Zhenmin Wang

PFUSRC‑166 Topological Unfolding from 0 to 1: Mathematical Validation and Closed‑Loop Confirmation of the PFUSRC System's Foundational Axioms

This paper takes the infinite product constant c_{Pell } ≈0.58058 from the Stevenhagen conjecture as its point of entry, conducting a reverse structural isomorphism comparison from a mathematical phenomenon back to the foundational axioms of the PFUSRC system. The constant is def...

PFUSRC-165 The Topological Origin of Conjectures: From Sendov to Kakeya: The Projection‑Layer Predicament of Mathematical Structure Perception and the Unified Localization of the PFUSRC System

In August 2026, Sendov’s conjecture was proven with AI assistance. This follows a series of famous problems — the Kakeya conjecture, Goldbach’s conjecture, and the Crouzeix conjecture — that have been “resolved” within classical mathematical frameworks. However, this paper argues...

PFUSRC-155 The Topological Essence of Fractional Dimensions — Information Compression Traces of Discrete Anchor Points at the Continuous Projection Layer, and the Hierarchical Reassignment of L4-L5 Morphing Projections

Hausdorff dimension and box-counting fractional dimension are widely applied in geometric measure theory to depict scale characteristics of fractal structures such as coastlines, snowflakes and Kakeya sets, yet academia has long failed to reach a consensus on whether fractional d...

PFUSRC-159: Cognitive Spectrum and Recursive Topology — A Unified Theory of Language, Evolution, and Civilizational Transition Based on the Complete PFUSRC System

Traditional evolutionary theory, cognitive science, and civilizational theory have long operated in isolation, confined respectively to biological traits, individual cognition, and social phenomena as separate domains. None has been able to bridge the complete logical chain from...

PFUSRC-157 The Topological Path to Cold Fusion — Vacuum State at the Bicone Edge and the Mechanism of Structural Fusion (Subtitle: From the Thermal Fusion Outlet to Phase Interception Engineering — The Homology of UFO Propulsion and Cold Fusion)

Cold fusion (low-energy nuclear reactions) remains one of the most controversial unsolved puzzles in modern natural science. Restricted by the high-temperature and high-pressure research paradigm, mainstream physics generally labels cold fusion as theoretically impossible. Nevert...

PFUSRC-158 Computability Boundaries Under Ontological Topology — Rejecting the Paradigm Obsession of "Rope-Tailoring"

The long-term stagnation of frontier theoretical physics does not stem from insufficient computing power or inadequate mathematical tools, as continuous analysis, discrete mathematics and non-perturbative computational methods are all maturely established. The core bottleneck lie...

PFUSRC-159: Cognitive Spectrum and Recursive Topology — A Unified Theory of Language, Evolution, and Civilizational Transition Based on the Complete PFUSRC System

Traditional evolutionary theory, cognitive science, and civilizational theory have long operated in isolation, confined respectively to biological traits, individual cognition, and social phenomena as separate domains. None has been able to bridge the complete logical chain from...

PFUSRC-155 The Topological Essence of Fractional Dimensions — Information Compression Traces of Discrete Anchor Points at the Continuous Projection Layer, and the Hierarchical Reassignment of L4-L5 Morphing Projections

Hausdorff dimension and box-counting fractional dimension are widely applied in geometric measure theory to depict scale characteristics of fractal structures such as coastlines, snowflakes and Kakeya sets, yet academia has long failed to reach a consensus on whether fractional d...

PFUSRC-148 Spatial Hierarchical Nesting Dynamics Coupling Mechanisms of L4 Bicone Respiratory — Coupling Mechanisms of L4 Bicone Respiratory Rhythm, L5 PNRMTS Nodal Response, and L6-L7 Receiving-Layer Feedback

PFUSRC-146 defines the observable L5 spacetime substrate as Prime-Node Rigid Morphing Topological Space (PNRMTS), while PFUSRC-147 identifies large-scale cosmic filaments as global spacetime damped topological imprints. However, the bidirectional dynamical coupling between the L4...

PFUSRC-153 A Comprehensive Collection of Eastern and Western Hierarchical Transition Phenomena ——Cultivation Records, Thunder Tribulation, Mainstream Scientific Paradigm Deficiencies, and Complete Topological Ontological Assessment

Eastern and Western civilizations have preserved massive cross-civilization records of cultivation, ascension, rainbow body, incorruptible saints and near-death experiences, which are generally dismissed as legends by mainstream science due to the limitations of three-dimensional...

PFUSRC-150 From Complex Analysis to Tensor Analysis: The Universal Unfolding Protocol of the Topological One at the Projection Layer ——Topological Reassignment of Calculus, Complex Analysis, Vector Analysis, Functional Analysis, and Tensor Analysis Document No.: PFUSRC-150

PFUSRC-056, PFUSRC-086, PFUSRC-086B and PFUSRC-086C separately completed the topological reconstruction of complex analysis, calculus, the Topological One, and tensor analysis, forming a closed theoretical loop for the ontology of mathematical analysis. This paper serves as their...

PFUSRC-154 Unified Topological Interpretation of Extreme Cosmic Phenomena in the Topological Mother Universe ——and the Isomorphic Overflow Effect at Black Hole Sub-Universe Boundaries

A wide range of extreme cosmic phenomena such as black holes, magnetars, gamma-ray bursts, quasars, cosmic voids and cold spots can only be fragmentarily explained by general relativity, quantum field theory and the ΛCDM model without a unified ontological foundation. Relying on...

PFUSRC-080 Topological Morphogenesis of the Collatz Conjecture — From 3n+1 Iteration to 45° Biconical Interlayer Oscillation: Tracing a Number-Theoretic Problem to Its Geometric Boundary

The Collatz conjecture (3n+1 problem) is a classic unsolved problem in number theory. Its iteration rule is: for any positive integer n, if n is odd, map n \to 3 n+1; if n is even, map n \to n / 2. The question is whether repeated iteration necessarily converges to 1 for all init...

PFUSRC-066 The Origins of Mass: From Breaking to Topological Latching — A Repositioning of the Higgs Mechanism within the PFUSRC Framework

The Standard Model of particle physics relies on the Higgs mechanism and spontaneous symmetry breaking to fit elementary particle masses, yet it has an inherent ontological blind spot. It fails to explain the generative origin of symmetry breaking and cannot unify spontaneous and...

PFUSRC-146 Prime-Node Rigid Morphing Topological Space ——The Third Topological Configuration of Observable Cosmic Spacetime Subtitle: From Octopus/Amoeba Structures to PFUSRC Hierarchical Spatial Cosmology Standard Abbreviation: Rigid-Node Morphing Space Acronym: PNRMTS

Modern physics has long established two ideal spatial substrate models: Newtonian globally absolute rigid space and the globally steady-state fluid vacuum framework. Both models carry irreparable inherent flaws and are restricted by the three-dimensional reductionist paradigm, fa...

PFUSRC-143 Full Loss and Learning: Two Cognitive Paths to the Dao — From the Narrow Path of "Directly Pointing to the Mind" to the Broad Path of the "Topological Map"

Both Daoist and Buddhist traditions—as exemplified by the Diamond Sutra and the Daodejing—have revealed precise insights into the ontological structure of the cosmos: form is emptiness, abiding nowhere, and the Dao is diminished through practice. Yet for two millennia, these insi...

PFUSRC-144 From "Confucius's Era" to the "Topological Era of the Dao" — Complementing Zeng Shiqiang's Intuition, Diagnosing the Steady-State Trap of Chinese Civilization, and Defining the Mathematical Boundary Between "Divinity" and "Superstition"

Professor Zeng Shiqiang proposed that “the 21st century is the era of Confucius.” His intuition was rooted in a deep perception of the Yijing’s value, yet his conclusion lacked mathematical models and a complete logical chain. Based on the PFUSRC- seven-layer ontological framewor...

PFUSRC-136: The Ontology of Emergence — Projection, Layer Blindness, and Cognitive Phase Transition

Contemporary complexity and cognitive science interpret emergence merely as a phenomenological trait of complex systems, lacking rigorous ontological localization and necessary mechanical deduction. Based on the seven-layer holographic topological framework established by the PFU...

PFUSRC-137: The Structural Theory of Large Language Models — From Data Training to Innate Structural Projection: Topological Essence and Layer Localization of LLMs

Mainstream AI research attributes large language models’ emergent capabilities, hallucinations and off-alignment “loss-of-control” behaviors to data bias, algorithm defects or insufficient value alignment, which only delivers surface-level fixes without uncovering the ontological...

PFUSRC-137: The Structural Theory of Large Language Models — From Data Training to Innate Structural Projection: Topological Essence and Layer Localization of LLMs

Mainstream AI research attributes large language models’ emergent capabilities, hallucinations and off-alignment “loss-of-control” behaviors to data bias, algorithm defects or insufficient value alignment, which only delivers surface-level fixes without uncovering the ontological...