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Begin with a visual introduction, study a complete manuscript, or follow its supporting evidence. These 15 papers and books have both an HTML reading edition and an HTML visual guide.
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Core papers
Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates
For a fixed operator action, seed rank counts the generators needed. The finite-dimensional single-operator count uses classical polynomial-module structure. Complete packet coordinates reconstruct vectors and operators from their components, connecting generation, relations, and transfer blocks.
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Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets
The paper gives coherent coordinate changes across refinement levels, exact formulas for refined operator blocks, weighted path inverses, and integral precision bounds.
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Paper III: Typed Transfer, Nonlinear Packets, and Obstruction Theory
Complete finite packets give exact coordinates for nonlinear maps. The paper develops composition, derivatives, and correction obstructions, with separate hypotheses for smooth transport and convergent expansions.
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Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data
Cyclic projections organize differential cycles, reciprocal coefficients, and addition laws. For the specified cyclic analytic family, the paper also develops zero geometry, products, and coefficient asymptotics.
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Paper V: Polyphase Signal Calculus
Residue projectors turn signals into exact polyphase channels and filters into transfer matrices. The same analysis–synthesis language describes perfect reconstruction, finite-depth Haar transforms, and edge-packet calculations.
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Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations
Transfer blocks express semigroup composition through intermediate packets. Refinement defects quantify disagreement between coarse and fine evolution, with stochastic, Bayesian, and analytic realizations.
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Paper VII: Quantum Seed Calculus
The finite theory studies seed generation, symmetry projectors, circuit paths, measurement, and channel blocks. Further chapters develop geometric and continuum research directions with their own stated obligations.
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Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization
Packet layouts give exact evaluation and composition rules, together with operation and storage counts for declared block structures. The paper separates these semantics from numerical and GPU realization questions.
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Paper IX: Arithmetic Packets, Dyadic Towers, and Local Polynomial Deformation
The paper develops exact coefficient reconstruction, coordinate transport, valuation estimates, and lifting constructions. Its later arithmetic results retain their individual field, ring, and precision hypotheses.
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Paper X: Universal Residual Seeds and Conditional Occupied-System Completion
Residual classes form separate lifting branches. The paper studies reconstruction along those branches and conditional completion in supplied compatible carriers, separating vertical lifting from horizontal existence.
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Paper XI: Packets, Arithmetic Realization, and Conditional Comparison
The paper resolves finite monodromy, Frobenius, and character packets and develops restricted comparison constructions. It separates those finite results from the general arithmetic realization problem.
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Paper XII: Patching Support, Hecke Packets, and Conditional Automorphic Completion
The paper develops algebraic support descent, finite Hecke packet decompositions, and conditional completion criteria. It distinguishes a point being supported from the additional arithmetic data needed for automorphy.
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Large Signal Model
Algebraic signal models and their mathematical foundations.
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Quantum and Circuits
Quantum models, channel interfaces, and circuit constructions.
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COS Method
Quadratic-form probability calculations, tail accuracy, and numerical evidence.
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