Books and research by Jinku Guo
Change, order and understanding
How does a world in continuous change give rise to order, life and understanding?
A book and a research programme explore this question across philosophy, mathematics, physics and computation. The book develops a multi-level account of reality and knowledge; the papers pursue explicit generating constructions and the relations they preserve.
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The book
The Practice of Seeking Truth from Facts
An exploration of how order, life, consciousness, society and meaning emerge from a world in constant change.
Drawing on physics, biology, neuroscience, complexity science, and Eastern and Western philosophy, the book develops a way of understanding reality across its different levels. Entropy, symmetry, emergence and self-organization become connected questions about how structures form and endure.
Its central concern is methodological: how to move beyond apparent paths, return to facts and processes, and discover the relations through which the world becomes intelligible. This perspective gives the collection its philosophical and methodological setting.
Book description and 31-chapter contents English preview PDF · 5 pages
The research programme begins with minimal unbiased compositional change. A common generating source connects arithmetic histories, compact gauge structure, long-range response and finite certified computation. Its results include a history-dependent natural-number system, quantitative prime projectors, a generated Yang-Mills spectral-gap theorem, and polynomial-cost trajectory certificates.
For the broader ideas, begin with Beyond Apparent Paths. For a mathematical construction, physical mechanism or verification record, follow one of the routes below.
Begin with natural-number arithmetic, then prime decomposition and generated spectra. Expression histories connect arithmetic values to later response and memory.
Read Compact Internal Space I and II, then the gravity criterion and coarse-graining. The third compact-space paper develops finite-window cosmic structure.
The Lean library gives declarations and theorem-to-paper mappings. V5 gives executable source records, interval certificates and observational comparisons.
9 papers
We construct natural-number arithmetic on an ordered family of correlation modes and retain the expressions by which its elements are generated. Minimal unbiased compositional change determines a rotation plane and a...
Construction of natural numbers · Arithmetic expression trees · Conditional expectation · Trace-class operators · Non-Markovian dynamics · Memory kernels
We construct decomposition and occupation operators on a generated correlation-spectral arithmetic system. Prime residue classes form the augmentation cotangent basis, and the corresponding one-word vectors span the...
Prime factorization · Hodge Laplacian · Prime projection · Möbius function · Riemann zeta function · Fock space
Nonlinear spectral evolution requires control of the frequencies present initially and those created by interaction. We study how spectral bounds can be retained with the construction of a state and reused in later...
Nonlinear evolution equations · Spectral Galerkin methods · Uniform error bounds · Analytic regularity · Spectral truncation · A posteriori error estimates
We study finite records whose accuracy for an infinite-dimensional nonlinear evolution can be checked without rerunning the producing algorithm. The model is a fixed Neumann reaction–diffusion equation with quadratic...
Polynomial bit complexity · Certified computation · Verifiable computation · Reaction–diffusion equations · Exact rational arithmetic · Proof certificates
From minimal unbiased compositional change we construct compact internal geometry and gauge–matter representations, and prove a mass gap for the generated Yang–Mills response. On the least-dimensional nontrivial compact...
Standard Model gauge group · Chiral fermions · Higgs doublet · Yang–Mills mass gap · Spectral geometry · Vacuum stability
Minimal unbiased compositional change generates the Gaussian source of the compact internal construction. We derive joint constraints on effective couplings and mass scales from its gauge and matter content, scalar...
Three fermion generations · Fermion mass hierarchies · Fermion mass relations · Gauge coupling constants · Higgs boson mass · Neutrino masses
We give a source-resolved spectral criterion for long-range tensor exchange between conserved matter sources. Exact channel elimination preserves the propagation kernel together with the source and readout maps and the...
Emergent gravity · Massless spin-2 fields · Universal gravitational coupling · Newtonian limit · Spectral positivity · Källén–Lehmann representation
We study when a reduced description preserves the response to an applied source. For systems defined by continuously differentiable state updates and observations a bounded surjective linear coarse map gives...
Coarse-graining · Model reduction · Linear response theory · Pole stability · Spectral residues · Memory kernels
Cosmic matter forms concentrations whose external force can often be described by their mass and spatial moments. Encounters and material exchange can make finer structure relevant again. We determine when field and...
Cosmic structure formation · Particle-mesh methods · Adaptive coarse-graining · Memory effects · A posteriori error estimates · Validated numerics