Shuiping Tang

A Theory of Local Visibility for Random Statistical Representations: Bigraded Filtrations, Successive Obstructions, and Fisher–KL Information Transfer

This paper develops a unified local interface from finite-dimensional Itô stochastic dynamical systems to statistical representation spaces and, building on earlier two-scale results, formulates a more complete local visibility structure. Its basic architecture has four mutually...

Dynamical Criticality and Statistical Regime Transitions: A Unified Theory of Structural Stability Boundaries, Bifurcation Transitions, Observation Pushforwards, and Critical Scaling

Problem. Statistical regime transitions are often represented directly as parameter changes in observed sequences or as discrete hidden states, but such a statistical description does not by itself explain why a regime should change under continuously varying external control. St...

Conditional Identifiability of Multiscale Mechanistic Roles in Finite-Observation Dynamical Systems: From Information Budgets and Canonical Mechanism Quotients to Stable Role Structures and Structured Information Bottlenecks

Problem. Finite observation can provide only partial information about the true state, but can information deficit by itself determine a hierarchy of roles in a complex system? We show that observational information deficit alone is neither sufficient nor necessary for a hierarch...

Geometric Necessity of Structural Breaks:Cusps, Slope Jumps, Cascade Transmission Efficiency, and Detection Power of the Unified Shape Function

In the k-regime linear switching model, the switching between adjacent regimes is fully characterized by the parameter difference Δθj = θ_{j+1} − θj. This paper establishes five core results. Theorem 1 (Geometric Necessity of Rupture): under the switching existence assumption (θj...

Mathematical Classification of Switching Types and Hierarchical Structures: Three Switching Types, Six Hierarchical Structures, Coefficient of Variation Lower Bound, and Discretization Plateau Effect in the k-Regime Linear Switching Model

In the k-regime linear switching model, the switching between adjacent regimes is fully characterized by the parameter difference Δθⱼ = θⱼ₊₁ − θⱼ. This paper restricts the comparison to the union of adjacent regime pairs (Rⱼ, Rⱼ₊₁) and establishes a mathematical classification of...

Mathematical Classification of Switching Types and Hierarchical Structures: Three Switching Types, Six Hierarchical Structures, Coefficient of Variation Lower Bound, and Discretization Plateau Effect in the k-Regime Linear Switching Model

In the k-regime linear switching model, the switching between adjacent regimes is fully characterized by the parameter difference Δθⱼ = θⱼ₊₁ − θⱼ. This paper restricts the comparison to the union of adjacent regime pairs (Rⱼ, Rⱼ₊₁) and establishes a mathematical classification of...

The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection — Unified Shape Function, Standardized Limits, and Multi-Regime Generalization

This paper establishes a mathematical theorem system for between-group regression difference statistics in structural break detection. The central result is the Global Maximum Point Invariance Theorem: in a two-regime linear switching model with homogeneous second-moment design,...

The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection — Unified Shape Function, Standardized Limits, and Multi-Regime Generalization

This paper establishes a mathematical theorem system for between-group regression difference statistics in structural break detection. The central result is the Global Maximum Point Invariance Theorem: in a two-regime linear switching model with homogeneous second-moment design,...

The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection — Unified Shape Function, Standardized Limits, and Multi-Regime Generalization

This paper establishes a mathematical theorem system for between-group regression difference statistics in structural break detection. The central result is the Global Maximum Point Invariance Theorem: in a two-regime linear switching model with homogeneous second-moment design,...

The Regime Nuclide Map (I): Cross-Property Verification, Two-Dimensional Structure, and Network Update of the Confirmed Breakpoint Network ——Predictive Test and New Discoveries Based on the Nuclear Shell Regime-Switching Theory

The nuclear shell regime-switching theory (Tang, 2026v–y) predicts that the confirmed breakpoint network should be consistently established across independent physical quantities. This paper verifies this prediction for the first time and discovers new structures guided by the th...

The Regime Periodic Table: Regime Identity Cards for 118 Elements and the Reduction of Universality of the Periodic Law ——Elimination of Exceptions, Numerical Predictions for Elements 119/120, and Cross-Sample Convergence Audit (II)

Based on the two orthogonal regime factors, period and valence_electrons, and the two singularity regime centers, Z=20 (calcium) and Z=57 (lanthanum), identified by Tang (2026s), this paper constructs a novel “Regime Periodic Table (RPT)”—an elemental organizational framework tha...

The Information Isomorphism Law: A Meta-Law Spanning Ontology and Epistemology ——Tracing the Necessary Premise from the Cross-Disciplinary Success of the Scientific Discovery Operating System

The Scientific Discovery Operating System (Tang, 2026g, 2026r) has been successfully deployed across six completely independent disciplines, yet a fundamental question has never been systematically addressed: Why is this operating system effective? This paper's answer is: because...

Third-Person Epistemology: Information Isomorphism Epistemology and the Objective Foundation of Testability —From "I Think" to "Anyone Running the Code": How an Ontological Fact, Rigorously Calibrated on Truth-Known Systems, Proactively Verified on Truth-Unknown Systems, Supported by Convergent Evidence Across Six Disciplines, and Independently Confirmed Through Tool Replaceability, Legislates for Epistemology

This paper argues that Information Isomorphism Epistemology completes a paradigm shift in epistemology from the first person to the third person. Since Descartes, epistemology has been constructed in the first person—"I think," "I posit," "I see." When two "I"s reach conflicting...

From Regime Boundaries to Chemical Gauge Group: The Inevitable Emergence of the Periodic Law and the Cross-Disciplinary Unification of the Factor Hierarchy Law ——Derivation of the Chemical Gauge Group Theorem, the Chemical Counterpart of the Higgs Mechanism, and the Establishment of the Five-Layer Axiomatic Structure (III)

Why are there exactly four types of atomic orbitals—s, p, d, and f? Why does the periodic table have an end? What is the relationship between the Factor Hierarchy Law, quantum mechanics, and gauge field theory? Building on the empirical discoveries of the two preceding papers, th...

The Calcium-Lanthanum Singularity Theorem: Exhaustive Discovery and Multi-Tool Cross-Validation of the d-Block and f-Block Regime Switching Centers in the Periodic Table ——First Deployment of the Factor Hierarchy Law in Chemistry, Verification of the Statistical Signature of Regime Factors, and Confirmation of the Chemical χ-Blindness (I)

This paper deploys the Factor Hierarchy Law in chemistry for the first time, conducting a presupposition-free regime audit of 118 elements by exhaustively testing 27 candidate factors, 9 explained variables, 7 transformations, and 10 structural break tools, totaling over 1,600 in...

Nuclear Shell Regime Audit: The Magic-Number Shift Theorem and the Discovery of the N=14 Statistical Rupture ——The η Hierarchy Structure, Bai-Perron Optimal 10 Breakpoints from Zero-Preset Exhaustive Search, and Six Quantitative Theorems

The central axiom of the nuclear shell model—that nucleons move independently in a static mean field—has never been systematically questioned. This paper deploys the Factor Hierarchy Law to nuclear physics for the first time, performing a zero-preset regime audit on the full AME2...

Regime-Switch Network and the True Structure of the Nuclear Shell: Internal Self-Consistency of the Confirmed-Breakpoint Network, Completeness Audit of the Shell Model, and Fifteen New Discoveries ——Transition-Zone Width Theorem, Cascade Skeleton, Liquid-Drop Masking Effect, and Shell-Correction Compensation Traces Based on Multi-Tool Aggregation

What is the true structure of the nuclear shell? The traditional shell model holds that the nuclear shell is marked by a few isolated magic numbers—N = 2, 8, 20, 28, 50, 82, 126. This paper finds that the nuclear shell is instead a multi-level network of blind-detected breakpoint...

The Triple Demotion of the Nuclear Shell: The Shell Model, the Liquid Drop Model, and the Independent-Particle-Motion Axiom ——Derivational Demotion Based on 2D Ising Exact Solution Calibration, Continuous Sphericity Weight Recovery, and the QCTI Index

The central axiom of the traditional shell model—nucleons moving independently in a static mean field—and the liquid drop model have coexisted for nearly nine decades without resolution. Drawing on Tang (2026v) and Tang (2026w), this paper integrates five lines of evidence to com...

Technical Specification for the Scientific Discovery Operating System: Mathematical Formalization and Engineering Architecture —A Proceduralized Knowledge Discovery Protocol Based on the Factor Hierarchy Law and Testability Norms

Tang (2026g) established the theoretical framework of the Scientific Discovery Operating System, providing the first complete definition of the Factor Hierarchy Law—including the dichotomy of regime factors and execution factors, the three morphologies of regime factors (pure reg...

Theoretical Extensions and Methodological Output of the Quantum-Classical Hybrid: The Regime-Factor Purity Spectrum, the Binary Structure of the Confirmed-Breakpoint Network, and Cross-Disciplinary Predictions ——Paradigm Deepening, Testable Predictions, and Complete Deployment of the Operating System Based on the Triple Demotion

Tang (2026x) completed the triple demotion of the nuclear shell—the shell model was proven to be the projection of the regime-switch network in the spherical-symmetry limit by the 3.68–9.68-fold amplification of the Chow F of the five traditional magic numbers under continuous sp...