal structure at the axiom level; LQG presupposes spatial manifold and gauge structure; string theory presupposes target spacetime in each of its formulations. Second, on the grounds of discreteness: SDT is the unique program in which discreteness is derived from a single foundational axiom; CST takes discreteness as an unfounded postulate; LQG derives discreteness as an entity-theoretic consequence of SU(2) gauge quantization; string theory derives discreteness as an entity-theoretic consequence of the string scale. Third, on category placement: SDT is the unique program belonging to the category of modal structure rather than entity structure; LQG, CST, and string theory all belong to the category of entity structure. Modal structure is categorically prior to entity structure: an entity-based program inherits the structural commitments of its posited entity, whereas a modal-structural program does not. Constructor Theory shares SDT's modal-structural categorial position; within this shared category, however, SDT extends substantively beyond Constructor Theory in three dimensions: actuality dimension (the realized-structure set R and its non-retraction), causal partial-order architecture (the dependency relation and its closure, from which time emerges), and four-type determination classification. The reverse direction (Constructor Theory does not derive SDT) does not hold. The paper supplies these claims with a two-layer rigorous mathematical foundation: three SDT meta-level structural theorems at grade A (the five-fold classification of chain pairs, the reference-frame invariance of inter-chain information flow, and the structural absence of algebraic cross-frame transformations), establishing intrinsic content of the discrete chain-pair geometry, together with three conditional Lorentz correspondence theorems and one symmetric-dialogue proposition at grade A− under explicit entity-theoretic premises (synchronization axioms S1, S2 and continuum embedding axiom CL1), drawing on the framework developed in the SDT graph dynamics formalization. The contribution lies in establishing categorical priority within the paper's three argued dimensions; questions of empirical predictive content and internal consistency of the compared programs lie outside the paper's scope.

This paper advances five foundational claims about causation, defended within the framework of Structural Determination Theory (SDT). First, structural causation, defined as the dependency relation Di​→Dj​ between determination events, is an irreducible meta-structural primitive: it cannot be reduced to counterfactual dependence (Lewis 1973), probability raising (Suppes 1970), physical process transmission (Salmon 1984), interventional manipulation (Woodward 2003), or temporal precedence (Reichenbach 1956). Second, structural causation is ontologically prior to time: time in SDT is the unfolding of the partial-order structure on the determination dependency graph GD​ under monotonic growth of the realized-structure set R. Third, the dependency chain along GD​, together with the constraint system Cv​, determines a structurally fixed admissible range Av​ that serves as a modal-structural primitive prior to any probabilistic structure. Fourth, the contemporary reductionist program in causal philosophy is, at the meta-structural level addressed by SDT, unnecessary. Fifth, structural causation is modal-structural rather than temporal, physical, probabilistic, or psychological. Building on these claims, range prediction is shown to be foundationally prior to probabilistic prediction in three classes of scenarios: minimax-class decisions, Knightian uncertainty, and quantum pure-randomness.

This paper proves that under a specified mapping from Structural Determination Theory (SDT) to quantum mechanics, the SDT axiom G5 (use exclusivity) implies the no-cloning theorem (Wootters and Zurek 1982; Dieks 1982). The implication is established by showing that any mapping image admitting a universal cloning operator violates G5: the output of cloning, containing two copies of a quantum state, corresponds under the mapping to a single realized structure entering two distinct structural layers. The reverse implication does not hold, for three independent reasons: SDT lacks unitary structure, G5 is more restrictive than no-cloning, and the SDT-to-QM mapping is not unique. The result upgrades the structural analogy "G5 ↔ no-cloning" recorded in the SDT-to-QM correspondence program to a conditional one-way formal implication, identifying G5 as a sufficient meta-structural condition for no-cloning. The paper does not derive quantum mechanics from SDT; it identifies the precise sense in which a meta-structural axiom about the role-instance structure of element membership translates, under mapping, into a quantum-mechanical no-go theorem about universal cloning.

This paper proves that the admissibility presheaf on the dependency graph GD of Structural Determination Theory (SDT) is a flabby sheaf in the Alexandroff topology, conditional on SDT legitimacy. Four cohomological conclusions follow uniformly: every restriction map is surjective; first Čech cohomology with abelian coefficients vanishes on every open cover; global sections exist on every open subset; and every local section extends to a global one. The result holds for the type-agnostic multi-product presheaf on the full GD​, including determinations involving Type II splits and Type IV merge-splits. The argument is internal to SDT: each step relies on SDT axioms G1–G5 and the legitimacy criterion of v5.9. The conclusion locates SDT's structural framework as topologically compatible with classical hidden-variable models in the Kochen–Specker sense, a positioning that clarifies the boundary of the SDT axiom system without committing to a derivation or refutation of the Kochen–Specker theorem. The boundary set by SDT's choice of Boolean admissibility structure is made explicit; orthomodular extensions are noted as future work outside the present scope.

Abstract. This paper develops the strict graph-theoretic formalization of the determination dependency graph G_D, the core structural object of Structural Determination Theory (SDT). G_D is defined as a four-tuple (V, →, ρ, λ) governed by seven structural axioms, an R-membership preservation axiom, and well-foundedness; local finiteness and bounded in-degree follow. The determination types of SDT (attribute transformation, split, merge, merge-split) are recast as a partition of V by the cardinality pair (|E_v|, |ρ(v)|). Six principal results follow: product-flow conservation, |R| = |consumed| + |free|; a constraint-load functional Λ(v) = Σ_{↓v} |ρ|, strictly increasing along ≺, governing the irreversibility of A-contraction; a dual forest decomposition splitting G_D's edges into a single-input out-forest and a single-output in-forest, with intersection in the Type I linear segments; width-and-height monotonicity yielding the time-space volume bound |V| ≤ w·h; an SDT spacetime duality theorem deriving the spatial-temporal complementarity of G_D from the classical Dilworth–Mirsky duality; and a five-dimensional structural asymmetry theorem (R-monotonicity, A-contraction, width monotonicity, height monotonicity, constraint-load accumulation) that constitutes the graph-theoretic content of SDT's time-emergence argument. The paper supplies the graph-theoretic foundation on which the higher-order constructions in the SDT mathematical series rest.

This paper applies the retrospective methodology of Structural Determination Theory (SDT) to the domain of conscious evolution, deriving a precise account of free will entirely from SDT's single ontological axiom—reality consists of distinctly differentiated structure. The argument proceeds without entering the traditional compatibilism–libertarianism–eliminativism debate from within; it establishes its claims by refutation form, parallel to SDT's self-refutation defense of its axiom and its refutation-style time argument. Four core developments are presented. First, applying all four constituents of the SDT axiom jointly to the premise that consciousness genuinely exists yields the conclusion that consciousness is structure. This is an ontological claim at the SDT meta-level. Second, conscious evolution unfolds through a two-layer determination structure: a forced layer (Type II split) producing the current sensation as an independent structure, and an open layer (Type III merge) integrating the sensation with the prior consciousness into the new consciousness. The two-layer structure is shown to be necessary, not chosen for parsimony, since combining consciousness and external physical structures into a single determination violates SDT's logical-consistency principle. Third, free will in this framework has three aspects: shaping the configuration space through accumulated structural content; non-influence on the determination itself, since openness when admissible-configuration cardinality exceeds one is not closed by any more fundamental fact; and acceptance of the determination's outcome by incorporating it into oneself, where the merge determination's occurrence is itself the acceptance event and accounts ontologically for the subjective sense of "free will" without invoking agency. Fourth, the existence argument takes a refutation form: SDT's meta-level admits two legitimate cardinality configurations of the admissible set, and any position denying the open one in conscious evolution must specify the global constraint and the realized-structure set such that all conscious determinations are restricted to the closed configuration. No position has met this burden of proof. The paper sidesteps the metaphysical baggage of libertarianism (no agent causation), the theological commitments at the limit of complete determinism, and the consistency problems of eliminativism (the subjective free-will feeling has a real ontological position rather than being a post-hoc constructed illusion). The ontological claims are limited to the four developments above and do not extend to the phenomenal aspect of consciousness, the origin of consciousness, the mind–body relation, the cognitive mechanism, or the specific process of will production—these are beyond SDT's scope.

本文采用结构判定理论(Structural Determination Theory, SDT)的逆向方法论,从 SDT 唯一的本体论公理"现实由明确区分的结构组成"出发,精确展开自由意志在意识演化领域的应用。论证形态采取反驳形式,与 SDT 公理辩护(自我消解)和时间论证(反驳形式)同源,本文不进入传统相容论–自由意志论–取消主义辩论的内部框架。 本文给出四个核心展开。第一,将 SDT 公理的全部四个元素(现实、由⋯组成、结构、明确区分)联合应用于"意识真实存在"这一前提,推出意识是结构。这是 SDT 元层的本体论断言。第二,意识演化通过两层判定结构展开:第一层是被迫判定(类型 II 分流),由已实现结构集通过全局约束强制产生当前感受作为独立 R 成员;第二层是开放判定(类型 III 合流),将感受与上一刻意识合流产生新意识。两层结构的必然性来自 SDT 元层的逻辑自洽原则——把意识与外部物理结构纳入同一判定违反一致性要求,不是简洁选择。第三,自由意志在 SDT 框架内有三个层面:通过累积结构内容塑造判定的可容许布局集;不影响判定本身,因为可容许布局的非唯一开放性不被任何更基础的事实闭合;接受判定结果并将其纳入自身,合流判定的发生本身就是接受事件,从本体论上对应主观自由意志感觉,无需诉诸主动性概念。第四,存在论证采取反驳形式:SDT 元层规定可容许布局基数有两种合法配置,任何主张意识演化中不存在开放配置的立场,需要给出全局约束与已实现结构集的具体内容,显示这些内容把意识判定的全部可容许布局限制到唯一选项。这一举证负担当前没有被任何立场达成。 本文绕开自由意志论的形而上学包袱(无主体因果)、决定论极限的神学含义、以及取消主义的一致性问题(主观自由意志感觉具有真实的本体论位置,不是事后建构的幻觉)。本体论断言限定为以上四点,不延伸到意识的现象方面、起源、与物质的关系、认知机制、意志产生的具体过程——这些超出 SDT 管辖范围。

Since the twentieth century, almost every scientific field concerned with time has made substantive progress. Physics moved from special to general relativity to quantum field theory, delivering precise mathematical structures of spacetime and testable empirical predictions. Neuroscience located the cerebral mechanisms of time perception and quantified subjective time distortion. Cognitive science measured the architectures of temporal memory, time estimation, and temporal representation. Computer science developed formalized temporal logics and partial-order temporal models for concurrent systems. Only the philosophy of time is the exception. From McTaggart 1908 to Cameron 2015, for over a century the discipline's central debate has not departed from the same set of questions: whether time passes, whether the past is real, whether the present is privileged, whether A-properties reduce to B-relations. The same questions, the same terminology, the same dichotomy (A-theory vs B-theory), the same back-and-forth, the same non-convergence. The discipline has been arguing in place for more than a hundred years. This stagnation has a sharper feature. The defenders of each position have long possessed the tools to dissolve their opponents but have, generally and persistently, declined to use them. The basic concepts on which any mainstream position relies — block, growing edge, moving spotlight, tensed properties, tenseless facts — can all be dissolved by the same kind of foundational interrogation: What is this object? On what does its ontological status rest? How is it distinguished from other basic objects? This interrogation requires no external theoretical resource; it merely applies, symmetrically, to the opponent's shared core primitives the same standard moves each position uses to attack others. Yet the actual form of disciplinary debate is that each position's attack stops precisely at the opponent's core primitives: B-theory attacks A-theory's rate of passage but does not interrogate the "event" A-theory uses; A-theory attacks B-theory's obligation to explain temporal experience but does not interrogate the tenseless facts B-theory uses; Presentism attacks Eternalism's "now" problem but does not interrogate the ontological grounds of the block as an object; Eternalism in turn attacks Presentism's truthmaker problem but does not interrogate the tensed properties Presentism uses. This stopping is neither academic courtesy nor respect for opponents. Defenders of each position know perfectly well that their own position rests on equally unfounded primitives; attacking the opponent's foundations would immediately trigger a symmetric attack on their own. The discipline has thus reached a kind of informed, mutually permitted silence: each side licenses the opponent's core primitives in exchange for licence over its own. This silence has lasted for over a century.

二十世纪以来,几乎所有与时间相关的科学领域都取得了实质进展。物理学从狭义相对论到广义相对论再到量子场论,给出了时空的精确数学结构与可检验的实验预言。神经科学定位了时间感知的脑机制并量化了主观时间扭曲。认知科学测度了时间记忆、时间估计、时间表征的认知架构。计算机科学发展出形式化的时态逻辑与并发系统的偏序时间模型。只有时间哲学是例外。从 McTaggart 1908 到 Cameron 2015,逾百年间这一学科的论争中心从未离开同一组问题:时间是否流逝,过去是否实在,现在是否享有特权,A-属性能否还原为 B-关系。同样的问题,同样的术语,同样的二分(A-theory vs B-theory),同样的反复,同样的不收敛。学科在原地论争超过一个世纪。 这一停滞还有一个更尖锐的特征。各立场的维护者其实早已掌握瓦解对手的工具,但他们普遍且长期地选择不使用它。任何主流立场所依赖的基本概念 — block, growing edge, moving spotlight, tensed properties, tenseless facts — 都可以被同一种奠基性追问轻易瓦解:**这个对象是什么?它的本体论身份依据何在?它如何与其他基本对象相区分?**这种追问不需要外部理论资源,只需把每个立场用于反驳对手的标准做法对称地施加于对手所共享的核心 primitives。然而学科论争的实际形态是,每个立场的攻击都精确地止步于对方的核心 primitives:B-theory 攻击 A-theory 的 rate of passage 但不追问 A-theory 使用的"事件"是什么;A-theory 攻击 B-theory 的流逝体验解释义务但不追问 B-theory 使用的 tenseless fact 是什么;Presentism 攻击 Eternalism 的"now"问题但不追问 Eternalism 使用的 block 作为对象的本体论根据;Eternalism 反过来攻击 Presentism 的 truthmaker 问题但不追问 Presentism 使用的 tensed property 是什么。这一止步不是出于学术礼节,也不是出于对对手的尊重。各立场维护者清楚地知道,自己的立场恰恰建立在同样未被奠基的 primitives 之上;攻击对方的奠基性会立即触发对自己奠基性的对称攻击。学科因此达成了一种知情的、相互默许的沉默:每方默许对方的核心 primitives,以换取对方对自己 primitives 的默许。这种沉默已经持续了一个多世纪。 这一沉默的具体形态,是各立场都依赖某些未被论证的基本概念作为立论支柱。这些概念在立场内部不被追问,在对立论争中也不被作为论争对象。学科对此达成了一种隐性约定:时间相关的某些基本对象 — 事件、流逝、tensed 存在、tenseless 存在、A-属性、block、edge、spotlight — 是合法的工具,无需各自被奠基。这一约定从不被显式辩护,然而它是学科得以运作的隐性条件,也是百年停滞的真正原因。

本文从一条本体论公理出发发展结构判定理论(Structural Determination Theory, SDT):*现实由明确区分的结构组成*。论证分三阶段进行。第一阶段把公理的四个构成项(*现实*、*结构*、*由……组成*、*明确区分*)分别归入既有哲学传统,并通过自我消解论证确立每一项的不可否认性。第二阶段把公理的本体论承诺展开为十一个形式化概念,核心包括已实现结构集 R、全局约束 G、判定 D 与判定依赖图 GD。第三阶段从这一概念基础推导三个核心论证:R 的不可收缩与单调增长(论证 1)、G 的常量性(论证 2)、时间从 GD 偏序结构展开中涌现(论证 3);一个结构推论从时间结构与零载体传播联合派生空间距离。SDT 不借用任何具体物理理论,不依赖任何经验数据,不预设任何时间或空间概念;所有论证通过对公理的概念展开进行。理论的主要贡献是:(i) 时间的结构涌现主义,联合满足 A-理论与 B-理论的核心关切而非在两者间妥协;(ii) 第四种独立的不可逆性,即**逻辑不可逆性**,与统计、热力学、初始条件三种类型相区别(参 Boltzmann 1877、Prigogine 1980、Albert 2000、Price 1996),从"已实现"自身的模态结构无条件地推出;(iii) 空间距离的派生地位,与时间的关系主义对称,共同支持 SDT 的 *via negativa* 策略;(iv) 按 (∣E∣,∣S∣)(|E|, |S|) (∣E∣,∣S∣) 基数对判定的四分类(类型 I 属性变化、类型 II 分流、类型 III 合流、类型 IV 合流分流),为复合现象提供穷尽的元结构框架;(v) 从单一公理推出五个结构性结论(DAG 结构序、本体论方向、规则背景稳定性、时间涌现、空间派生),为传统上彼此独立的形而上学领域提供统一的形式基础。

Abstract. This paper renders Structural Determination Theory (SDT) as a formal deductive system in classical multi-sorted first-order logic, with ZFC as the metatheory. The central formal device is a two-tier explication relation (object-level and meta-level) that makes "conceptual explication" (the inherent unfolding of a single axiom together with the meaning of the terms it uses) a precisely defined formal relation, distinct from derivation from an axiom-set. This distinction is load-bearing: a formalization that conflated the two would render SDT, by its own formal output, a multi-premise theory rather than the single-axiom theory it claims to be. The paper formalizes the single axiom and its three-level semantic unfolding, formalizes the self-refutation argument as a four-branch reductio at the meta-level, gives formal definitions of all eleven core concepts (E, P, G, R, C, A, L, D, τ, T, G_D) each accompanied by a conservativity lemma, and certifies the four core arguments (R non-retraction, G constancy, time emergence, spacetime trichotomy) as strict object-level explications. Three metamathematical results are established: the minimal closure properties of the explication relation, the conservativity total theorem (no definition introduces new ontological commitment), and the relative consistency of the full system in ZF via a constructive model. The graph-theoretic content invoked here (the determination dependency graph G_D) is restated to the level the formal derivations require; its full development is canonical in the companion paper GD v6.0.

What if the measurement problem, Bell non-locality, the quantum-classical boundary, and the information paradox all have the same underlying structure — and that structure can be read off from a single ontological axiom? This paper applies **Structural Determination Theory (SDT)** to thirty-five open problems in quantum foundations. SDT derives all its commitments from one axiom — *reality consists of distinctly differentiated structure* — without presupposing physics, time, or space. Its central formal tool is a fourfold classification of determination events by input-output cardinality (∣E∣,∣S∣)(|E|, |S|) (∣E∣,∣S∣): Type I (single in, single out), Type II (single in, multiple out), Type III (multiple in, single out), Type IV (multiple in, multiple out). The methodological core is an epistemological observation: any measurement must physically encode its result somewhere, which requires a probe particle — making every measurement a Type IV determination by necessity. This dissolves the measurement problem structurally: measurement is an ordinary multi-particle collision, not a special event needing a special mechanism. The main results, organized into seven progressive clusters: Measurement problem dissolves under the read-out principle. Quantum-classical transition is continuous variation of determination-graph predecessor density, with no ontological boundary. *Bell non-locality* is borne by a joint-state decomposition Type IV determination (DAD_A DA​) that synchronously produces correlated stable states for both sides, followed by a probe interaction (DBD_B DB​) constrained via Pathway Two — no signaling, no action at a distance. Entangled pairs (e.g., SPDC output) are single realized-structure members with internally joint specifications of particle roles; this grounds entanglement non-locality without two-particle reductionism. Information preservation in black-hole evaporation follows from non-retraction of the realized-structure set, independently of unitarity. Time emergence: the Wheeler-DeWitt equation's absence of time is consistent with SDT because SDT derives time from the partial-order structure of the determination graph, not as a presupposed background. Three supplementary analyses extend the scope: decoherence receives a two-level structural account (microscopic Type IV interactions + coarse-grained Type II branching); the spin-statistics theorem is located as a GG G-internal consistency requirement rather than a meta-structural theorem; spontaneous symmetry breaking is analyzed via structural openness (∣A∣>1|A|>1 ∣A∣>1) in symmetry-orbit directions — with Goldstone masslessness as the entity-theoretic expression of that openness, and the Higgs mechanism as a GG G-modification that closes it. SDT is not an interpretation of quantum mechanics. It operates one level above: it provides the structural conditions any entity theory of quantum phenomena must satisfy, leaving specific dynamics, probabilities, and particle types to physics. The paper closes with dialogue against ten major interpretive stances (Copenhagen through pilot-wave) and a methodological reflection on the SDT-physics division of labor.

This paper develops Structural Determination Theory (SDT) from a single ontological axiom: reality consists of distinctly differentiated structure. The argument proceeds in three stages. The first establishes the axiom's undeniability within SDT's scope by self-refutation arguments on each of the axiom's four constituents (reality, structure, "consists of", distinctly differentiated). The second unfolds the axiom's ontological commitments into eleven formal concepts, centrally the realized-structure set R, the global constraint G, determination D, and the determination dependency graph G_D. The third derives three core arguments: R's non-retraction and monotonic growth (Argument 1), G's constancy (Argument 2), and time's emergence from the partial-order growth of G_D (Argument 3); a structural corollary derives spatial distance from the same framework. SDT presupposes no concept of time or space and borrows no specific physical theory; all arguments proceed by conceptual explication of the axiom. The theory's principal contributions are: (i) a structural emergentism of time that jointly fulfills the core concerns of A-theory and B-theory; (ii) a fourth, independent kind of irreversibility — logical irreversibility — distinct from the statistical, thermodynamic, and initial-condition types, derived unconditionally from the modal structure of "realized" itself; (iii) the derived status of spatial distance, symmetric with the relationism of time and jointly supporting SDT's via negativa strategy; (iv) a fourfold classification of determinations by (|E|, |S|) cardinality (Type I attribute transformation, Type II split, Type III merge, Type IV merge-split); (v) the derivation of five structural conclusions from a single axiom, providing a unified formal basis for traditionally independent metaphysical domains.