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Paper ITyped operator systems, seed rank, and exact packet coordinates
Paper IIRefinement, weighted transfer, and integral separation
Paper IIITyped transfer, nonlinear packets, and obstruction theory
Paper IVCyclic analytic functions, reciprocal families, and spectral zero data
Paper VMultiresolution Signal Calculus
Paper VITransfer semigroups and memory
Paper VIIQuantum Seeds and Effective Dynamics
Paper VIIIPacket Operator Algorithms, Exact Compilation, and GPU Realization
Paper IXEuler Congruences
Paper XUniversal Residual Seeds
Paper XITame and Wild Packet Geometry for Local Langlands
Paper XIIPatching Support, Hecke Packets, and Conditional Automorphic Completion

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Special FunctionsSpecial Functions: Function families and their structure
Proof Path TheoryCertificates, compression, discovery fields, and mathematical memory
Komorebi SpaceCoherent realizations, obstructions, and descent
Realization BoundariesFinite Grammar, Infinite Groups, and the Limits of Reconstruction
Komorebi MethodologyMathematical Discovery, Realization, and the Discipline of Proof
Quantum and CircuitsQuantum and Circuits: Arithmetic, symmetry, and catalysis
Large Signal ModelRealization, refinement, and predictive closure
Machine-Native ReasoningEvidence, methods, and accountable revision
The K-COS MethodStructured Gaussian Quadratic Forms, Spectral Compression, and Certified Extreme-Tail Evaluation

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Part I · Transfer semigroups and applications (21)

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The transfer-semigroup realization
Packet blocks of a semigroup
Refinement defects and the Duhamel identity
Markov seeds and stochastic transfer
Markov lumping as exact refinement
Conditional expectation as a stochastic projector
Bayesian conditioning as a normalized nonlinear operator
Exact Bayesian refinement and information-loss packets
Bayesian flows, conjugacy, and hidden states
Fractional powers as spectral packet transfer
Green operators and the Poisson seed
Finite-state Feynman--Kac transfer
Exact elimination of latent packets
Survival and hazard semigroups
One common operator language
Numerical certificates
Remaining conjectural extensions
Computational implementation
Conclusion
Lean verification and scope

Part II · Extended mathematical development (20)

Part II: Extended mathematical development
Introduction
Packet resolved semigroups
Generator defects and functional calculus
Refinement towers and limiting evolution
Finite Markov transfer and lumping
Conditional expectation and martingale packets
Gaussian transfer and Hermite packets
Bayesian transfer and evidence packets
Bayesian coarsening and finite sufficiency
Bayesian flows and hidden Markov recursion
Fractional functional calculus
Green operators and finite difference transfer
Finite state Feynman Kac transfer
Schur Feshbach elimination
Memory modes and controlled compression
Survival, moments, and competing risks
Finite illustrations and computational checks
Limits and further questions
Conclusion

Part III · Retained results and operator calculus (8)

Part III: Retained results and operator calculus
Transfer paths and product-topology limits
Reversible coarse dynamics
Prior-restricted sufficiency and filtering
Fractional modes and killed transfer
Memory compression, rational realization, and phase-type consequences
Earlier exact examples
Holomorphic operator substitution

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