Linear

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Contents

• Positive polynomial derivative-layer Gramian
• Invertible physical scaling and native Gramian limit
• Normalized observation on derivative layers
• Discounted Observability Energy Identity
• Discounted Observability Gramian Equation
• Discounted Observability Gramian Kernel
• Discounted Observability Gramian Positivity
• Factorial Taylor error for bounded observations
• Finite Observability Energy Balance
• Finite Observability Equivalence
• Finite Real Zero-Fill Register
• Sharp native adaptive gain-ray capacity
• Critical complete-target exclusion
• Complete recovery on one literal trajectory
• Critical scalar identities have three source directions
• The whole pure-M endpoint obstruction
• Whole worlds and literal acquisition histories
• Identical-row worlds and complete suffix annihilation
• Shifted Euler interpolation and exact gain readout
• Diagonal rigidity of bounded-degree evaluations
• Trace-kernel nuisance geometry for mixed words
• Three source directions in every mixed word
• Gaussian observation laws and conditional information
• Graded Congruence Spectrum
• Gramian Behavior-Quotient Metric
• Hilbert moment coercivity
• Least-Squares Reconstruction Noise Bound
• Normalized coordinates of observable trajectories
• Observation Rank Monotonicity
• Observation Rank Submodularity
• One-Observer Operator Non-Reconstruction
• Fixed-noise exponential-Gramian information expansion
• Polynomial gain and unrestricted deterministic feedback
• An explicit observation floor on every positive window
• Prime-Time Gramian Energy Identity
• Reachable Observable Quotient Descent
• Robust Frame Bounds
• Exact deterministic recovery from Hilbert trajectories
• Small signed entry compensation and exact acquisition
• Source Contribution Decomposition
• Noise scales for finite power-controlled spectra